aboutsummaryrefslogtreecommitdiffstats
path: root/buch/papers
diff options
context:
space:
mode:
authorAndreas Müller <andreas.mueller@ost.ch>2022-05-31 11:24:55 +0200
committerGitHub <noreply@github.com>2022-05-31 11:24:55 +0200
commite346d4c723832171978eb13bfec5f9bcfd1200b9 (patch)
tree05f43553bee044b0493d9bccc259c1f1580ce092 /buch/papers
parentbesselgrid fix (diff)
parentsplit main into section files (diff)
downloadSeminarSpezielleFunktionen-e346d4c723832171978eb13bfec5f9bcfd1200b9.tar.gz
SeminarSpezielleFunktionen-e346d4c723832171978eb13bfec5f9bcfd1200b9.zip
Merge pull request #17 from ntobler/master
ellfilter draft
Diffstat (limited to '')
-rw-r--r--buch/papers/ellfilter/Makefile.inc17
-rw-r--r--buch/papers/ellfilter/einleitung.tex56
-rw-r--r--buch/papers/ellfilter/elliptic.tex92
-rw-r--r--buch/papers/ellfilter/jacobi.tex189
-rw-r--r--buch/papers/ellfilter/main.tex27
-rw-r--r--buch/papers/ellfilter/packages.tex17
-rw-r--r--buch/papers/ellfilter/presentation/presentation.tex413
-rw-r--r--buch/papers/ellfilter/python/F_N_butterworth.pgf1083
-rw-r--r--buch/papers/ellfilter/python/F_N_chebychev.pgf1066
-rw-r--r--buch/papers/ellfilter/python/F_N_chebychev2.pgf1023
-rw-r--r--buch/papers/ellfilter/python/F_N_elliptic.pgf847
-rw-r--r--buch/papers/ellfilter/python/chebychef.py66
-rw-r--r--buch/papers/ellfilter/python/elliptic.pgf709
-rw-r--r--buch/papers/ellfilter/python/elliptic.py356
-rw-r--r--buch/papers/ellfilter/python/elliptic2.py149
-rw-r--r--buch/papers/ellfilter/python/k.pgf1157
-rw-r--r--buch/papers/ellfilter/python/plot_params.py9
-rw-r--r--buch/papers/ellfilter/references.bib41
-rw-r--r--buch/papers/ellfilter/teil0.tex22
-rw-r--r--buch/papers/ellfilter/teil1.tex55
-rw-r--r--buch/papers/ellfilter/teil2.tex40
-rw-r--r--buch/papers/ellfilter/teil3.tex40
-rw-r--r--buch/papers/ellfilter/tikz/arccos.tikz.tex66
-rw-r--r--buch/papers/ellfilter/tikz/arccos2.tikz.tex45
-rw-r--r--buch/papers/ellfilter/tikz/cd.tikz.tex87
-rw-r--r--buch/papers/ellfilter/tikz/cd2.tikz.tex84
-rw-r--r--buch/papers/ellfilter/tikz/fundamental_rectangle.tikz.tex26
-rw-r--r--buch/papers/ellfilter/tikz/sn.tikz.tex86
-rw-r--r--buch/papers/ellfilter/tschebyscheff.tex133
29 files changed, 7785 insertions, 216 deletions
diff --git a/buch/papers/ellfilter/Makefile.inc b/buch/papers/ellfilter/Makefile.inc
index 8f20278..97e4089 100644
--- a/buch/papers/ellfilter/Makefile.inc
+++ b/buch/papers/ellfilter/Makefile.inc
@@ -3,12 +3,11 @@
#
# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
#
-dependencies-ellfilter = \
- papers/ellfilter/packages.tex \
- papers/ellfilter/main.tex \
- papers/ellfilter/references.bib \
- papers/ellfilter/teil0.tex \
- papers/ellfilter/teil1.tex \
- papers/ellfilter/teil2.tex \
- papers/ellfilter/teil3.tex
-
+dependencies-ellfilter = \
+ papers/ellfilter/packages.tex \
+ papers/ellfilter/main.tex \
+ papers/ellfilter/references.bib \
+ papers/ellfilter/einleitung.tex \
+ papers/ellfilter/tschebyscheff.tex \
+ papers/ellfilter/jacobi.tex \
+ papers/ellfilter/elliptic.tex
diff --git a/buch/papers/ellfilter/einleitung.tex b/buch/papers/ellfilter/einleitung.tex
new file mode 100644
index 0000000..37fd89f
--- /dev/null
+++ b/buch/papers/ellfilter/einleitung.tex
@@ -0,0 +1,56 @@
+\section{Einleitung}
+
+% Lineare filter
+
+% Filter, Signalverarbeitung
+
+
+Der womöglich wichtigste Filtertyp ist das Tiefpassfilter.
+Dieses soll im Durchlassbereich unter der Grenzfrequenz $\Omega_p$ unverstärkt durchlassen und alle anderen Frequenzen vollständig auslöschen.
+
+% Bei der Implementierung von Filtern
+
+In der Elektrotechnik führen Schaltungen mit linearen Bauelementen wie Kondensatoren, Spulen und Widerständen immer zu linearen zeitinvarianten Systemen (LTI-System von englich \textit{time-invariant system}).
+Die Übertragungsfunktion im Frequenzbereich $|H(\Omega)|$ eines solchen Systems ist dabei immer eine rationale Funktion, also eine Division von zwei Polynomen.
+Die Polynome habe dabei immer reelle oder komplex-konjugierte Nullstellen.
+
+
+\begin{equation} \label{ellfilter:eq:h_omega}
+ | H(\Omega)|^2 = \frac{1}{1 + \varepsilon_p^2 F_N^2(w)}, \quad w=\frac{\Omega}{\Omega_p}
+\end{equation}
+
+$\Omega = 2 \pi f$ ist die analoge Frequenz
+
+
+% Linear filter
+Damit das Filter implementierbar und stabil ist, muss $H(\Omega)^2$ eine rationale Funktion sein, deren Nullstellen und Pole auf der linken Halbebene liegen.
+
+$N \in \mathbb{N} $ gibt dabei die Ordnung des Filters vor, also die maximale Anzahl Pole oder Nullstellen.
+
+Damit ein Filter die Passband Kondition erfüllt muss $|F_N(w)| \leq 1 \forall |w| \leq 1$ und für $|w| \geq 1$ sollte die Funktion möglichst schnell divergieren.
+Eine einfaches Polynom, dass das erfüllt, erhalten wir wenn $F_N(w) = w^N$.
+Tatsächlich erhalten wir damit das Butterworth Filter, wie in Abbildung \ref{ellfilter:fig:butterworth} ersichtlich.
+\begin{figure}
+ \centering
+ \input{papers/ellfilter/python/F_N_butterworth.pgf}
+ \caption{$F_N$ für Butterworth filter. Der grüne Bereich definiert die erlaubten Werte für alle $F_N$-Funktionen.}
+ \label{ellfilter:fig:butterworth}
+\end{figure}
+
+wenn $F_N(w)$ eine rationale Funktion ist, ist auch $H(\Omega)$ eine rationale Funktion und daher ein lineares Filter. %proof?
+
+\begin{align}
+ F_N(w) & =
+ \begin{cases}
+ w^N & \text{Butterworth} \\
+ T_N(w) & \text{Tschebyscheff, Typ 1} \\
+ [k_1 T_N (k^{-1} w^{-1})]^{-1} & \text{Tschebyscheff, Typ 2} \\
+ R_N(w, \xi) & \text{Elliptisch (Cauer)} \\
+ \end{cases}
+\end{align}
+
+Mit der Ausnahme vom Butterworth filter sind alle Filter nach speziellen Funktionen benannt.
+Alle diese Filter sind optimal für unterschiedliche Anwendungsgebiete.
+Das Butterworth-Filter, zum Beispiel, ist maximal flach im Durchlassbereich.
+Das Tschebyscheff-1 Filter sind maximal steil für eine definierte Welligkeit im Durchlassbereich, währendem es im Sperrbereich monoton abfallend ist.
+Es scheint so als sind gewisse Eigenschaften dieser speziellen Funktionen verantwortlich für die Optimalität dieser Filter.
diff --git a/buch/papers/ellfilter/elliptic.tex b/buch/papers/ellfilter/elliptic.tex
new file mode 100644
index 0000000..88bfbfe
--- /dev/null
+++ b/buch/papers/ellfilter/elliptic.tex
@@ -0,0 +1,92 @@
+\section{Elliptische rationale Funktionen}
+
+Kommen wir nun zum eigentlichen Teil dieses Papers, den elliptischen rationalen Funktionen
+\begin{align}
+ R_N(\xi, w) &= \cd \left(N~f_1(\xi)~\cd^{-1}(w, 1/\xi), f_2(\xi)\right) \\
+ &= \cd \left(N~\frac{K_1}{K}~\cd^{-1}(w, k), k_1)\right) , \quad k= 1/\xi, k_1 = 1/f(\xi) \\
+ &= \cd \left(N~K_1~z , k_1 \right), \quad w= \cd(z K, k)
+\end{align}
+
+
+sieht ähnlich aus wie die trigonometrische Darstellung der Tschebyschef-Polynome \eqref{ellfilter:eq:chebychef_polynomials}
+Anstelle vom Kosinus kommt hier die $\cd$-Funktion zum Einsatz.
+Die Ordnungszahl $N$ kommt auch als Faktor for.
+Zusätzlich werden noch zwei verschiedene elliptische Module $k$ und $k_1$ gebraucht.
+
+
+
+Sinus entspricht $\sn$
+
+Damit die Nullstellen an ähnlichen Positionen zu liegen kommen wie bei den Tschebyscheff-Polynomen, muss die $\cd$-Funktion gewählt werden.
+
+Die $\cd^{-1}(w, k)$-Funktion ist um $K$ verschoben zur $\sn^{-1}(w, k)$-Funktion, wie ersichtlich in Abbildung \ref{ellfilter:fig:cd}.
+\begin{figure}
+ \centering
+ \input{papers/ellfilter/tikz/cd.tikz.tex}
+ \caption{
+ $z$-Ebene der Funktion $z = \sn^{-1}(w, k)$.
+ Die Funktion ist in der realen Achse $4K$-periodisch und in der imaginären Achse $2jK^\prime$-periodisch.
+ }
+ \label{ellfilter:fig:cd}
+\end{figure}
+Auffallend ist, dass sich alle Nullstellen und Polstellen um $K$ verschoben haben.
+
+Durch das Konzept vom fundamentalen Rechteck, siehe Abbildung \ref{ellfilter:fig:fundamental_rectangle} können für alle inversen Jaccobi elliptischen Funktionen die Positionen der Null- und Polstellen anhand eines Diagramms ermittelt werden.
+Der erste Buchstabe bestimmt die Position der Nullstelle und der zweite Buchstabe die Polstelle.
+\begin{figure}
+ \centering
+ \input{papers/ellfilter/tikz/fundamental_rectangle.tikz.tex}
+ \caption{
+ Fundamentales Rechteck der inversen Jaccobi elliptischen Funktionen.
+ }
+ \label{ellfilter:fig:fundamental_rectangle}
+\end{figure}
+
+Auffallend an der $w = \sn(z, k)$-Funktion ist, dass sich $w$ auf der reellen Achse wie der Kosinus immer zwischen $-1$ und $1$ bewegt, während bei $\mathrm{Im(z) = K^\prime}$ die Werte zwischen $\pm 1/k$ und $\pm \infty$ verlaufen.
+Die Funktion hat also Equirippel-Verhalten um $w=0$ und um $w=\pm \infty$.
+Falls es möglich ist diese Werte abzufahren im Sti der Tschebyscheff-Polynome, kann ein Filter gebaut werden, dass Equirippel-Verhalten im Durchlass- und Sperrbereich aufweist.
+
+
+
+Analog zu Abbildung \ref{ellfilter:fig:arccos2} können wir auch bei den elliptisch rationalen Funktionen die komplexe $z$-Ebene betrachten, wie ersichtlich in Abbildung \ref{ellfilter:fig:cd2}, um die besser zu verstehen.
+\begin{figure}
+ \centering
+ \input{papers/ellfilter/tikz/cd2.tikz.tex}
+ \caption{
+ $z_1$-Ebene der elliptischen rationalen Funktionen.
+ Je grösser die Ordnung $N$ gewählt wird, desto mehr Nullstellen passiert.
+ }
+ \label{ellfilter:fig:cd2}
+\end{figure}
+% Da die $\cd^{-1}$-Funktion
+
+
+
+\begin{figure}
+ \centering
+ \input{papers/ellfilter/python/F_N_elliptic.pgf}
+ \caption{$F_N$ für ein elliptischs filter.}
+ \label{ellfilter:fig:elliptic}
+\end{figure}
+
+\subsection{Degree Equation}
+
+Der $\cd^{-1}$ Term muss so verzogen werden, dass die umgebene $\cd$-Funktion die Nullstellen und Pole trifft.
+Dies trifft ein wenn die Degree Equation erfüllt ist.
+
+\begin{equation}
+ N \frac{K^\prime}{K} = \frac{K^\prime_1}{K_1}
+\end{equation}
+
+
+Leider ist das lösen dieser Gleichung nicht trivial.
+Die Rechnung wird in \ref{ellfilter:bib:orfanidis} im Detail angeschaut.
+
+
+\subsection{Polynome?}
+
+Bei den Tschebyscheff-Polynomen haben wir gesehen, dass die Trigonometrische Formel zu einfachen Polynomen umgewandelt werden kann.
+Im gegensatz zum $\cos^{-1}$ hat der $\cd^{-1}$ nicht nur Nullstellen sondern auch Pole.
+Somit entstehen bei den elliptischen rationalen Funktionen, wie es der name auch deutet, rationale Funktionen, also ein Bruch von zwei Polynomen.
+
+Da Transformationen einer rationalen Funktionen mit Grundrechenarten, wie es in \eqref{ellfilter:eq:h_omega} der Fall ist, immer noch rationale Funktionen ergeben, stellt dies kein Problem für die Implementierung dar.
diff --git a/buch/papers/ellfilter/jacobi.tex b/buch/papers/ellfilter/jacobi.tex
new file mode 100644
index 0000000..6a208fa
--- /dev/null
+++ b/buch/papers/ellfilter/jacobi.tex
@@ -0,0 +1,189 @@
+\section{Jacobische elliptische Funktionen}
+
+%TODO $z$ or $u$ for parameter?
+
+Für das elliptische Filter wird statt der, für das Tschebyscheff-Filter benutzen Kreis-Trigonometrie die elliptischen Funktionen gebraucht.
+Der Begriff elliptische Funktion wird für sehr viele Funktionen gebraucht, daher ist es hier wichtig zu erwähnen, dass es ausschliesslich um die Jacobischen elliptischen Funktionen geht.
+
+Im Wesentlichen erweitern die Jacobi elliptischen Funktionen die trigonometrische Funktionen für Ellipsen.
+Zum Beispiel gibt es analog zum Sinus den elliptischen $\sn(z, k)$.
+Im Gegensatz zum den trigonometrischen Funktionen haben die elliptischen Funktionen zwei parameter.
+Zum einen gibt es den \textit{elliptische Modul} $k$, der die Exzentrizität der Ellipse parametrisiert.
+Zum andern das Winkelargument $z$.
+Im Kreis ist der Radius für alle Winkel konstant, bei Ellipsen ändert sich das.
+Dies hat zur Folge, dass bei einer Ellipse die Kreisbodenstrecke nicht linear zum Winkel verläuft.
+Darum kann hier nicht der gewohnte Winkel verwendet werden.
+Das Winkelargument $z$ kann durch das elliptische Integral erster Art
+\begin{equation}
+ z
+ =
+ F(\phi, k)
+ =
+ \int_{0}^{\phi}
+ \frac{
+ d\theta
+ }{
+ \sqrt{
+ 1-k^2 \sin^2 \theta
+ }
+ }
+ =
+ \int_{0}^{\phi}
+ \frac{
+ dt
+ }{
+ \sqrt{
+ (1-t^2)(1-k^2 t^2)
+ }
+ } %TODO which is right? are both functions from phi?
+\end{equation}
+mit dem Winkel $\phi$ in Verbindung liegt.
+
+Dabei wird das vollständige und unvollständige Elliptische integral unterschieden.
+Beim vollständigen Integral
+\begin{equation}
+ K(k)
+ =
+ \int_{0}^{\pi / 2}
+ \frac{
+ d\theta
+ }{
+ \sqrt{
+ 1-k^2 \sin^2 \theta
+ }
+ }
+\end{equation}
+wird über ein viertel Ellipsenbogen integriert also bis $\phi=\pi/2$ und liefert das Winkelargument für eine Vierteldrehung.
+Die Zahl wird oft auch abgekürzt mit $K = K(k)$ und ist für das elliptische Filter sehr relevant.
+Alle elliptishen Funktionen sind somit $4K$-periodisch.
+
+Neben dem $\sn$ gibt es zwei weitere basis-elliptische Funktionen $\cn$ und $\dn$.
+Dazu kommen noch weitere abgeleitete Funktionen, die durch Quotienten und Kehrwerte dieser Funktionen zustande kommen.
+Insgesamt sind es die zwölf Funktionen
+\begin{equation*}
+ \sn \quad
+ \ns \quad
+ \scelliptic \quad
+ \sd \quad
+ \cn \quad
+ \nc \quad
+ \cs \quad
+ \cd \quad
+ \dn \quad
+ \nd \quad
+ \ds \quad
+ \dc.
+\end{equation*}
+
+Die Jacobischen elliptischen Funktionen können mit der inversen Funktion des kompletten elliptischen Integrals erster Art
+\begin{equation}
+ \phi = F^{-1}(z, k)
+\end{equation}
+definiert werden. Dabei ist zu beachten dass nur das $z$ Argument der Funktion invertiert wird, also
+\begin{equation}
+ z = F(\phi, k)
+ \Leftrightarrow
+ \phi = F^{-1}(z, k).
+\end{equation}
+Mithilfe von $F^{-1}$ kann zum Beispiel $sn^{-1}$ mit dem Elliptischen integral dargestellt werden:
+\begin{equation}
+ \sin(\phi)
+ =
+ \sin \left( F^{-1}(z, k) \right)
+ =
+ \sn(z, k)
+ =
+ w
+\end{equation}
+
+\begin{equation}
+ \phi
+ =
+ F^{-1}(z, k)
+ =
+ \sin^{-1} \big( \sn (z, k ) \big)
+ =
+ \sin^{-1} ( w )
+\end{equation}
+
+\begin{equation}
+ F(\phi, k)
+ =
+ z
+ =
+ F( \sin^{-1} \big( \sn (z, k ) \big) , k)
+ =
+ F( \sin^{-1} ( w ), k)
+\end{equation}
+
+\begin{equation}
+ \sn^{-1}(w, k)
+ =
+ F(\phi, k),
+ \quad
+ \phi = \sin^{-1}(w)
+\end{equation}
+
+\begin{align}
+ \sn^{-1}(w, k)
+ & =
+ \int_{0}^{\phi}
+ \frac{
+ d\theta
+ }{
+ \sqrt{
+ 1-k^2 \sin^2 \theta
+ }
+ },
+ \quad
+ \phi = \sin^{-1}(w)
+ \\
+ & =
+ \int_{0}^{w}
+ \frac{
+ dt
+ }{
+ \sqrt{
+ (1-t^2)(1-k^2 t^2)
+ }
+ }
+\end{align}
+
+Beim $\cos^{-1}(x)$ haben wir gesehen, dass die analytische Fortsetzung bei $x < -1$ und $x > 1$ rechtwinklig in die Komplexen zahlen wandert.
+Wenn man das gleiche mit $\sn^{-1}(w, k)$ macht, erkennt man zwei interessante Stellen.
+Die erste ist die gleiche wie beim $\cos^{-1}(x)$ nämlich bei $t = \pm 1$.
+Der erste Term unter der Wurzel wird dann negativ, während der zweite noch positiv ist, da $k \leq 1$.
+\begin{equation}
+ \frac{
+ 1
+ }{
+ \sqrt{
+ (1-t^2)(1-k^2 t^2)
+ }
+ }
+ \in \mathbb{R}
+ \quad \forall \quad
+ -1 \leq t \leq 1
+\end{equation}
+Die zweite stelle passiert wenn beide Faktoren unter der Wurzel negativ werden, was bei $t = 1/k$ der Fall ist.
+
+
+
+
+Funktion in relle und komplexe Richtung periodisch
+
+In der reellen Richtung ist sie $4K(k)$-periodisch und in der imaginären Richtung $4K^\prime(k)$-periodisch.
+
+
+
+%TODO sn^{-1} grafik
+
+\begin{figure}
+ \centering
+ \input{papers/ellfilter/tikz/sn.tikz.tex}
+ \caption{
+ $z$-Ebene der Funktion $z = \sn^{-1}(w, k)$.
+ Die Funktion ist in der realen Achse $4K$-periodisch und in der imaginären Achse $2jK^\prime$-periodisch.
+ }
+ % \label{ellfilter:fig:cd2}
+\end{figure}
diff --git a/buch/papers/ellfilter/main.tex b/buch/papers/ellfilter/main.tex
index 26aaec1..c58dfa7 100644
--- a/buch/papers/ellfilter/main.tex
+++ b/buch/papers/ellfilter/main.tex
@@ -8,29 +8,10 @@
\begin{refsection}
\chapterauthor{Nicolas Tobler}
-Ein paar Hinweise für die korrekte Formatierung des Textes
-\begin{itemize}
-\item
-Absätze werden gebildet, indem man eine Leerzeile einfügt.
-Die Verwendung von \verb+\\+ ist nur in Tabellen und Arrays gestattet.
-\item
-Die explizite Platzierung von Bildern ist nicht erlaubt, entsprechende
-Optionen werden gelöscht.
-Verwenden Sie Labels und Verweise, um auf Bilder hinzuweisen.
-\item
-Beginnen Sie jeden Satz auf einer neuen Zeile.
-Damit ermöglichen Sie dem Versionsverwaltungssysteme, Änderungen
-in verschiedenen Sätzen von verschiedenen Autoren ohne Konflikt
-anzuwenden.
-\item
-Bilden Sie auch für Formeln kurze Zeilen, einerseits der besseren
-Übersicht wegen, aber auch um GIT die Arbeit zu erleichtern.
-\end{itemize}
-
-\input{papers/ellfilter/teil0.tex}
-\input{papers/ellfilter/teil1.tex}
-\input{papers/ellfilter/teil2.tex}
-\input{papers/ellfilter/teil3.tex}
+\input{papers/ellfilter/einleitung.tex}
+\input{papers/ellfilter/tschebyscheff.tex}
+\input{papers/ellfilter/jacobi.tex}
+\input{papers/ellfilter/elliptic.tex}
\printbibliography[heading=subbibliography]
\end{refsection}
diff --git a/buch/papers/ellfilter/packages.tex b/buch/papers/ellfilter/packages.tex
index c94db34..9a550e2 100644
--- a/buch/papers/ellfilter/packages.tex
+++ b/buch/papers/ellfilter/packages.tex
@@ -8,3 +8,20 @@
% following example
%\usepackage{packagename}
+% \usepackage[dvipsnames]{xcolor}
+
+\usetikzlibrary{trees,shapes,decorations}
+
+\DeclareMathOperator{\sn}{\mathrm{sn}}
+\DeclareMathOperator{\ns}{\mathrm{ns}}
+\DeclareMathOperator{\scelliptic}{\mathrm{sc}}
+\DeclareMathOperator{\sd}{\mathrm{sd}}
+\DeclareMathOperator{\cn}{\mathrm{cn}}
+\DeclareMathOperator{\nc}{\mathrm{nc}}
+\DeclareMathOperator{\cs}{\mathrm{cs}}
+\DeclareMathOperator{\cd}{\mathrm{cd}}
+\DeclareMathOperator{\dn}{\mathrm{dn}}
+\DeclareMathOperator{\nd}{\mathrm{nd}}
+\DeclareMathOperator{\ds}{\mathrm{ds}}
+\DeclareMathOperator{\dc}{\mathrm{dc}}
+
diff --git a/buch/papers/ellfilter/presentation/presentation.tex b/buch/papers/ellfilter/presentation/presentation.tex
new file mode 100644
index 0000000..7fdb864
--- /dev/null
+++ b/buch/papers/ellfilter/presentation/presentation.tex
@@ -0,0 +1,413 @@
+\documentclass[ngerman, aspectratio=169, xcolor={rgb}]{beamer}
+
+% style
+\mode<presentation>{
+ \usetheme{Frankfurt}
+}
+%packages
+\usepackage[utf8]{inputenc}\DeclareUnicodeCharacter{2212}{-}
+\usepackage[english]{babel}
+\usepackage{graphicx}
+\usepackage{array}
+
+\newcolumntype{L}[1]{>{\raggedright\let\newline\\\arraybackslash\hspace{0pt}}m{#1}}
+\usepackage{ragged2e}
+
+\usepackage{bm} % bold math
+\usepackage{amsfonts}
+\usepackage{amssymb}
+\usepackage{mathtools}
+\usepackage{amsmath}
+\usepackage{multirow} % multi row in tables
+\usepackage{booktabs} %toprule midrule bottomrue in tables
+\usepackage{scrextend}
+\usepackage{textgreek}
+\usepackage[rgb]{xcolor}
+
+\usepackage{ marvosym } % \Lightning
+
+\usepackage{multimedia} % embedded videos
+
+\usepackage{tikz}
+\usepackage{pgf}
+\usepackage{pgfplots}
+
+\usepackage{algorithmic}
+
+%citations
+\usepackage[style=verbose,backend=biber]{biblatex}
+\addbibresource{references.bib}
+
+
+%math font
+\usefonttheme[onlymath]{serif}
+
+%Beamer Template modifications
+%\definecolor{mainColor}{HTML}{0065A3} % HSR blue
+\definecolor{mainColor}{HTML}{D72864} % OST pink
+\definecolor{invColor}{HTML}{28d79b} % OST pink
+\definecolor{dgreen}{HTML}{38ad36} % Dark green
+
+%\definecolor{mainColor}{HTML}{000000} % HSR blue
+\setbeamercolor{palette primary}{bg=white,fg=mainColor}
+\setbeamercolor{palette secondary}{bg=orange,fg=mainColor}
+\setbeamercolor{palette tertiary}{bg=yellow,fg=red}
+\setbeamercolor{palette quaternary}{bg=mainColor,fg=white} %bg = Top bar, fg = active top bar topic
+\setbeamercolor{structure}{fg=black} % itemize, enumerate, etc (bullet points)
+\setbeamercolor{section in toc}{fg=black} % TOC sections
+\setbeamertemplate{section in toc}[sections numbered]
+\setbeamertemplate{subsection in toc}{%
+ \hspace{1.2em}{$\bullet$}~\inserttocsubsection\par}
+
+\setbeamertemplate{itemize items}[circle]
+\setbeamertemplate{description item}[circle]
+\setbeamertemplate{title page}[default][colsep=-4bp,rounded=true]
+\beamertemplatenavigationsymbolsempty
+
+\setbeamercolor{footline}{fg=gray}
+\setbeamertemplate{footline}{%
+ \hfill\usebeamertemplate***{navigation symbols}
+ \hspace{0.5cm}
+ \insertframenumber{}\hspace{0.2cm}\vspace{0.2cm}
+}
+
+\usepackage{caption}
+\captionsetup{labelformat=empty}
+
+%Title Page
+\title{Elliptische Filter}
+\subtitle{Eine Anwendung der Jaccobi elliptischen Funktionen}
+\author{Nicolas Tobler}
+% \institute{OST Ostschweizer Fachhochschule}
+% \institute{\includegraphics[scale=0.3]{../img/ost_logo.png}}
+\date{\today}
+
+\input{../packages.tex}
+
+\newcommand*{\QED}{\hfill\ensuremath{\blacksquare}}%
+
+\newcommand*{\HL}{\textcolor{mainColor}}
+\newcommand*{\RD}{\textcolor{red}}
+\newcommand*{\BL}{\textcolor{blue}}
+\newcommand*{\GN}{\textcolor{dgreen}}
+
+\definecolor{darkgreen}{rgb}{0,0.6,0}
+
+
+\makeatletter
+\newcount\my@repeat@count
+\newcommand{\myrepeat}[2]{%
+ \begingroup
+ \my@repeat@count=\z@
+ \@whilenum\my@repeat@count<#1\do{#2\advance\my@repeat@count\@ne}%
+ \endgroup
+}
+\makeatother
+
+\usetikzlibrary{automata,arrows,positioning,calc,shapes.geometric, fadings}
+
+\begin{document}
+
+ \begin{frame}
+ \titlepage
+ \end{frame}
+
+ \begin{frame}
+ \frametitle{Content}
+ \tableofcontents
+ \end{frame}
+
+ \section{Linear Filter}
+
+ \begin{frame}
+ \frametitle{Lineare Filter}
+
+
+ \begin{equation}
+ | H(\Omega)|^2 = \frac{1}{1 + \varepsilon_p^2 F_N^2(w)}, \quad w=\frac{\Omega}{\Omega_p}
+ \end{equation}
+
+ \pause
+
+ \begin{equation}
+ F_N(w) = w^N
+ \end{equation}
+
+ \end{frame}
+
+ \begin{frame}
+ \frametitle{Beispiel: Butterworth Filter}
+
+ \begin{equation}
+ F_N(w) = w^N
+ \end{equation}
+
+ \begin{center}
+ \input{../python/F_N_butterworth.pgf}
+ \end{center}
+
+ \end{frame}
+
+
+ \begin{frame}
+ \frametitle{Arten von linearen filtern}
+
+ \begin{align*}
+ F_N(w) & =
+ \begin{cases}
+ w^N & \text{Butterworth} \\
+ T_N(w) & \text{Tschebyscheff, Typ 1} \\
+ [k_1 T_N (k^{-1} w^{-1})]^{-1} & \text{Tschebyscheff, Typ 2} \\
+ R_N(w,\xi) & \text{Elliptisch (Cauer)} \\
+ \end{cases}
+ \end{align*}
+
+ \end{frame}
+
+ \section{Tschebycheff Filter}
+
+ \begin{frame}
+ \frametitle{Tschebyscheff-Polynome}
+
+
+ \begin{columns}
+ \begin{column}[T]{0.35\textwidth}
+
+ \begin{align*}
+ T_{0}(x)&=1\\
+ T_{1}(x)&=x\\
+ T_{2}(x)&=2x^{2}-1\\
+ T_{3}(x)&=4x^{3}-3x\\
+ T_{n+1}(x)&=2x~T_{n}(x)-T_{n-1}(x)
+ \end{align*}
+
+ \end{column}
+ \begin{column}[T]{0.65\textwidth}
+
+ \begin{center}
+ \resizebox{\textwidth}{!}{
+ \input{../python/F_N_chebychev2.pgf}
+ }
+ \end{center}
+
+ \end{column}
+ \end{columns}
+
+
+
+ \end{frame}
+
+ \begin{frame}
+ \frametitle{Tschebyscheff-Filter}
+
+ \begin{equation*}
+ | H(\Omega)|^2 = \frac{1}{1 + \varepsilon_p^2 T_N^2(w)}, \quad w=\frac{\Omega}{\Omega_p}
+ \end{equation*}
+
+ \begin{center}
+ \scalebox{0.9}{
+ \input{../python/F_N_chebychev.pgf}
+ }
+ \end{center}
+
+ \end{frame}
+
+
+ \begin{frame}
+ \frametitle{Tschebyscheff-Filter}
+
+ Darstellung mit trigonometrischen Funktionen:
+
+ \begin{align} \label{ellfilter:eq:chebychef_polynomials}
+ T_N(w) &= \cos \left( N \cos^{-1}(w) \right) \\
+ &= \cos \left(N~z \right), \quad w= \cos(z)
+ \end{align}
+
+
+ \end{frame}
+
+ \begin{frame}
+ \frametitle{Tschebyscheff-Filter}
+
+ \begin{equation*}
+ z = \cos^{-1}(w)
+ \end{equation*}
+
+ \begin{center}
+ \scalebox{0.85}{
+ \input{../tikz/arccos.tikz.tex}
+ }
+ \end{center}
+
+ \end{frame}
+
+ \begin{frame}
+ \frametitle{Tschebyscheff-Filter}
+
+ \begin{equation*}
+ z_1 = N~\cos^{-1}(w)
+ \end{equation*}
+
+ \begin{center}
+ \scalebox{0.85}{
+ \input{../tikz/arccos2.tikz.tex}
+ }
+ \end{center}
+
+ \end{frame}
+
+
+ \section{Jaccobi elliptische Funktionen}
+
+ \begin{frame}
+ \frametitle{Jaccobi elliptische Funktionen}
+
+
+ \begin{equation}
+ z
+ =
+ F(\phi, k)
+ =
+ \int_{0}^{\phi}
+ \frac{
+ d\theta
+ }{
+ \sqrt{
+ 1-k^2 \sin^2 \theta
+ }
+ }
+ =
+ \int_{0}^{\phi}
+ \frac{
+ dt
+ }{
+ \sqrt{
+ (1-t^2)(1-k^2 t^2)
+ }
+ }
+ \end{equation}
+
+ \begin{equation}
+ K(k)
+ =
+ \int_{0}^{\pi / 2}
+ \frac{
+ d\theta
+ }{
+ \sqrt{
+ 1-k^2 \sin^2 \theta
+ }
+ }
+ \end{equation}
+
+
+
+ \end{frame}
+
+ \begin{frame}
+ \frametitle{Jaccobi elliptische Funktionen}
+
+ \begin{equation*}
+ z = \sn^{-1}(w, k)
+ \end{equation*}
+
+ \begin{center}
+ \scalebox{0.7}{
+ \input{../tikz/sn.tikz.tex}
+ }
+ \end{center}
+
+ \end{frame}
+
+ \begin{frame}
+ \frametitle{Fundamentales Rechteck}
+
+ Nullstelle beim ersten Buchstabe, Polstelle beim zweiten Buchstabe
+
+ \begin{center}
+ \scalebox{0.8}{
+ \input{../tikz/fundamental_rectangle.tikz.tex}
+ }
+ \end{center}
+
+ \end{frame}
+
+
+ \begin{frame}
+ \frametitle{Jaccobi elliptische Funktionen}
+
+ \begin{equation*}
+ z = \cd^{-1}(w, k)
+ \end{equation*}
+
+ \begin{center}
+ \scalebox{0.7}{
+ \input{../tikz/cd.tikz.tex}
+
+ }
+ \end{center}
+
+ \end{frame}
+
+ \begin{frame}
+ \frametitle{Periodizität in realer und imaginärer Richtung}
+
+ \begin{center}
+ \input{../python/k.pgf}
+ \end{center}
+
+
+ \end{frame}
+
+ \begin{frame}
+ \frametitle{Elliptisches Filter}
+
+ \begin{equation*}
+ z_1 = N~\frac{K_1}{K}~\cd^{-1}(w, k)
+ \end{equation*}
+
+ \begin{center}
+ \scalebox{0.8}{
+ \input{../tikz/cd2.tikz.tex}
+ }
+ \end{center}
+
+ \end{frame}
+
+ \begin{frame}
+ \frametitle{Elliptisches Filter}
+
+ \begin{columns}
+
+ \begin{column}[T]{0.5\textwidth}
+
+ \begin{center}
+ \resizebox{\textwidth}{!}{
+ \input{../python/F_N_elliptic.pgf}
+ }
+ \end{center}
+
+ \end{column}
+ \begin{column}[T]{0.5\textwidth}
+
+ \begin{center}
+ \resizebox{\textwidth}{!}{
+ \input{../python/elliptic.pgf}
+ }
+ \end{center}
+
+ \end{column}
+ \end{columns}
+
+ \end{frame}
+
+ \begin{frame}
+ \frametitle{Gradgleichung}
+
+ \begin{equation}
+ N \frac{K^\prime}{K} = \frac{K^\prime_1}{K_1}
+ \end{equation}
+
+ \end{frame}
+
+ \end{document}
diff --git a/buch/papers/ellfilter/python/F_N_butterworth.pgf b/buch/papers/ellfilter/python/F_N_butterworth.pgf
new file mode 100644
index 0000000..857e363
--- /dev/null
+++ b/buch/papers/ellfilter/python/F_N_butterworth.pgf
@@ -0,0 +1,1083 @@
+%% Creator: Matplotlib, PGF backend
+%%
+%% To include the figure in your LaTeX document, write
+%% \input{<filename>.pgf}
+%%
+%% Make sure the required packages are loaded in your preamble
+%% \usepackage{pgf}
+%%
+%% Also ensure that all the required font packages are loaded; for instance,
+%% the lmodern package is sometimes necessary when using math font.
+%% \usepackage{lmodern}
+%%
+%% Figures using additional raster images can only be included by \input if
+%% they are in the same directory as the main LaTeX file. For loading figures
+%% from other directories you can use the `import` package
+%% \usepackage{import}
+%%
+%% and then include the figures with
+%% \import{<path to file>}{<filename>.pgf}
+%%
+%% Matplotlib used the following preamble
+%%
+\begingroup%
+\makeatletter%
+\begin{pgfpicture}%
+\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{4.000000in}{2.500000in}}%
+\pgfusepath{use as bounding box, clip}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetmiterjoin%
+\pgfsetlinewidth{0.000000pt}%
+\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetstrokeopacity{0.000000}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{4.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{4.000000in}{2.500000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{2.500000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathclose%
+\pgfusepath{}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetmiterjoin%
+\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.000000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetstrokeopacity{0.000000}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.630330in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{3.727004in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{3.727004in}{2.301955in}}%
+\pgfpathlineto{\pgfqpoint{0.630330in}{2.301955in}}%
+\pgfpathlineto{\pgfqpoint{0.630330in}{0.548769in}}%
+\pgfpathclose%
+\pgfusepath{fill}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.630330in}{0.548769in}}{\pgfqpoint{3.096674in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetbuttcap%
+\pgfsetmiterjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.501961,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetfillopacity{0.200000}%
+\pgfsetlinewidth{0.000000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetstrokeopacity{0.200000}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.630330in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{2.694779in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{2.694779in}{1.425362in}}%
+\pgfpathlineto{\pgfqpoint{0.630330in}{1.425362in}}%
+\pgfpathlineto{\pgfqpoint{0.630330in}{0.548769in}}%
+\pgfpathclose%
+\pgfusepath{fill}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.630330in}{0.548769in}}{\pgfqpoint{3.096674in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetbuttcap%
+\pgfsetmiterjoin%
+\definecolor{currentfill}{rgb}{1.000000,0.647059,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetfillopacity{0.200000}%
+\pgfsetlinewidth{0.000000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetstrokeopacity{0.200000}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{2.694779in}{1.425362in}}%
+\pgfpathlineto{\pgfqpoint{3.727004in}{1.425362in}}%
+\pgfpathlineto{\pgfqpoint{3.727004in}{2.301955in}}%
+\pgfpathlineto{\pgfqpoint{2.694779in}{2.301955in}}%
+\pgfpathlineto{\pgfqpoint{2.694779in}{1.425362in}}%
+\pgfpathclose%
+\pgfusepath{fill}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.630330in}{0.548769in}}{\pgfqpoint{3.096674in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.630330in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{0.630330in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{0.630330in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.630330in,y=0.451547in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.00}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.630330in}{0.548769in}}{\pgfqpoint{3.096674in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{1.146442in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{1.146442in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{1.146442in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=1.146442in,y=0.451547in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.25}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.630330in}{0.548769in}}{\pgfqpoint{3.096674in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{1.662555in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{1.662555in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{1.662555in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=1.662555in,y=0.451547in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.50}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.630330in}{0.548769in}}{\pgfqpoint{3.096674in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{2.178667in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{2.178667in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{2.178667in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=2.178667in,y=0.451547in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.75}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.630330in}{0.548769in}}{\pgfqpoint{3.096674in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{2.694779in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{2.694779in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{2.694779in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=2.694779in,y=0.451547in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {1.00}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.630330in}{0.548769in}}{\pgfqpoint{3.096674in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{3.210892in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{3.210892in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{3.210892in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=3.210892in,y=0.451547in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {1.25}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.630330in}{0.548769in}}{\pgfqpoint{3.096674in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{3.727004in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{3.727004in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{3.727004in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=3.727004in,y=0.451547in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {1.50}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=2.178667in,y=0.272534in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle w\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.630330in}{0.548769in}}{\pgfqpoint{3.096674in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.630330in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{3.727004in}{0.548769in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{0.630330in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.355638in, y=0.500544in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.0}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.630330in}{0.548769in}}{\pgfqpoint{3.096674in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.630330in}{0.987065in}}%
+\pgfpathlineto{\pgfqpoint{3.727004in}{0.987065in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{0.630330in}{0.987065in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.355638in, y=0.938840in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.5}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.630330in}{0.548769in}}{\pgfqpoint{3.096674in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.630330in}{1.425362in}}%
+\pgfpathlineto{\pgfqpoint{3.727004in}{1.425362in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{0.630330in}{1.425362in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.355638in, y=1.377137in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {1.0}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.630330in}{0.548769in}}{\pgfqpoint{3.096674in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.630330in}{1.863658in}}%
+\pgfpathlineto{\pgfqpoint{3.727004in}{1.863658in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{0.630330in}{1.863658in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.355638in, y=1.815433in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {1.5}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.630330in}{0.548769in}}{\pgfqpoint{3.096674in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.630330in}{2.301955in}}%
+\pgfpathlineto{\pgfqpoint{3.727004in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{0.630330in}{2.301955in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.355638in, y=2.253730in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {2.0}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.300082in,y=1.425362in,,bottom,rotate=90.000000]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle F^2_N(w)\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.630330in}{0.548769in}}{\pgfqpoint{3.096674in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{1.505625pt}%
+\definecolor{currentstroke}{rgb}{0.121569,0.466667,0.705882}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.630330in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{0.661609in}{0.548970in}}%
+\pgfpathlineto{\pgfqpoint{0.692889in}{0.549574in}}%
+\pgfpathlineto{\pgfqpoint{0.724168in}{0.550580in}}%
+\pgfpathlineto{\pgfqpoint{0.755448in}{0.551989in}}%
+\pgfpathlineto{\pgfqpoint{0.786727in}{0.553800in}}%
+\pgfpathlineto{\pgfqpoint{0.818007in}{0.556013in}}%
+\pgfpathlineto{\pgfqpoint{0.849287in}{0.558629in}}%
+\pgfpathlineto{\pgfqpoint{0.880566in}{0.561648in}}%
+\pgfpathlineto{\pgfqpoint{0.911846in}{0.565069in}}%
+\pgfpathlineto{\pgfqpoint{0.943125in}{0.568893in}}%
+\pgfpathlineto{\pgfqpoint{0.974405in}{0.573119in}}%
+\pgfpathlineto{\pgfqpoint{1.005684in}{0.577747in}}%
+\pgfpathlineto{\pgfqpoint{1.036964in}{0.582778in}}%
+\pgfpathlineto{\pgfqpoint{1.068243in}{0.588211in}}%
+\pgfpathlineto{\pgfqpoint{1.099523in}{0.594047in}}%
+\pgfpathlineto{\pgfqpoint{1.130802in}{0.600286in}}%
+\pgfpathlineto{\pgfqpoint{1.162082in}{0.606927in}}%
+\pgfpathlineto{\pgfqpoint{1.193361in}{0.613970in}}%
+\pgfpathlineto{\pgfqpoint{1.224641in}{0.621416in}}%
+\pgfpathlineto{\pgfqpoint{1.255921in}{0.629264in}}%
+\pgfpathlineto{\pgfqpoint{1.287200in}{0.637515in}}%
+\pgfpathlineto{\pgfqpoint{1.318480in}{0.646168in}}%
+\pgfpathlineto{\pgfqpoint{1.349759in}{0.655224in}}%
+\pgfpathlineto{\pgfqpoint{1.381039in}{0.664682in}}%
+\pgfpathlineto{\pgfqpoint{1.412318in}{0.674543in}}%
+\pgfpathlineto{\pgfqpoint{1.443598in}{0.684806in}}%
+\pgfpathlineto{\pgfqpoint{1.474877in}{0.695471in}}%
+\pgfpathlineto{\pgfqpoint{1.506157in}{0.706539in}}%
+\pgfpathlineto{\pgfqpoint{1.537436in}{0.718010in}}%
+\pgfpathlineto{\pgfqpoint{1.568716in}{0.729883in}}%
+\pgfpathlineto{\pgfqpoint{1.599995in}{0.742159in}}%
+\pgfpathlineto{\pgfqpoint{1.631275in}{0.754837in}}%
+\pgfpathlineto{\pgfqpoint{1.662555in}{0.767917in}}%
+\pgfpathlineto{\pgfqpoint{1.693834in}{0.781400in}}%
+\pgfpathlineto{\pgfqpoint{1.725114in}{0.795285in}}%
+\pgfpathlineto{\pgfqpoint{1.756393in}{0.809573in}}%
+\pgfpathlineto{\pgfqpoint{1.787673in}{0.824264in}}%
+\pgfpathlineto{\pgfqpoint{1.818952in}{0.839357in}}%
+\pgfpathlineto{\pgfqpoint{1.850232in}{0.854852in}}%
+\pgfpathlineto{\pgfqpoint{1.881511in}{0.870750in}}%
+\pgfpathlineto{\pgfqpoint{1.912791in}{0.887050in}}%
+\pgfpathlineto{\pgfqpoint{1.944070in}{0.903753in}}%
+\pgfpathlineto{\pgfqpoint{1.975350in}{0.920858in}}%
+\pgfpathlineto{\pgfqpoint{2.006629in}{0.938366in}}%
+\pgfpathlineto{\pgfqpoint{2.037909in}{0.956276in}}%
+\pgfpathlineto{\pgfqpoint{2.069189in}{0.974589in}}%
+\pgfpathlineto{\pgfqpoint{2.100468in}{0.993304in}}%
+\pgfpathlineto{\pgfqpoint{2.131748in}{1.012421in}}%
+\pgfpathlineto{\pgfqpoint{2.163027in}{1.031941in}}%
+\pgfpathlineto{\pgfqpoint{2.194307in}{1.051864in}}%
+\pgfpathlineto{\pgfqpoint{2.225586in}{1.072189in}}%
+\pgfpathlineto{\pgfqpoint{2.256866in}{1.092917in}}%
+\pgfpathlineto{\pgfqpoint{2.288145in}{1.114047in}}%
+\pgfpathlineto{\pgfqpoint{2.319425in}{1.135579in}}%
+\pgfpathlineto{\pgfqpoint{2.350704in}{1.157514in}}%
+\pgfpathlineto{\pgfqpoint{2.381984in}{1.179851in}}%
+\pgfpathlineto{\pgfqpoint{2.413263in}{1.202591in}}%
+\pgfpathlineto{\pgfqpoint{2.444543in}{1.225734in}}%
+\pgfpathlineto{\pgfqpoint{2.475823in}{1.249279in}}%
+\pgfpathlineto{\pgfqpoint{2.507102in}{1.273226in}}%
+\pgfpathlineto{\pgfqpoint{2.538382in}{1.297576in}}%
+\pgfpathlineto{\pgfqpoint{2.569661in}{1.322328in}}%
+\pgfpathlineto{\pgfqpoint{2.600941in}{1.347483in}}%
+\pgfpathlineto{\pgfqpoint{2.632220in}{1.373040in}}%
+\pgfpathlineto{\pgfqpoint{2.663500in}{1.399000in}}%
+\pgfpathlineto{\pgfqpoint{2.694779in}{1.425362in}}%
+\pgfpathlineto{\pgfqpoint{2.726059in}{1.452126in}}%
+\pgfpathlineto{\pgfqpoint{2.757338in}{1.479294in}}%
+\pgfpathlineto{\pgfqpoint{2.788618in}{1.506863in}}%
+\pgfpathlineto{\pgfqpoint{2.819897in}{1.534835in}}%
+\pgfpathlineto{\pgfqpoint{2.851177in}{1.563210in}}%
+\pgfpathlineto{\pgfqpoint{2.882457in}{1.591987in}}%
+\pgfpathlineto{\pgfqpoint{2.913736in}{1.621166in}}%
+\pgfpathlineto{\pgfqpoint{2.945016in}{1.650748in}}%
+\pgfpathlineto{\pgfqpoint{2.976295in}{1.680733in}}%
+\pgfpathlineto{\pgfqpoint{3.007575in}{1.711120in}}%
+\pgfpathlineto{\pgfqpoint{3.038854in}{1.741909in}}%
+\pgfpathlineto{\pgfqpoint{3.070134in}{1.773101in}}%
+\pgfpathlineto{\pgfqpoint{3.101413in}{1.804696in}}%
+\pgfpathlineto{\pgfqpoint{3.132693in}{1.836692in}}%
+\pgfpathlineto{\pgfqpoint{3.163972in}{1.869092in}}%
+\pgfpathlineto{\pgfqpoint{3.195252in}{1.901894in}}%
+\pgfpathlineto{\pgfqpoint{3.226531in}{1.935098in}}%
+\pgfpathlineto{\pgfqpoint{3.257811in}{1.968705in}}%
+\pgfpathlineto{\pgfqpoint{3.289091in}{2.002714in}}%
+\pgfpathlineto{\pgfqpoint{3.320370in}{2.037126in}}%
+\pgfpathlineto{\pgfqpoint{3.351650in}{2.071940in}}%
+\pgfpathlineto{\pgfqpoint{3.382929in}{2.107156in}}%
+\pgfpathlineto{\pgfqpoint{3.414209in}{2.142776in}}%
+\pgfpathlineto{\pgfqpoint{3.445488in}{2.178797in}}%
+\pgfpathlineto{\pgfqpoint{3.476768in}{2.215221in}}%
+\pgfpathlineto{\pgfqpoint{3.508047in}{2.252048in}}%
+\pgfpathlineto{\pgfqpoint{3.539327in}{2.289277in}}%
+\pgfpathlineto{\pgfqpoint{3.561409in}{2.315844in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.630330in}{0.548769in}}{\pgfqpoint{3.096674in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{1.505625pt}%
+\definecolor{currentstroke}{rgb}{1.000000,0.498039,0.054902}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.630330in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{0.661609in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{0.692889in}{0.548770in}}%
+\pgfpathlineto{\pgfqpoint{0.724168in}{0.548773in}}%
+\pgfpathlineto{\pgfqpoint{0.755448in}{0.548781in}}%
+\pgfpathlineto{\pgfqpoint{0.786727in}{0.548798in}}%
+\pgfpathlineto{\pgfqpoint{0.818007in}{0.548829in}}%
+\pgfpathlineto{\pgfqpoint{0.849287in}{0.548880in}}%
+\pgfpathlineto{\pgfqpoint{0.880566in}{0.548958in}}%
+\pgfpathlineto{\pgfqpoint{0.911846in}{0.549072in}}%
+\pgfpathlineto{\pgfqpoint{0.943125in}{0.549231in}}%
+\pgfpathlineto{\pgfqpoint{0.974405in}{0.549445in}}%
+\pgfpathlineto{\pgfqpoint{1.005684in}{0.549727in}}%
+\pgfpathlineto{\pgfqpoint{1.036964in}{0.550088in}}%
+\pgfpathlineto{\pgfqpoint{1.068243in}{0.550544in}}%
+\pgfpathlineto{\pgfqpoint{1.099523in}{0.551108in}}%
+\pgfpathlineto{\pgfqpoint{1.130802in}{0.551796in}}%
+\pgfpathlineto{\pgfqpoint{1.162082in}{0.552627in}}%
+\pgfpathlineto{\pgfqpoint{1.193361in}{0.553618in}}%
+\pgfpathlineto{\pgfqpoint{1.224641in}{0.554789in}}%
+\pgfpathlineto{\pgfqpoint{1.255921in}{0.556160in}}%
+\pgfpathlineto{\pgfqpoint{1.287200in}{0.557753in}}%
+\pgfpathlineto{\pgfqpoint{1.318480in}{0.559591in}}%
+\pgfpathlineto{\pgfqpoint{1.349759in}{0.561697in}}%
+\pgfpathlineto{\pgfqpoint{1.381039in}{0.564096in}}%
+\pgfpathlineto{\pgfqpoint{1.412318in}{0.566815in}}%
+\pgfpathlineto{\pgfqpoint{1.443598in}{0.569880in}}%
+\pgfpathlineto{\pgfqpoint{1.474877in}{0.573320in}}%
+\pgfpathlineto{\pgfqpoint{1.506157in}{0.577165in}}%
+\pgfpathlineto{\pgfqpoint{1.537436in}{0.581444in}}%
+\pgfpathlineto{\pgfqpoint{1.568716in}{0.586189in}}%
+\pgfpathlineto{\pgfqpoint{1.599995in}{0.591434in}}%
+\pgfpathlineto{\pgfqpoint{1.631275in}{0.597211in}}%
+\pgfpathlineto{\pgfqpoint{1.662555in}{0.603556in}}%
+\pgfpathlineto{\pgfqpoint{1.693834in}{0.610505in}}%
+\pgfpathlineto{\pgfqpoint{1.725114in}{0.618095in}}%
+\pgfpathlineto{\pgfqpoint{1.756393in}{0.626364in}}%
+\pgfpathlineto{\pgfqpoint{1.787673in}{0.635351in}}%
+\pgfpathlineto{\pgfqpoint{1.818952in}{0.645098in}}%
+\pgfpathlineto{\pgfqpoint{1.850232in}{0.655645in}}%
+\pgfpathlineto{\pgfqpoint{1.881511in}{0.667035in}}%
+\pgfpathlineto{\pgfqpoint{1.912791in}{0.679313in}}%
+\pgfpathlineto{\pgfqpoint{1.944070in}{0.692523in}}%
+\pgfpathlineto{\pgfqpoint{1.975350in}{0.706710in}}%
+\pgfpathlineto{\pgfqpoint{2.006629in}{0.721923in}}%
+\pgfpathlineto{\pgfqpoint{2.037909in}{0.738209in}}%
+\pgfpathlineto{\pgfqpoint{2.069189in}{0.755618in}}%
+\pgfpathlineto{\pgfqpoint{2.100468in}{0.774200in}}%
+\pgfpathlineto{\pgfqpoint{2.131748in}{0.794006in}}%
+\pgfpathlineto{\pgfqpoint{2.163027in}{0.815091in}}%
+\pgfpathlineto{\pgfqpoint{2.194307in}{0.837506in}}%
+\pgfpathlineto{\pgfqpoint{2.225586in}{0.861307in}}%
+\pgfpathlineto{\pgfqpoint{2.256866in}{0.886550in}}%
+\pgfpathlineto{\pgfqpoint{2.288145in}{0.913292in}}%
+\pgfpathlineto{\pgfqpoint{2.319425in}{0.941592in}}%
+\pgfpathlineto{\pgfqpoint{2.350704in}{0.971508in}}%
+\pgfpathlineto{\pgfqpoint{2.381984in}{1.003102in}}%
+\pgfpathlineto{\pgfqpoint{2.413263in}{1.036434in}}%
+\pgfpathlineto{\pgfqpoint{2.444543in}{1.071567in}}%
+\pgfpathlineto{\pgfqpoint{2.475823in}{1.108565in}}%
+\pgfpathlineto{\pgfqpoint{2.507102in}{1.147494in}}%
+\pgfpathlineto{\pgfqpoint{2.538382in}{1.188418in}}%
+\pgfpathlineto{\pgfqpoint{2.569661in}{1.231405in}}%
+\pgfpathlineto{\pgfqpoint{2.600941in}{1.276523in}}%
+\pgfpathlineto{\pgfqpoint{2.632220in}{1.323841in}}%
+\pgfpathlineto{\pgfqpoint{2.663500in}{1.373430in}}%
+\pgfpathlineto{\pgfqpoint{2.694779in}{1.425362in}}%
+\pgfpathlineto{\pgfqpoint{2.726059in}{1.479708in}}%
+\pgfpathlineto{\pgfqpoint{2.757338in}{1.536544in}}%
+\pgfpathlineto{\pgfqpoint{2.788618in}{1.595942in}}%
+\pgfpathlineto{\pgfqpoint{2.819897in}{1.657980in}}%
+\pgfpathlineto{\pgfqpoint{2.851177in}{1.722735in}}%
+\pgfpathlineto{\pgfqpoint{2.882457in}{1.790285in}}%
+\pgfpathlineto{\pgfqpoint{2.913736in}{1.860708in}}%
+\pgfpathlineto{\pgfqpoint{2.945016in}{1.934086in}}%
+\pgfpathlineto{\pgfqpoint{2.976295in}{2.010499in}}%
+\pgfpathlineto{\pgfqpoint{3.007575in}{2.090031in}}%
+\pgfpathlineto{\pgfqpoint{3.038854in}{2.172766in}}%
+\pgfpathlineto{\pgfqpoint{3.070134in}{2.258787in}}%
+\pgfpathlineto{\pgfqpoint{3.090098in}{2.315844in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.630330in}{0.548769in}}{\pgfqpoint{3.096674in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{1.505625pt}%
+\definecolor{currentstroke}{rgb}{0.172549,0.627451,0.172549}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.630330in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{0.661609in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{0.692889in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{0.724168in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{0.755448in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{0.786727in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{0.818007in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{0.849287in}{0.548770in}}%
+\pgfpathlineto{\pgfqpoint{0.880566in}{0.548772in}}%
+\pgfpathlineto{\pgfqpoint{0.911846in}{0.548774in}}%
+\pgfpathlineto{\pgfqpoint{0.943125in}{0.548779in}}%
+\pgfpathlineto{\pgfqpoint{0.974405in}{0.548788in}}%
+\pgfpathlineto{\pgfqpoint{1.005684in}{0.548800in}}%
+\pgfpathlineto{\pgfqpoint{1.036964in}{0.548820in}}%
+\pgfpathlineto{\pgfqpoint{1.068243in}{0.548849in}}%
+\pgfpathlineto{\pgfqpoint{1.099523in}{0.548890in}}%
+\pgfpathlineto{\pgfqpoint{1.130802in}{0.548947in}}%
+\pgfpathlineto{\pgfqpoint{1.162082in}{0.549025in}}%
+\pgfpathlineto{\pgfqpoint{1.193361in}{0.549130in}}%
+\pgfpathlineto{\pgfqpoint{1.224641in}{0.549268in}}%
+\pgfpathlineto{\pgfqpoint{1.255921in}{0.549448in}}%
+\pgfpathlineto{\pgfqpoint{1.287200in}{0.549678in}}%
+\pgfpathlineto{\pgfqpoint{1.318480in}{0.549971in}}%
+\pgfpathlineto{\pgfqpoint{1.349759in}{0.550339in}}%
+\pgfpathlineto{\pgfqpoint{1.381039in}{0.550796in}}%
+\pgfpathlineto{\pgfqpoint{1.412318in}{0.551358in}}%
+\pgfpathlineto{\pgfqpoint{1.443598in}{0.552045in}}%
+\pgfpathlineto{\pgfqpoint{1.474877in}{0.552878in}}%
+\pgfpathlineto{\pgfqpoint{1.506157in}{0.553880in}}%
+\pgfpathlineto{\pgfqpoint{1.537436in}{0.555077in}}%
+\pgfpathlineto{\pgfqpoint{1.568716in}{0.556500in}}%
+\pgfpathlineto{\pgfqpoint{1.599995in}{0.558181in}}%
+\pgfpathlineto{\pgfqpoint{1.631275in}{0.560156in}}%
+\pgfpathlineto{\pgfqpoint{1.662555in}{0.562466in}}%
+\pgfpathlineto{\pgfqpoint{1.693834in}{0.565152in}}%
+\pgfpathlineto{\pgfqpoint{1.725114in}{0.568265in}}%
+\pgfpathlineto{\pgfqpoint{1.756393in}{0.571855in}}%
+\pgfpathlineto{\pgfqpoint{1.787673in}{0.575980in}}%
+\pgfpathlineto{\pgfqpoint{1.818952in}{0.580702in}}%
+\pgfpathlineto{\pgfqpoint{1.850232in}{0.586087in}}%
+\pgfpathlineto{\pgfqpoint{1.881511in}{0.592209in}}%
+\pgfpathlineto{\pgfqpoint{1.912791in}{0.599146in}}%
+\pgfpathlineto{\pgfqpoint{1.944070in}{0.606983in}}%
+\pgfpathlineto{\pgfqpoint{1.975350in}{0.615811in}}%
+\pgfpathlineto{\pgfqpoint{2.006629in}{0.625726in}}%
+\pgfpathlineto{\pgfqpoint{2.037909in}{0.636835in}}%
+\pgfpathlineto{\pgfqpoint{2.069189in}{0.649249in}}%
+\pgfpathlineto{\pgfqpoint{2.100468in}{0.663089in}}%
+\pgfpathlineto{\pgfqpoint{2.131748in}{0.678481in}}%
+\pgfpathlineto{\pgfqpoint{2.163027in}{0.695564in}}%
+\pgfpathlineto{\pgfqpoint{2.194307in}{0.714481in}}%
+\pgfpathlineto{\pgfqpoint{2.225586in}{0.735388in}}%
+\pgfpathlineto{\pgfqpoint{2.256866in}{0.758448in}}%
+\pgfpathlineto{\pgfqpoint{2.288145in}{0.783835in}}%
+\pgfpathlineto{\pgfqpoint{2.319425in}{0.811733in}}%
+\pgfpathlineto{\pgfqpoint{2.350704in}{0.842338in}}%
+\pgfpathlineto{\pgfqpoint{2.381984in}{0.875855in}}%
+\pgfpathlineto{\pgfqpoint{2.413263in}{0.912502in}}%
+\pgfpathlineto{\pgfqpoint{2.444543in}{0.952509in}}%
+\pgfpathlineto{\pgfqpoint{2.475823in}{0.996118in}}%
+\pgfpathlineto{\pgfqpoint{2.507102in}{1.043583in}}%
+\pgfpathlineto{\pgfqpoint{2.538382in}{1.095172in}}%
+\pgfpathlineto{\pgfqpoint{2.569661in}{1.151168in}}%
+\pgfpathlineto{\pgfqpoint{2.600941in}{1.211867in}}%
+\pgfpathlineto{\pgfqpoint{2.632220in}{1.277579in}}%
+\pgfpathlineto{\pgfqpoint{2.663500in}{1.348630in}}%
+\pgfpathlineto{\pgfqpoint{2.694779in}{1.425362in}}%
+\pgfpathlineto{\pgfqpoint{2.726059in}{1.508132in}}%
+\pgfpathlineto{\pgfqpoint{2.757338in}{1.597316in}}%
+\pgfpathlineto{\pgfqpoint{2.788618in}{1.693303in}}%
+\pgfpathlineto{\pgfqpoint{2.819897in}{1.796505in}}%
+\pgfpathlineto{\pgfqpoint{2.851177in}{1.907347in}}%
+\pgfpathlineto{\pgfqpoint{2.882457in}{2.026275in}}%
+\pgfpathlineto{\pgfqpoint{2.913736in}{2.153756in}}%
+\pgfpathlineto{\pgfqpoint{2.945016in}{2.290274in}}%
+\pgfpathlineto{\pgfqpoint{2.950492in}{2.315844in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.630330in}{0.548769in}}{\pgfqpoint{3.096674in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{1.505625pt}%
+\definecolor{currentstroke}{rgb}{0.839216,0.152941,0.156863}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.630330in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{0.661609in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{0.692889in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{0.724168in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{0.755448in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{0.786727in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{0.818007in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{0.849287in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{0.880566in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{0.911846in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{0.943125in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{0.974405in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{1.005684in}{0.548770in}}%
+\pgfpathlineto{\pgfqpoint{1.036964in}{0.548771in}}%
+\pgfpathlineto{\pgfqpoint{1.068243in}{0.548772in}}%
+\pgfpathlineto{\pgfqpoint{1.099523in}{0.548775in}}%
+\pgfpathlineto{\pgfqpoint{1.130802in}{0.548779in}}%
+\pgfpathlineto{\pgfqpoint{1.162082in}{0.548786in}}%
+\pgfpathlineto{\pgfqpoint{1.193361in}{0.548796in}}%
+\pgfpathlineto{\pgfqpoint{1.224641in}{0.548810in}}%
+\pgfpathlineto{\pgfqpoint{1.255921in}{0.548831in}}%
+\pgfpathlineto{\pgfqpoint{1.287200in}{0.548861in}}%
+\pgfpathlineto{\pgfqpoint{1.318480in}{0.548902in}}%
+\pgfpathlineto{\pgfqpoint{1.349759in}{0.548959in}}%
+\pgfpathlineto{\pgfqpoint{1.381039in}{0.549037in}}%
+\pgfpathlineto{\pgfqpoint{1.412318in}{0.549140in}}%
+\pgfpathlineto{\pgfqpoint{1.443598in}{0.549277in}}%
+\pgfpathlineto{\pgfqpoint{1.474877in}{0.549456in}}%
+\pgfpathlineto{\pgfqpoint{1.506157in}{0.549689in}}%
+\pgfpathlineto{\pgfqpoint{1.537436in}{0.549987in}}%
+\pgfpathlineto{\pgfqpoint{1.568716in}{0.550366in}}%
+\pgfpathlineto{\pgfqpoint{1.599995in}{0.550845in}}%
+\pgfpathlineto{\pgfqpoint{1.631275in}{0.551446in}}%
+\pgfpathlineto{\pgfqpoint{1.662555in}{0.552193in}}%
+\pgfpathlineto{\pgfqpoint{1.693834in}{0.553117in}}%
+\pgfpathlineto{\pgfqpoint{1.725114in}{0.554251in}}%
+\pgfpathlineto{\pgfqpoint{1.756393in}{0.555637in}}%
+\pgfpathlineto{\pgfqpoint{1.787673in}{0.557321in}}%
+\pgfpathlineto{\pgfqpoint{1.818952in}{0.559354in}}%
+\pgfpathlineto{\pgfqpoint{1.850232in}{0.561799in}}%
+\pgfpathlineto{\pgfqpoint{1.881511in}{0.564725in}}%
+\pgfpathlineto{\pgfqpoint{1.912791in}{0.568210in}}%
+\pgfpathlineto{\pgfqpoint{1.944070in}{0.572343in}}%
+\pgfpathlineto{\pgfqpoint{1.975350in}{0.577226in}}%
+\pgfpathlineto{\pgfqpoint{2.006629in}{0.582972in}}%
+\pgfpathlineto{\pgfqpoint{2.037909in}{0.589709in}}%
+\pgfpathlineto{\pgfqpoint{2.069189in}{0.597579in}}%
+\pgfpathlineto{\pgfqpoint{2.100468in}{0.606742in}}%
+\pgfpathlineto{\pgfqpoint{2.131748in}{0.617377in}}%
+\pgfpathlineto{\pgfqpoint{2.163027in}{0.629681in}}%
+\pgfpathlineto{\pgfqpoint{2.194307in}{0.643875in}}%
+\pgfpathlineto{\pgfqpoint{2.225586in}{0.660200in}}%
+\pgfpathlineto{\pgfqpoint{2.256866in}{0.678928in}}%
+\pgfpathlineto{\pgfqpoint{2.288145in}{0.700353in}}%
+\pgfpathlineto{\pgfqpoint{2.319425in}{0.724803in}}%
+\pgfpathlineto{\pgfqpoint{2.350704in}{0.752636in}}%
+\pgfpathlineto{\pgfqpoint{2.381984in}{0.784247in}}%
+\pgfpathlineto{\pgfqpoint{2.413263in}{0.820066in}}%
+\pgfpathlineto{\pgfqpoint{2.444543in}{0.860565in}}%
+\pgfpathlineto{\pgfqpoint{2.475823in}{0.906258in}}%
+\pgfpathlineto{\pgfqpoint{2.507102in}{0.957706in}}%
+\pgfpathlineto{\pgfqpoint{2.538382in}{1.015520in}}%
+\pgfpathlineto{\pgfqpoint{2.569661in}{1.080363in}}%
+\pgfpathlineto{\pgfqpoint{2.600941in}{1.152955in}}%
+\pgfpathlineto{\pgfqpoint{2.632220in}{1.234078in}}%
+\pgfpathlineto{\pgfqpoint{2.663500in}{1.324575in}}%
+\pgfpathlineto{\pgfqpoint{2.694779in}{1.425362in}}%
+\pgfpathlineto{\pgfqpoint{2.726059in}{1.537424in}}%
+\pgfpathlineto{\pgfqpoint{2.757338in}{1.661827in}}%
+\pgfpathlineto{\pgfqpoint{2.788618in}{1.799717in}}%
+\pgfpathlineto{\pgfqpoint{2.819897in}{1.952328in}}%
+\pgfpathlineto{\pgfqpoint{2.851177in}{2.120989in}}%
+\pgfpathlineto{\pgfqpoint{2.882457in}{2.307124in}}%
+\pgfpathlineto{\pgfqpoint{2.883786in}{2.315844in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetmiterjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.630330in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{0.630330in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetmiterjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{3.727004in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{3.727004in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetmiterjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.630330in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{3.727004in}{0.548769in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetmiterjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.630330in}{2.301955in}}%
+\pgfpathlineto{\pgfqpoint{3.727004in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetmiterjoin%
+\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetfillopacity{0.800000}%
+\pgfsetlinewidth{1.003750pt}%
+\definecolor{currentstroke}{rgb}{0.800000,0.800000,0.800000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetstrokeopacity{0.800000}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.727552in}{1.416153in}}%
+\pgfpathlineto{\pgfqpoint{1.553360in}{1.416153in}}%
+\pgfpathquadraticcurveto{\pgfqpoint{1.581138in}{1.416153in}}{\pgfqpoint{1.581138in}{1.443930in}}%
+\pgfpathlineto{\pgfqpoint{1.581138in}{2.204733in}}%
+\pgfpathquadraticcurveto{\pgfqpoint{1.581138in}{2.232510in}}{\pgfqpoint{1.553360in}{2.232510in}}%
+\pgfpathlineto{\pgfqpoint{0.727552in}{2.232510in}}%
+\pgfpathquadraticcurveto{\pgfqpoint{0.699774in}{2.232510in}}{\pgfqpoint{0.699774in}{2.204733in}}%
+\pgfpathlineto{\pgfqpoint{0.699774in}{1.443930in}}%
+\pgfpathquadraticcurveto{\pgfqpoint{0.699774in}{1.416153in}}{\pgfqpoint{0.727552in}{1.416153in}}%
+\pgfpathlineto{\pgfqpoint{0.727552in}{1.416153in}}%
+\pgfpathclose%
+\pgfusepath{stroke,fill}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{1.505625pt}%
+\definecolor{currentstroke}{rgb}{0.121569,0.466667,0.705882}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.755330in}{2.128344in}}%
+\pgfpathlineto{\pgfqpoint{0.894219in}{2.128344in}}%
+\pgfpathlineto{\pgfqpoint{1.033108in}{2.128344in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=1.144219in,y=2.079733in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle N=1\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{1.505625pt}%
+\definecolor{currentstroke}{rgb}{1.000000,0.498039,0.054902}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.755330in}{1.934671in}}%
+\pgfpathlineto{\pgfqpoint{0.894219in}{1.934671in}}%
+\pgfpathlineto{\pgfqpoint{1.033108in}{1.934671in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=1.144219in,y=1.886060in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle N=2\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{1.505625pt}%
+\definecolor{currentstroke}{rgb}{0.172549,0.627451,0.172549}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.755330in}{1.740998in}}%
+\pgfpathlineto{\pgfqpoint{0.894219in}{1.740998in}}%
+\pgfpathlineto{\pgfqpoint{1.033108in}{1.740998in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=1.144219in,y=1.692387in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle N=3\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{1.505625pt}%
+\definecolor{currentstroke}{rgb}{0.839216,0.152941,0.156863}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.755330in}{1.547325in}}%
+\pgfpathlineto{\pgfqpoint{0.894219in}{1.547325in}}%
+\pgfpathlineto{\pgfqpoint{1.033108in}{1.547325in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=1.144219in,y=1.498714in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle N=4\)}%
+\end{pgfscope}%
+\end{pgfpicture}%
+\makeatother%
+\endgroup%
diff --git a/buch/papers/ellfilter/python/F_N_chebychev.pgf b/buch/papers/ellfilter/python/F_N_chebychev.pgf
new file mode 100644
index 0000000..72d5834
--- /dev/null
+++ b/buch/papers/ellfilter/python/F_N_chebychev.pgf
@@ -0,0 +1,1066 @@
+%% Creator: Matplotlib, PGF backend
+%%
+%% To include the figure in your LaTeX document, write
+%% \input{<filename>.pgf}
+%%
+%% Make sure the required packages are loaded in your preamble
+%% \usepackage{pgf}
+%%
+%% Also ensure that all the required font packages are loaded; for instance,
+%% the lmodern package is sometimes necessary when using math font.
+%% \usepackage{lmodern}
+%%
+%% Figures using additional raster images can only be included by \input if
+%% they are in the same directory as the main LaTeX file. For loading figures
+%% from other directories you can use the `import` package
+%% \usepackage{import}
+%%
+%% and then include the figures with
+%% \import{<path to file>}{<filename>.pgf}
+%%
+%% Matplotlib used the following preamble
+%%
+\begingroup%
+\makeatletter%
+\begin{pgfpicture}%
+\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{4.000000in}{2.500000in}}%
+\pgfusepath{use as bounding box, clip}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetmiterjoin%
+\pgfsetlinewidth{0.000000pt}%
+\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetstrokeopacity{0.000000}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{4.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{4.000000in}{2.500000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{2.500000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathclose%
+\pgfusepath{}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetmiterjoin%
+\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.000000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetstrokeopacity{0.000000}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.630330in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{3.727004in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{3.727004in}{2.301955in}}%
+\pgfpathlineto{\pgfqpoint{0.630330in}{2.301955in}}%
+\pgfpathlineto{\pgfqpoint{0.630330in}{0.548769in}}%
+\pgfpathclose%
+\pgfusepath{fill}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.630330in}{0.548769in}}{\pgfqpoint{3.096674in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetbuttcap%
+\pgfsetmiterjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.501961,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetfillopacity{0.200000}%
+\pgfsetlinewidth{0.000000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetstrokeopacity{0.200000}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.630330in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{2.694779in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{2.694779in}{1.425362in}}%
+\pgfpathlineto{\pgfqpoint{0.630330in}{1.425362in}}%
+\pgfpathlineto{\pgfqpoint{0.630330in}{0.548769in}}%
+\pgfpathclose%
+\pgfusepath{fill}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.630330in}{0.548769in}}{\pgfqpoint{3.096674in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetbuttcap%
+\pgfsetmiterjoin%
+\definecolor{currentfill}{rgb}{1.000000,0.647059,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetfillopacity{0.200000}%
+\pgfsetlinewidth{0.000000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetstrokeopacity{0.200000}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{2.694779in}{1.425362in}}%
+\pgfpathlineto{\pgfqpoint{3.727004in}{1.425362in}}%
+\pgfpathlineto{\pgfqpoint{3.727004in}{2.301955in}}%
+\pgfpathlineto{\pgfqpoint{2.694779in}{2.301955in}}%
+\pgfpathlineto{\pgfqpoint{2.694779in}{1.425362in}}%
+\pgfpathclose%
+\pgfusepath{fill}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.630330in}{0.548769in}}{\pgfqpoint{3.096674in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.630330in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{0.630330in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{0.630330in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.630330in,y=0.451547in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.00}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.630330in}{0.548769in}}{\pgfqpoint{3.096674in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{1.146442in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{1.146442in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{1.146442in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=1.146442in,y=0.451547in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.25}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.630330in}{0.548769in}}{\pgfqpoint{3.096674in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{1.662555in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{1.662555in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{1.662555in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=1.662555in,y=0.451547in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.50}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.630330in}{0.548769in}}{\pgfqpoint{3.096674in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{2.178667in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{2.178667in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{2.178667in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=2.178667in,y=0.451547in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.75}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.630330in}{0.548769in}}{\pgfqpoint{3.096674in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{2.694779in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{2.694779in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{2.694779in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=2.694779in,y=0.451547in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {1.00}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.630330in}{0.548769in}}{\pgfqpoint{3.096674in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{3.210892in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{3.210892in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{3.210892in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=3.210892in,y=0.451547in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {1.25}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.630330in}{0.548769in}}{\pgfqpoint{3.096674in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{3.727004in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{3.727004in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{3.727004in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=3.727004in,y=0.451547in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {1.50}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=2.178667in,y=0.272534in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle w\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.630330in}{0.548769in}}{\pgfqpoint{3.096674in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.630330in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{3.727004in}{0.548769in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{0.630330in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.355638in, y=0.500544in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.0}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.630330in}{0.548769in}}{\pgfqpoint{3.096674in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.630330in}{0.987065in}}%
+\pgfpathlineto{\pgfqpoint{3.727004in}{0.987065in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{0.630330in}{0.987065in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.355638in, y=0.938840in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.5}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.630330in}{0.548769in}}{\pgfqpoint{3.096674in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.630330in}{1.425362in}}%
+\pgfpathlineto{\pgfqpoint{3.727004in}{1.425362in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{0.630330in}{1.425362in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.355638in, y=1.377137in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {1.0}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.630330in}{0.548769in}}{\pgfqpoint{3.096674in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.630330in}{1.863658in}}%
+\pgfpathlineto{\pgfqpoint{3.727004in}{1.863658in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{0.630330in}{1.863658in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.355638in, y=1.815433in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {1.5}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.630330in}{0.548769in}}{\pgfqpoint{3.096674in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.630330in}{2.301955in}}%
+\pgfpathlineto{\pgfqpoint{3.727004in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{0.630330in}{2.301955in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.355638in, y=2.253730in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {2.0}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.300082in,y=1.425362in,,bottom,rotate=90.000000]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle F^2_N(w)\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.630330in}{0.548769in}}{\pgfqpoint{3.096674in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{1.505625pt}%
+\definecolor{currentstroke}{rgb}{0.121569,0.466667,0.705882}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.630330in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{0.661609in}{0.548970in}}%
+\pgfpathlineto{\pgfqpoint{0.692889in}{0.549574in}}%
+\pgfpathlineto{\pgfqpoint{0.724168in}{0.550580in}}%
+\pgfpathlineto{\pgfqpoint{0.755448in}{0.551989in}}%
+\pgfpathlineto{\pgfqpoint{0.786727in}{0.553800in}}%
+\pgfpathlineto{\pgfqpoint{0.818007in}{0.556013in}}%
+\pgfpathlineto{\pgfqpoint{0.849287in}{0.558629in}}%
+\pgfpathlineto{\pgfqpoint{0.880566in}{0.561648in}}%
+\pgfpathlineto{\pgfqpoint{0.911846in}{0.565069in}}%
+\pgfpathlineto{\pgfqpoint{0.943125in}{0.568893in}}%
+\pgfpathlineto{\pgfqpoint{0.974405in}{0.573119in}}%
+\pgfpathlineto{\pgfqpoint{1.005684in}{0.577747in}}%
+\pgfpathlineto{\pgfqpoint{1.036964in}{0.582778in}}%
+\pgfpathlineto{\pgfqpoint{1.068243in}{0.588211in}}%
+\pgfpathlineto{\pgfqpoint{1.099523in}{0.594047in}}%
+\pgfpathlineto{\pgfqpoint{1.130802in}{0.600286in}}%
+\pgfpathlineto{\pgfqpoint{1.162082in}{0.606927in}}%
+\pgfpathlineto{\pgfqpoint{1.193361in}{0.613970in}}%
+\pgfpathlineto{\pgfqpoint{1.224641in}{0.621416in}}%
+\pgfpathlineto{\pgfqpoint{1.255921in}{0.629264in}}%
+\pgfpathlineto{\pgfqpoint{1.287200in}{0.637515in}}%
+\pgfpathlineto{\pgfqpoint{1.318480in}{0.646168in}}%
+\pgfpathlineto{\pgfqpoint{1.349759in}{0.655224in}}%
+\pgfpathlineto{\pgfqpoint{1.381039in}{0.664682in}}%
+\pgfpathlineto{\pgfqpoint{1.412318in}{0.674543in}}%
+\pgfpathlineto{\pgfqpoint{1.443598in}{0.684806in}}%
+\pgfpathlineto{\pgfqpoint{1.474877in}{0.695471in}}%
+\pgfpathlineto{\pgfqpoint{1.506157in}{0.706539in}}%
+\pgfpathlineto{\pgfqpoint{1.537436in}{0.718010in}}%
+\pgfpathlineto{\pgfqpoint{1.568716in}{0.729883in}}%
+\pgfpathlineto{\pgfqpoint{1.599995in}{0.742159in}}%
+\pgfpathlineto{\pgfqpoint{1.631275in}{0.754837in}}%
+\pgfpathlineto{\pgfqpoint{1.662555in}{0.767917in}}%
+\pgfpathlineto{\pgfqpoint{1.693834in}{0.781400in}}%
+\pgfpathlineto{\pgfqpoint{1.725114in}{0.795285in}}%
+\pgfpathlineto{\pgfqpoint{1.756393in}{0.809573in}}%
+\pgfpathlineto{\pgfqpoint{1.787673in}{0.824264in}}%
+\pgfpathlineto{\pgfqpoint{1.818952in}{0.839357in}}%
+\pgfpathlineto{\pgfqpoint{1.850232in}{0.854852in}}%
+\pgfpathlineto{\pgfqpoint{1.881511in}{0.870750in}}%
+\pgfpathlineto{\pgfqpoint{1.912791in}{0.887050in}}%
+\pgfpathlineto{\pgfqpoint{1.944070in}{0.903753in}}%
+\pgfpathlineto{\pgfqpoint{1.975350in}{0.920858in}}%
+\pgfpathlineto{\pgfqpoint{2.006629in}{0.938366in}}%
+\pgfpathlineto{\pgfqpoint{2.037909in}{0.956276in}}%
+\pgfpathlineto{\pgfqpoint{2.069189in}{0.974589in}}%
+\pgfpathlineto{\pgfqpoint{2.100468in}{0.993304in}}%
+\pgfpathlineto{\pgfqpoint{2.131748in}{1.012421in}}%
+\pgfpathlineto{\pgfqpoint{2.163027in}{1.031941in}}%
+\pgfpathlineto{\pgfqpoint{2.194307in}{1.051864in}}%
+\pgfpathlineto{\pgfqpoint{2.225586in}{1.072189in}}%
+\pgfpathlineto{\pgfqpoint{2.256866in}{1.092917in}}%
+\pgfpathlineto{\pgfqpoint{2.288145in}{1.114047in}}%
+\pgfpathlineto{\pgfqpoint{2.319425in}{1.135579in}}%
+\pgfpathlineto{\pgfqpoint{2.350704in}{1.157514in}}%
+\pgfpathlineto{\pgfqpoint{2.381984in}{1.179851in}}%
+\pgfpathlineto{\pgfqpoint{2.413263in}{1.202591in}}%
+\pgfpathlineto{\pgfqpoint{2.444543in}{1.225734in}}%
+\pgfpathlineto{\pgfqpoint{2.475823in}{1.249279in}}%
+\pgfpathlineto{\pgfqpoint{2.507102in}{1.273226in}}%
+\pgfpathlineto{\pgfqpoint{2.538382in}{1.297576in}}%
+\pgfpathlineto{\pgfqpoint{2.569661in}{1.322328in}}%
+\pgfpathlineto{\pgfqpoint{2.600941in}{1.347483in}}%
+\pgfpathlineto{\pgfqpoint{2.632220in}{1.373040in}}%
+\pgfpathlineto{\pgfqpoint{2.663500in}{1.399000in}}%
+\pgfpathlineto{\pgfqpoint{2.694779in}{1.425362in}}%
+\pgfpathlineto{\pgfqpoint{2.726059in}{1.452126in}}%
+\pgfpathlineto{\pgfqpoint{2.757338in}{1.479294in}}%
+\pgfpathlineto{\pgfqpoint{2.788618in}{1.506863in}}%
+\pgfpathlineto{\pgfqpoint{2.819897in}{1.534835in}}%
+\pgfpathlineto{\pgfqpoint{2.851177in}{1.563210in}}%
+\pgfpathlineto{\pgfqpoint{2.882457in}{1.591987in}}%
+\pgfpathlineto{\pgfqpoint{2.913736in}{1.621166in}}%
+\pgfpathlineto{\pgfqpoint{2.945016in}{1.650748in}}%
+\pgfpathlineto{\pgfqpoint{2.976295in}{1.680733in}}%
+\pgfpathlineto{\pgfqpoint{3.007575in}{1.711120in}}%
+\pgfpathlineto{\pgfqpoint{3.038854in}{1.741909in}}%
+\pgfpathlineto{\pgfqpoint{3.070134in}{1.773101in}}%
+\pgfpathlineto{\pgfqpoint{3.101413in}{1.804696in}}%
+\pgfpathlineto{\pgfqpoint{3.132693in}{1.836692in}}%
+\pgfpathlineto{\pgfqpoint{3.163972in}{1.869092in}}%
+\pgfpathlineto{\pgfqpoint{3.195252in}{1.901894in}}%
+\pgfpathlineto{\pgfqpoint{3.226531in}{1.935098in}}%
+\pgfpathlineto{\pgfqpoint{3.257811in}{1.968705in}}%
+\pgfpathlineto{\pgfqpoint{3.289091in}{2.002714in}}%
+\pgfpathlineto{\pgfqpoint{3.320370in}{2.037126in}}%
+\pgfpathlineto{\pgfqpoint{3.351650in}{2.071940in}}%
+\pgfpathlineto{\pgfqpoint{3.382929in}{2.107156in}}%
+\pgfpathlineto{\pgfqpoint{3.414209in}{2.142776in}}%
+\pgfpathlineto{\pgfqpoint{3.445488in}{2.178797in}}%
+\pgfpathlineto{\pgfqpoint{3.476768in}{2.215221in}}%
+\pgfpathlineto{\pgfqpoint{3.508047in}{2.252048in}}%
+\pgfpathlineto{\pgfqpoint{3.539327in}{2.289277in}}%
+\pgfpathlineto{\pgfqpoint{3.561409in}{2.315844in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.630330in}{0.548769in}}{\pgfqpoint{3.096674in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{1.505625pt}%
+\definecolor{currentstroke}{rgb}{1.000000,0.498039,0.054902}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.630330in}{1.425362in}}%
+\pgfpathlineto{\pgfqpoint{0.661609in}{1.424557in}}%
+\pgfpathlineto{\pgfqpoint{0.692889in}{1.422145in}}%
+\pgfpathlineto{\pgfqpoint{0.724168in}{1.418132in}}%
+\pgfpathlineto{\pgfqpoint{0.755448in}{1.412530in}}%
+\pgfpathlineto{\pgfqpoint{0.786727in}{1.405354in}}%
+\pgfpathlineto{\pgfqpoint{0.818007in}{1.396623in}}%
+\pgfpathlineto{\pgfqpoint{0.849287in}{1.386363in}}%
+\pgfpathlineto{\pgfqpoint{0.880566in}{1.374602in}}%
+\pgfpathlineto{\pgfqpoint{0.911846in}{1.361373in}}%
+\pgfpathlineto{\pgfqpoint{0.943125in}{1.346715in}}%
+\pgfpathlineto{\pgfqpoint{0.974405in}{1.330668in}}%
+\pgfpathlineto{\pgfqpoint{1.005684in}{1.313281in}}%
+\pgfpathlineto{\pgfqpoint{1.036964in}{1.294603in}}%
+\pgfpathlineto{\pgfqpoint{1.068243in}{1.274690in}}%
+\pgfpathlineto{\pgfqpoint{1.099523in}{1.253603in}}%
+\pgfpathlineto{\pgfqpoint{1.130802in}{1.231405in}}%
+\pgfpathlineto{\pgfqpoint{1.162082in}{1.208165in}}%
+\pgfpathlineto{\pgfqpoint{1.193361in}{1.183956in}}%
+\pgfpathlineto{\pgfqpoint{1.224641in}{1.158856in}}%
+\pgfpathlineto{\pgfqpoint{1.255921in}{1.132948in}}%
+\pgfpathlineto{\pgfqpoint{1.287200in}{1.106316in}}%
+\pgfpathlineto{\pgfqpoint{1.318480in}{1.079053in}}%
+\pgfpathlineto{\pgfqpoint{1.349759in}{1.051254in}}%
+\pgfpathlineto{\pgfqpoint{1.381039in}{1.023019in}}%
+\pgfpathlineto{\pgfqpoint{1.412318in}{0.994451in}}%
+\pgfpathlineto{\pgfqpoint{1.443598in}{0.965659in}}%
+\pgfpathlineto{\pgfqpoint{1.474877in}{0.936757in}}%
+\pgfpathlineto{\pgfqpoint{1.506157in}{0.907863in}}%
+\pgfpathlineto{\pgfqpoint{1.537436in}{0.879097in}}%
+\pgfpathlineto{\pgfqpoint{1.568716in}{0.850586in}}%
+\pgfpathlineto{\pgfqpoint{1.599995in}{0.822462in}}%
+\pgfpathlineto{\pgfqpoint{1.631275in}{0.794859in}}%
+\pgfpathlineto{\pgfqpoint{1.662555in}{0.767917in}}%
+\pgfpathlineto{\pgfqpoint{1.693834in}{0.741781in}}%
+\pgfpathlineto{\pgfqpoint{1.725114in}{0.716598in}}%
+\pgfpathlineto{\pgfqpoint{1.756393in}{0.692523in}}%
+\pgfpathlineto{\pgfqpoint{1.787673in}{0.669711in}}%
+\pgfpathlineto{\pgfqpoint{1.818952in}{0.648326in}}%
+\pgfpathlineto{\pgfqpoint{1.850232in}{0.628534in}}%
+\pgfpathlineto{\pgfqpoint{1.881511in}{0.610505in}}%
+\pgfpathlineto{\pgfqpoint{1.912791in}{0.594414in}}%
+\pgfpathlineto{\pgfqpoint{1.944070in}{0.580441in}}%
+\pgfpathlineto{\pgfqpoint{1.975350in}{0.568771in}}%
+\pgfpathlineto{\pgfqpoint{2.006629in}{0.559591in}}%
+\pgfpathlineto{\pgfqpoint{2.037909in}{0.553095in}}%
+\pgfpathlineto{\pgfqpoint{2.069189in}{0.549479in}}%
+\pgfpathlineto{\pgfqpoint{2.100468in}{0.548946in}}%
+\pgfpathlineto{\pgfqpoint{2.131748in}{0.551703in}}%
+\pgfpathlineto{\pgfqpoint{2.163027in}{0.557958in}}%
+\pgfpathlineto{\pgfqpoint{2.194307in}{0.567929in}}%
+\pgfpathlineto{\pgfqpoint{2.225586in}{0.581833in}}%
+\pgfpathlineto{\pgfqpoint{2.256866in}{0.599896in}}%
+\pgfpathlineto{\pgfqpoint{2.288145in}{0.622346in}}%
+\pgfpathlineto{\pgfqpoint{2.319425in}{0.649414in}}%
+\pgfpathlineto{\pgfqpoint{2.350704in}{0.681340in}}%
+\pgfpathlineto{\pgfqpoint{2.381984in}{0.718364in}}%
+\pgfpathlineto{\pgfqpoint{2.413263in}{0.760732in}}%
+\pgfpathlineto{\pgfqpoint{2.444543in}{0.808696in}}%
+\pgfpathlineto{\pgfqpoint{2.475823in}{0.862510in}}%
+\pgfpathlineto{\pgfqpoint{2.507102in}{0.922433in}}%
+\pgfpathlineto{\pgfqpoint{2.538382in}{0.988730in}}%
+\pgfpathlineto{\pgfqpoint{2.569661in}{1.061668in}}%
+\pgfpathlineto{\pgfqpoint{2.600941in}{1.141521in}}%
+\pgfpathlineto{\pgfqpoint{2.632220in}{1.228566in}}%
+\pgfpathlineto{\pgfqpoint{2.663500in}{1.323084in}}%
+\pgfpathlineto{\pgfqpoint{2.694779in}{1.425362in}}%
+\pgfpathlineto{\pgfqpoint{2.726059in}{1.535689in}}%
+\pgfpathlineto{\pgfqpoint{2.757338in}{1.654362in}}%
+\pgfpathlineto{\pgfqpoint{2.788618in}{1.781678in}}%
+\pgfpathlineto{\pgfqpoint{2.819897in}{1.917942in}}%
+\pgfpathlineto{\pgfqpoint{2.851177in}{2.063463in}}%
+\pgfpathlineto{\pgfqpoint{2.882457in}{2.218553in}}%
+\pgfpathlineto{\pgfqpoint{2.900903in}{2.315844in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.630330in}{0.548769in}}{\pgfqpoint{3.096674in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{1.505625pt}%
+\definecolor{currentstroke}{rgb}{0.172549,0.627451,0.172549}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.630330in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{0.661609in}{0.550579in}}%
+\pgfpathlineto{\pgfqpoint{0.692889in}{0.555996in}}%
+\pgfpathlineto{\pgfqpoint{0.724168in}{0.564979in}}%
+\pgfpathlineto{\pgfqpoint{0.755448in}{0.577464in}}%
+\pgfpathlineto{\pgfqpoint{0.786727in}{0.593357in}}%
+\pgfpathlineto{\pgfqpoint{0.818007in}{0.612541in}}%
+\pgfpathlineto{\pgfqpoint{0.849287in}{0.634873in}}%
+\pgfpathlineto{\pgfqpoint{0.880566in}{0.660185in}}%
+\pgfpathlineto{\pgfqpoint{0.911846in}{0.688287in}}%
+\pgfpathlineto{\pgfqpoint{0.943125in}{0.718965in}}%
+\pgfpathlineto{\pgfqpoint{0.974405in}{0.751984in}}%
+\pgfpathlineto{\pgfqpoint{1.005684in}{0.787089in}}%
+\pgfpathlineto{\pgfqpoint{1.036964in}{0.824004in}}%
+\pgfpathlineto{\pgfqpoint{1.068243in}{0.862437in}}%
+\pgfpathlineto{\pgfqpoint{1.099523in}{0.902078in}}%
+\pgfpathlineto{\pgfqpoint{1.130802in}{0.942605in}}%
+\pgfpathlineto{\pgfqpoint{1.162082in}{0.983681in}}%
+\pgfpathlineto{\pgfqpoint{1.193361in}{1.024958in}}%
+\pgfpathlineto{\pgfqpoint{1.224641in}{1.066081in}}%
+\pgfpathlineto{\pgfqpoint{1.255921in}{1.106686in}}%
+\pgfpathlineto{\pgfqpoint{1.287200in}{1.146406in}}%
+\pgfpathlineto{\pgfqpoint{1.318480in}{1.184870in}}%
+\pgfpathlineto{\pgfqpoint{1.349759in}{1.221710in}}%
+\pgfpathlineto{\pgfqpoint{1.381039in}{1.256559in}}%
+\pgfpathlineto{\pgfqpoint{1.412318in}{1.289056in}}%
+\pgfpathlineto{\pgfqpoint{1.443598in}{1.318849in}}%
+\pgfpathlineto{\pgfqpoint{1.474877in}{1.345598in}}%
+\pgfpathlineto{\pgfqpoint{1.506157in}{1.368977in}}%
+\pgfpathlineto{\pgfqpoint{1.537436in}{1.388677in}}%
+\pgfpathlineto{\pgfqpoint{1.568716in}{1.404413in}}%
+\pgfpathlineto{\pgfqpoint{1.599995in}{1.415923in}}%
+\pgfpathlineto{\pgfqpoint{1.631275in}{1.422973in}}%
+\pgfpathlineto{\pgfqpoint{1.662555in}{1.425362in}}%
+\pgfpathlineto{\pgfqpoint{1.693834in}{1.422924in}}%
+\pgfpathlineto{\pgfqpoint{1.725114in}{1.415535in}}%
+\pgfpathlineto{\pgfqpoint{1.756393in}{1.403113in}}%
+\pgfpathlineto{\pgfqpoint{1.787673in}{1.385624in}}%
+\pgfpathlineto{\pgfqpoint{1.818952in}{1.363088in}}%
+\pgfpathlineto{\pgfqpoint{1.850232in}{1.335583in}}%
+\pgfpathlineto{\pgfqpoint{1.881511in}{1.303245in}}%
+\pgfpathlineto{\pgfqpoint{1.912791in}{1.266280in}}%
+\pgfpathlineto{\pgfqpoint{1.944070in}{1.224962in}}%
+\pgfpathlineto{\pgfqpoint{1.975350in}{1.179644in}}%
+\pgfpathlineto{\pgfqpoint{2.006629in}{1.130759in}}%
+\pgfpathlineto{\pgfqpoint{2.037909in}{1.078826in}}%
+\pgfpathlineto{\pgfqpoint{2.069189in}{1.024455in}}%
+\pgfpathlineto{\pgfqpoint{2.100468in}{0.968355in}}%
+\pgfpathlineto{\pgfqpoint{2.131748in}{0.911337in}}%
+\pgfpathlineto{\pgfqpoint{2.163027in}{0.854319in}}%
+\pgfpathlineto{\pgfqpoint{2.194307in}{0.798335in}}%
+\pgfpathlineto{\pgfqpoint{2.225586in}{0.744537in}}%
+\pgfpathlineto{\pgfqpoint{2.256866in}{0.694207in}}%
+\pgfpathlineto{\pgfqpoint{2.288145in}{0.648754in}}%
+\pgfpathlineto{\pgfqpoint{2.319425in}{0.609730in}}%
+\pgfpathlineto{\pgfqpoint{2.350704in}{0.578830in}}%
+\pgfpathlineto{\pgfqpoint{2.381984in}{0.557901in}}%
+\pgfpathlineto{\pgfqpoint{2.413263in}{0.548947in}}%
+\pgfpathlineto{\pgfqpoint{2.444543in}{0.554140in}}%
+\pgfpathlineto{\pgfqpoint{2.475823in}{0.575820in}}%
+\pgfpathlineto{\pgfqpoint{2.507102in}{0.616509in}}%
+\pgfpathlineto{\pgfqpoint{2.538382in}{0.678913in}}%
+\pgfpathlineto{\pgfqpoint{2.569661in}{0.765934in}}%
+\pgfpathlineto{\pgfqpoint{2.600941in}{0.880671in}}%
+\pgfpathlineto{\pgfqpoint{2.632220in}{1.026434in}}%
+\pgfpathlineto{\pgfqpoint{2.663500in}{1.206748in}}%
+\pgfpathlineto{\pgfqpoint{2.694779in}{1.425362in}}%
+\pgfpathlineto{\pgfqpoint{2.726059in}{1.686256in}}%
+\pgfpathlineto{\pgfqpoint{2.757338in}{1.993649in}}%
+\pgfpathlineto{\pgfqpoint{2.785461in}{2.315844in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.630330in}{0.548769in}}{\pgfqpoint{3.096674in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{1.505625pt}%
+\definecolor{currentstroke}{rgb}{0.839216,0.152941,0.156863}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.630330in}{1.425362in}}%
+\pgfpathlineto{\pgfqpoint{0.661609in}{1.422146in}}%
+\pgfpathlineto{\pgfqpoint{0.692889in}{1.412542in}}%
+\pgfpathlineto{\pgfqpoint{0.724168in}{1.396682in}}%
+\pgfpathlineto{\pgfqpoint{0.755448in}{1.374785in}}%
+\pgfpathlineto{\pgfqpoint{0.786727in}{1.347155in}}%
+\pgfpathlineto{\pgfqpoint{0.818007in}{1.314175in}}%
+\pgfpathlineto{\pgfqpoint{0.849287in}{1.276306in}}%
+\pgfpathlineto{\pgfqpoint{0.880566in}{1.234079in}}%
+\pgfpathlineto{\pgfqpoint{0.911846in}{1.188091in}}%
+\pgfpathlineto{\pgfqpoint{0.943125in}{1.138997in}}%
+\pgfpathlineto{\pgfqpoint{0.974405in}{1.087504in}}%
+\pgfpathlineto{\pgfqpoint{1.005684in}{1.034360in}}%
+\pgfpathlineto{\pgfqpoint{1.036964in}{0.980345in}}%
+\pgfpathlineto{\pgfqpoint{1.068243in}{0.926267in}}%
+\pgfpathlineto{\pgfqpoint{1.099523in}{0.872943in}}%
+\pgfpathlineto{\pgfqpoint{1.130802in}{0.821195in}}%
+\pgfpathlineto{\pgfqpoint{1.162082in}{0.771836in}}%
+\pgfpathlineto{\pgfqpoint{1.193361in}{0.725662in}}%
+\pgfpathlineto{\pgfqpoint{1.224641in}{0.683436in}}%
+\pgfpathlineto{\pgfqpoint{1.255921in}{0.645879in}}%
+\pgfpathlineto{\pgfqpoint{1.287200in}{0.613660in}}%
+\pgfpathlineto{\pgfqpoint{1.318480in}{0.587381in}}%
+\pgfpathlineto{\pgfqpoint{1.349759in}{0.567570in}}%
+\pgfpathlineto{\pgfqpoint{1.381039in}{0.554667in}}%
+\pgfpathlineto{\pgfqpoint{1.412318in}{0.549018in}}%
+\pgfpathlineto{\pgfqpoint{1.443598in}{0.550860in}}%
+\pgfpathlineto{\pgfqpoint{1.474877in}{0.560318in}}%
+\pgfpathlineto{\pgfqpoint{1.506157in}{0.577394in}}%
+\pgfpathlineto{\pgfqpoint{1.537436in}{0.601962in}}%
+\pgfpathlineto{\pgfqpoint{1.568716in}{0.633764in}}%
+\pgfpathlineto{\pgfqpoint{1.599995in}{0.672404in}}%
+\pgfpathlineto{\pgfqpoint{1.631275in}{0.717346in}}%
+\pgfpathlineto{\pgfqpoint{1.662555in}{0.767917in}}%
+\pgfpathlineto{\pgfqpoint{1.693834in}{0.823307in}}%
+\pgfpathlineto{\pgfqpoint{1.725114in}{0.882572in}}%
+\pgfpathlineto{\pgfqpoint{1.756393in}{0.944644in}}%
+\pgfpathlineto{\pgfqpoint{1.787673in}{1.008337in}}%
+\pgfpathlineto{\pgfqpoint{1.818952in}{1.072360in}}%
+\pgfpathlineto{\pgfqpoint{1.850232in}{1.135334in}}%
+\pgfpathlineto{\pgfqpoint{1.881511in}{1.195810in}}%
+\pgfpathlineto{\pgfqpoint{1.912791in}{1.252288in}}%
+\pgfpathlineto{\pgfqpoint{1.944070in}{1.303249in}}%
+\pgfpathlineto{\pgfqpoint{1.975350in}{1.347179in}}%
+\pgfpathlineto{\pgfqpoint{2.006629in}{1.382608in}}%
+\pgfpathlineto{\pgfqpoint{2.037909in}{1.408144in}}%
+\pgfpathlineto{\pgfqpoint{2.069189in}{1.422523in}}%
+\pgfpathlineto{\pgfqpoint{2.100468in}{1.424652in}}%
+\pgfpathlineto{\pgfqpoint{2.131748in}{1.413666in}}%
+\pgfpathlineto{\pgfqpoint{2.163027in}{1.388989in}}%
+\pgfpathlineto{\pgfqpoint{2.194307in}{1.350397in}}%
+\pgfpathlineto{\pgfqpoint{2.225586in}{1.298092in}}%
+\pgfpathlineto{\pgfqpoint{2.256866in}{1.232780in}}%
+\pgfpathlineto{\pgfqpoint{2.288145in}{1.155757in}}%
+\pgfpathlineto{\pgfqpoint{2.319425in}{1.069002in}}%
+\pgfpathlineto{\pgfqpoint{2.350704in}{0.975275in}}%
+\pgfpathlineto{\pgfqpoint{2.381984in}{0.878228in}}%
+\pgfpathlineto{\pgfqpoint{2.413263in}{0.782522in}}%
+\pgfpathlineto{\pgfqpoint{2.444543in}{0.693947in}}%
+\pgfpathlineto{\pgfqpoint{2.475823in}{0.619562in}}%
+\pgfpathlineto{\pgfqpoint{2.507102in}{0.567831in}}%
+\pgfpathlineto{\pgfqpoint{2.538382in}{0.548781in}}%
+\pgfpathlineto{\pgfqpoint{2.569661in}{0.574165in}}%
+\pgfpathlineto{\pgfqpoint{2.600941in}{0.657630in}}%
+\pgfpathlineto{\pgfqpoint{2.632220in}{0.814902in}}%
+\pgfpathlineto{\pgfqpoint{2.663500in}{1.063985in}}%
+\pgfpathlineto{\pgfqpoint{2.694779in}{1.425362in}}%
+\pgfpathlineto{\pgfqpoint{2.726059in}{1.922215in}}%
+\pgfpathlineto{\pgfqpoint{2.744758in}{2.315844in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetmiterjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.630330in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{0.630330in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetmiterjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{3.727004in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{3.727004in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetmiterjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.630330in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{3.727004in}{0.548769in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetmiterjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.630330in}{2.301955in}}%
+\pgfpathlineto{\pgfqpoint{3.727004in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetmiterjoin%
+\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetfillopacity{0.800000}%
+\pgfsetlinewidth{1.003750pt}%
+\definecolor{currentstroke}{rgb}{0.800000,0.800000,0.800000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetstrokeopacity{0.800000}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{2.803974in}{0.618213in}}%
+\pgfpathlineto{\pgfqpoint{3.629782in}{0.618213in}}%
+\pgfpathquadraticcurveto{\pgfqpoint{3.657560in}{0.618213in}}{\pgfqpoint{3.657560in}{0.645991in}}%
+\pgfpathlineto{\pgfqpoint{3.657560in}{1.406793in}}%
+\pgfpathquadraticcurveto{\pgfqpoint{3.657560in}{1.434571in}}{\pgfqpoint{3.629782in}{1.434571in}}%
+\pgfpathlineto{\pgfqpoint{2.803974in}{1.434571in}}%
+\pgfpathquadraticcurveto{\pgfqpoint{2.776196in}{1.434571in}}{\pgfqpoint{2.776196in}{1.406793in}}%
+\pgfpathlineto{\pgfqpoint{2.776196in}{0.645991in}}%
+\pgfpathquadraticcurveto{\pgfqpoint{2.776196in}{0.618213in}}{\pgfqpoint{2.803974in}{0.618213in}}%
+\pgfpathlineto{\pgfqpoint{2.803974in}{0.618213in}}%
+\pgfpathclose%
+\pgfusepath{stroke,fill}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{1.505625pt}%
+\definecolor{currentstroke}{rgb}{0.121569,0.466667,0.705882}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{2.831751in}{1.330404in}}%
+\pgfpathlineto{\pgfqpoint{2.970640in}{1.330404in}}%
+\pgfpathlineto{\pgfqpoint{3.109529in}{1.330404in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=3.220640in,y=1.281793in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle N=1\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{1.505625pt}%
+\definecolor{currentstroke}{rgb}{1.000000,0.498039,0.054902}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{2.831751in}{1.136732in}}%
+\pgfpathlineto{\pgfqpoint{2.970640in}{1.136732in}}%
+\pgfpathlineto{\pgfqpoint{3.109529in}{1.136732in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=3.220640in,y=1.088120in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle N=2\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{1.505625pt}%
+\definecolor{currentstroke}{rgb}{0.172549,0.627451,0.172549}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{2.831751in}{0.943059in}}%
+\pgfpathlineto{\pgfqpoint{2.970640in}{0.943059in}}%
+\pgfpathlineto{\pgfqpoint{3.109529in}{0.943059in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=3.220640in,y=0.894448in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle N=3\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{1.505625pt}%
+\definecolor{currentstroke}{rgb}{0.839216,0.152941,0.156863}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{2.831751in}{0.749386in}}%
+\pgfpathlineto{\pgfqpoint{2.970640in}{0.749386in}}%
+\pgfpathlineto{\pgfqpoint{3.109529in}{0.749386in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=3.220640in,y=0.700775in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle N=4\)}%
+\end{pgfscope}%
+\end{pgfpicture}%
+\makeatother%
+\endgroup%
diff --git a/buch/papers/ellfilter/python/F_N_chebychev2.pgf b/buch/papers/ellfilter/python/F_N_chebychev2.pgf
new file mode 100644
index 0000000..43ebb91
--- /dev/null
+++ b/buch/papers/ellfilter/python/F_N_chebychev2.pgf
@@ -0,0 +1,1023 @@
+%% Creator: Matplotlib, PGF backend
+%%
+%% To include the figure in your LaTeX document, write
+%% \input{<filename>.pgf}
+%%
+%% Make sure the required packages are loaded in your preamble
+%% \usepackage{pgf}
+%%
+%% Also ensure that all the required font packages are loaded; for instance,
+%% the lmodern package is sometimes necessary when using math font.
+%% \usepackage{lmodern}
+%%
+%% Figures using additional raster images can only be included by \input if
+%% they are in the same directory as the main LaTeX file. For loading figures
+%% from other directories you can use the `import` package
+%% \usepackage{import}
+%%
+%% and then include the figures with
+%% \import{<path to file>}{<filename>.pgf}
+%%
+%% Matplotlib used the following preamble
+%%
+\begingroup%
+\makeatletter%
+\begin{pgfpicture}%
+\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{5.500000in}{2.500000in}}%
+\pgfusepath{use as bounding box, clip}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetmiterjoin%
+\pgfsetlinewidth{0.000000pt}%
+\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetstrokeopacity{0.000000}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{5.500000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{5.500000in}{2.500000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{2.500000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathclose%
+\pgfusepath{}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetmiterjoin%
+\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.000000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetstrokeopacity{0.000000}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.617954in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{5.350000in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{5.350000in}{2.301955in}}%
+\pgfpathlineto{\pgfqpoint{0.617954in}{2.301955in}}%
+\pgfpathlineto{\pgfqpoint{0.617954in}{0.548769in}}%
+\pgfpathclose%
+\pgfusepath{fill}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.617954in}{0.548769in}}{\pgfqpoint{4.732046in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{1.012292in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{1.012292in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{1.012292in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=1.012292in,y=0.451547in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {\ensuremath{-}1.0}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.617954in}{0.548769in}}{\pgfqpoint{4.732046in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{1.998134in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{1.998134in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{1.998134in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=1.998134in,y=0.451547in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {\ensuremath{-}0.5}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.617954in}{0.548769in}}{\pgfqpoint{4.732046in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{2.983977in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{2.983977in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{2.983977in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=2.983977in,y=0.451547in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.0}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.617954in}{0.548769in}}{\pgfqpoint{4.732046in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{3.969820in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{3.969820in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{3.969820in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=3.969820in,y=0.451547in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.5}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.617954in}{0.548769in}}{\pgfqpoint{4.732046in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{4.955663in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{4.955663in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{4.955663in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=4.955663in,y=0.451547in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {1.0}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=2.983977in,y=0.272534in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle w\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.617954in}{0.548769in}}{\pgfqpoint{4.732046in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.617954in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{5.350000in}{0.548769in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{0.617954in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.343262in, y=0.500544in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {\ensuremath{-}2}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.617954in}{0.548769in}}{\pgfqpoint{4.732046in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.617954in}{0.987065in}}%
+\pgfpathlineto{\pgfqpoint{5.350000in}{0.987065in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{0.617954in}{0.987065in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.343262in, y=0.938840in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {\ensuremath{-}1}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.617954in}{0.548769in}}{\pgfqpoint{4.732046in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.617954in}{1.425362in}}%
+\pgfpathlineto{\pgfqpoint{5.350000in}{1.425362in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{0.617954in}{1.425362in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.451287in, y=1.377137in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.617954in}{0.548769in}}{\pgfqpoint{4.732046in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.617954in}{1.863658in}}%
+\pgfpathlineto{\pgfqpoint{5.350000in}{1.863658in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{0.617954in}{1.863658in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.451287in, y=1.815433in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {1}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.617954in}{0.548769in}}{\pgfqpoint{4.732046in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.617954in}{2.301955in}}%
+\pgfpathlineto{\pgfqpoint{5.350000in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{0.617954in}{2.301955in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.451287in, y=2.253730in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {2}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.287707in,y=1.425362in,,bottom,rotate=90.000000]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle T_N(w)\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.617954in}{0.548769in}}{\pgfqpoint{4.732046in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{1.505625pt}%
+\definecolor{currentstroke}{rgb}{0.121569,0.466667,0.705882}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.815123in}{0.538250in}}%
+\pgfpathlineto{\pgfqpoint{0.867228in}{0.667673in}}%
+\pgfpathlineto{\pgfqpoint{0.919332in}{0.789210in}}%
+\pgfpathlineto{\pgfqpoint{0.971437in}{0.903055in}}%
+\pgfpathlineto{\pgfqpoint{1.023541in}{1.009402in}}%
+\pgfpathlineto{\pgfqpoint{1.075646in}{1.108444in}}%
+\pgfpathlineto{\pgfqpoint{1.123409in}{1.192982in}}%
+\pgfpathlineto{\pgfqpoint{1.171171in}{1.271695in}}%
+\pgfpathlineto{\pgfqpoint{1.218934in}{1.344733in}}%
+\pgfpathlineto{\pgfqpoint{1.266696in}{1.412244in}}%
+\pgfpathlineto{\pgfqpoint{1.314459in}{1.474380in}}%
+\pgfpathlineto{\pgfqpoint{1.362221in}{1.531289in}}%
+\pgfpathlineto{\pgfqpoint{1.409984in}{1.583121in}}%
+\pgfpathlineto{\pgfqpoint{1.453404in}{1.625960in}}%
+\pgfpathlineto{\pgfqpoint{1.496825in}{1.664840in}}%
+\pgfpathlineto{\pgfqpoint{1.540245in}{1.699871in}}%
+\pgfpathlineto{\pgfqpoint{1.583666in}{1.731168in}}%
+\pgfpathlineto{\pgfqpoint{1.627086in}{1.758841in}}%
+\pgfpathlineto{\pgfqpoint{1.670507in}{1.783003in}}%
+\pgfpathlineto{\pgfqpoint{1.713927in}{1.803767in}}%
+\pgfpathlineto{\pgfqpoint{1.757348in}{1.821245in}}%
+\pgfpathlineto{\pgfqpoint{1.800768in}{1.835549in}}%
+\pgfpathlineto{\pgfqpoint{1.844189in}{1.846792in}}%
+\pgfpathlineto{\pgfqpoint{1.887609in}{1.855086in}}%
+\pgfpathlineto{\pgfqpoint{1.935372in}{1.860937in}}%
+\pgfpathlineto{\pgfqpoint{1.983135in}{1.863505in}}%
+\pgfpathlineto{\pgfqpoint{2.030897in}{1.862940in}}%
+\pgfpathlineto{\pgfqpoint{2.078660in}{1.859391in}}%
+\pgfpathlineto{\pgfqpoint{2.130764in}{1.852293in}}%
+\pgfpathlineto{\pgfqpoint{2.182869in}{1.842015in}}%
+\pgfpathlineto{\pgfqpoint{2.239316in}{1.827518in}}%
+\pgfpathlineto{\pgfqpoint{2.295762in}{1.809766in}}%
+\pgfpathlineto{\pgfqpoint{2.356551in}{1.787290in}}%
+\pgfpathlineto{\pgfqpoint{2.421682in}{1.759685in}}%
+\pgfpathlineto{\pgfqpoint{2.491154in}{1.726641in}}%
+\pgfpathlineto{\pgfqpoint{2.564969in}{1.687966in}}%
+\pgfpathlineto{\pgfqpoint{2.647468in}{1.641059in}}%
+\pgfpathlineto{\pgfqpoint{2.738651in}{1.585589in}}%
+\pgfpathlineto{\pgfqpoint{2.851545in}{1.513148in}}%
+\pgfpathlineto{\pgfqpoint{3.064305in}{1.371911in}}%
+\pgfpathlineto{\pgfqpoint{3.207593in}{1.278793in}}%
+\pgfpathlineto{\pgfqpoint{3.307460in}{1.217378in}}%
+\pgfpathlineto{\pgfqpoint{3.394301in}{1.167524in}}%
+\pgfpathlineto{\pgfqpoint{3.472458in}{1.126261in}}%
+\pgfpathlineto{\pgfqpoint{3.541931in}{1.093000in}}%
+\pgfpathlineto{\pgfqpoint{3.607061in}{1.065165in}}%
+\pgfpathlineto{\pgfqpoint{3.667850in}{1.042451in}}%
+\pgfpathlineto{\pgfqpoint{3.724297in}{1.024458in}}%
+\pgfpathlineto{\pgfqpoint{3.780743in}{1.009703in}}%
+\pgfpathlineto{\pgfqpoint{3.832848in}{0.999169in}}%
+\pgfpathlineto{\pgfqpoint{3.884953in}{0.991798in}}%
+\pgfpathlineto{\pgfqpoint{3.932715in}{0.987985in}}%
+\pgfpathlineto{\pgfqpoint{3.980478in}{0.987142in}}%
+\pgfpathlineto{\pgfqpoint{4.028240in}{0.989420in}}%
+\pgfpathlineto{\pgfqpoint{4.076003in}{0.994966in}}%
+\pgfpathlineto{\pgfqpoint{4.119423in}{1.002971in}}%
+\pgfpathlineto{\pgfqpoint{4.162844in}{1.013914in}}%
+\pgfpathlineto{\pgfqpoint{4.206264in}{1.027907in}}%
+\pgfpathlineto{\pgfqpoint{4.249685in}{1.045063in}}%
+\pgfpathlineto{\pgfqpoint{4.293105in}{1.065493in}}%
+\pgfpathlineto{\pgfqpoint{4.336526in}{1.089310in}}%
+\pgfpathlineto{\pgfqpoint{4.379946in}{1.116627in}}%
+\pgfpathlineto{\pgfqpoint{4.423367in}{1.147556in}}%
+\pgfpathlineto{\pgfqpoint{4.466787in}{1.182209in}}%
+\pgfpathlineto{\pgfqpoint{4.510208in}{1.220699in}}%
+\pgfpathlineto{\pgfqpoint{4.553628in}{1.263138in}}%
+\pgfpathlineto{\pgfqpoint{4.597049in}{1.309638in}}%
+\pgfpathlineto{\pgfqpoint{4.644812in}{1.365612in}}%
+\pgfpathlineto{\pgfqpoint{4.692574in}{1.426786in}}%
+\pgfpathlineto{\pgfqpoint{4.740337in}{1.493310in}}%
+\pgfpathlineto{\pgfqpoint{4.788099in}{1.565332in}}%
+\pgfpathlineto{\pgfqpoint{4.835862in}{1.643002in}}%
+\pgfpathlineto{\pgfqpoint{4.883624in}{1.726469in}}%
+\pgfpathlineto{\pgfqpoint{4.931387in}{1.815884in}}%
+\pgfpathlineto{\pgfqpoint{4.983491in}{1.920387in}}%
+\pgfpathlineto{\pgfqpoint{5.035596in}{2.032338in}}%
+\pgfpathlineto{\pgfqpoint{5.087701in}{2.151934in}}%
+\pgfpathlineto{\pgfqpoint{5.139805in}{2.279368in}}%
+\pgfpathlineto{\pgfqpoint{5.152831in}{2.312474in}}%
+\pgfpathlineto{\pgfqpoint{5.152831in}{2.312474in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.617954in}{0.548769in}}{\pgfqpoint{4.732046in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{1.505625pt}%
+\definecolor{currentstroke}{rgb}{1.000000,0.498039,0.054902}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.963285in}{2.315844in}}%
+\pgfpathlineto{\pgfqpoint{0.988805in}{2.065008in}}%
+\pgfpathlineto{\pgfqpoint{1.014857in}{1.843281in}}%
+\pgfpathlineto{\pgfqpoint{1.036568in}{1.682977in}}%
+\pgfpathlineto{\pgfqpoint{1.058278in}{1.543280in}}%
+\pgfpathlineto{\pgfqpoint{1.079988in}{1.422723in}}%
+\pgfpathlineto{\pgfqpoint{1.101698in}{1.319903in}}%
+\pgfpathlineto{\pgfqpoint{1.123409in}{1.233476in}}%
+\pgfpathlineto{\pgfqpoint{1.140777in}{1.175276in}}%
+\pgfpathlineto{\pgfqpoint{1.158145in}{1.126117in}}%
+\pgfpathlineto{\pgfqpoint{1.175513in}{1.085395in}}%
+\pgfpathlineto{\pgfqpoint{1.192881in}{1.052526in}}%
+\pgfpathlineto{\pgfqpoint{1.210250in}{1.026952in}}%
+\pgfpathlineto{\pgfqpoint{1.223276in}{1.012233in}}%
+\pgfpathlineto{\pgfqpoint{1.236302in}{1.001095in}}%
+\pgfpathlineto{\pgfqpoint{1.249328in}{0.993325in}}%
+\pgfpathlineto{\pgfqpoint{1.262354in}{0.988718in}}%
+\pgfpathlineto{\pgfqpoint{1.275380in}{0.987075in}}%
+\pgfpathlineto{\pgfqpoint{1.288407in}{0.988202in}}%
+\pgfpathlineto{\pgfqpoint{1.301433in}{0.991914in}}%
+\pgfpathlineto{\pgfqpoint{1.318801in}{1.000572in}}%
+\pgfpathlineto{\pgfqpoint{1.336169in}{1.013093in}}%
+\pgfpathlineto{\pgfqpoint{1.353537in}{1.029086in}}%
+\pgfpathlineto{\pgfqpoint{1.375248in}{1.053389in}}%
+\pgfpathlineto{\pgfqpoint{1.401300in}{1.087971in}}%
+\pgfpathlineto{\pgfqpoint{1.431694in}{1.134386in}}%
+\pgfpathlineto{\pgfqpoint{1.466431in}{1.193454in}}%
+\pgfpathlineto{\pgfqpoint{1.514193in}{1.281335in}}%
+\pgfpathlineto{\pgfqpoint{1.648797in}{1.533319in}}%
+\pgfpathlineto{\pgfqpoint{1.692217in}{1.606504in}}%
+\pgfpathlineto{\pgfqpoint{1.731296in}{1.666194in}}%
+\pgfpathlineto{\pgfqpoint{1.766032in}{1.713499in}}%
+\pgfpathlineto{\pgfqpoint{1.796426in}{1.750004in}}%
+\pgfpathlineto{\pgfqpoint{1.826821in}{1.781659in}}%
+\pgfpathlineto{\pgfqpoint{1.852873in}{1.804782in}}%
+\pgfpathlineto{\pgfqpoint{1.878925in}{1.824113in}}%
+\pgfpathlineto{\pgfqpoint{1.904978in}{1.839604in}}%
+\pgfpathlineto{\pgfqpoint{1.931030in}{1.851242in}}%
+\pgfpathlineto{\pgfqpoint{1.957082in}{1.859041in}}%
+\pgfpathlineto{\pgfqpoint{1.983135in}{1.863047in}}%
+\pgfpathlineto{\pgfqpoint{2.009187in}{1.863329in}}%
+\pgfpathlineto{\pgfqpoint{2.035239in}{1.859984in}}%
+\pgfpathlineto{\pgfqpoint{2.061291in}{1.853128in}}%
+\pgfpathlineto{\pgfqpoint{2.087344in}{1.842898in}}%
+\pgfpathlineto{\pgfqpoint{2.113396in}{1.829452in}}%
+\pgfpathlineto{\pgfqpoint{2.143790in}{1.809929in}}%
+\pgfpathlineto{\pgfqpoint{2.174185in}{1.786560in}}%
+\pgfpathlineto{\pgfqpoint{2.208921in}{1.755558in}}%
+\pgfpathlineto{\pgfqpoint{2.243658in}{1.720467in}}%
+\pgfpathlineto{\pgfqpoint{2.282736in}{1.676770in}}%
+\pgfpathlineto{\pgfqpoint{2.330499in}{1.618420in}}%
+\pgfpathlineto{\pgfqpoint{2.386945in}{1.544378in}}%
+\pgfpathlineto{\pgfqpoint{2.491154in}{1.401257in}}%
+\pgfpathlineto{\pgfqpoint{2.573653in}{1.290423in}}%
+\pgfpathlineto{\pgfqpoint{2.630100in}{1.219842in}}%
+\pgfpathlineto{\pgfqpoint{2.677863in}{1.165204in}}%
+\pgfpathlineto{\pgfqpoint{2.716941in}{1.124786in}}%
+\pgfpathlineto{\pgfqpoint{2.756020in}{1.088796in}}%
+\pgfpathlineto{\pgfqpoint{2.790756in}{1.060903in}}%
+\pgfpathlineto{\pgfqpoint{2.825492in}{1.037164in}}%
+\pgfpathlineto{\pgfqpoint{2.855887in}{1.019988in}}%
+\pgfpathlineto{\pgfqpoint{2.886281in}{1.006308in}}%
+\pgfpathlineto{\pgfqpoint{2.916675in}{0.996229in}}%
+\pgfpathlineto{\pgfqpoint{2.947070in}{0.989827in}}%
+\pgfpathlineto{\pgfqpoint{2.973122in}{0.987304in}}%
+\pgfpathlineto{\pgfqpoint{2.999174in}{0.987534in}}%
+\pgfpathlineto{\pgfqpoint{3.025227in}{0.990514in}}%
+\pgfpathlineto{\pgfqpoint{3.051279in}{0.996229in}}%
+\pgfpathlineto{\pgfqpoint{3.081673in}{1.006308in}}%
+\pgfpathlineto{\pgfqpoint{3.112068in}{1.019988in}}%
+\pgfpathlineto{\pgfqpoint{3.142462in}{1.037164in}}%
+\pgfpathlineto{\pgfqpoint{3.172856in}{1.057704in}}%
+\pgfpathlineto{\pgfqpoint{3.207593in}{1.085092in}}%
+\pgfpathlineto{\pgfqpoint{3.242329in}{1.116388in}}%
+\pgfpathlineto{\pgfqpoint{3.281408in}{1.155866in}}%
+\pgfpathlineto{\pgfqpoint{3.324828in}{1.204423in}}%
+\pgfpathlineto{\pgfqpoint{3.372591in}{1.262618in}}%
+\pgfpathlineto{\pgfqpoint{3.433379in}{1.342111in}}%
+\pgfpathlineto{\pgfqpoint{3.533247in}{1.479174in}}%
+\pgfpathlineto{\pgfqpoint{3.615746in}{1.590473in}}%
+\pgfpathlineto{\pgfqpoint{3.667850in}{1.656113in}}%
+\pgfpathlineto{\pgfqpoint{3.711271in}{1.706362in}}%
+\pgfpathlineto{\pgfqpoint{3.750349in}{1.747148in}}%
+\pgfpathlineto{\pgfqpoint{3.785086in}{1.779222in}}%
+\pgfpathlineto{\pgfqpoint{3.815480in}{1.803631in}}%
+\pgfpathlineto{\pgfqpoint{3.845874in}{1.824284in}}%
+\pgfpathlineto{\pgfqpoint{3.876269in}{1.840876in}}%
+\pgfpathlineto{\pgfqpoint{3.902321in}{1.851653in}}%
+\pgfpathlineto{\pgfqpoint{3.928373in}{1.859081in}}%
+\pgfpathlineto{\pgfqpoint{3.954425in}{1.863021in}}%
+\pgfpathlineto{\pgfqpoint{3.980478in}{1.863350in}}%
+\pgfpathlineto{\pgfqpoint{4.002188in}{1.860795in}}%
+\pgfpathlineto{\pgfqpoint{4.023898in}{1.855619in}}%
+\pgfpathlineto{\pgfqpoint{4.049951in}{1.845904in}}%
+\pgfpathlineto{\pgfqpoint{4.076003in}{1.832340in}}%
+\pgfpathlineto{\pgfqpoint{4.102055in}{1.814925in}}%
+\pgfpathlineto{\pgfqpoint{4.128108in}{1.793690in}}%
+\pgfpathlineto{\pgfqpoint{4.154160in}{1.768700in}}%
+\pgfpathlineto{\pgfqpoint{4.184554in}{1.734938in}}%
+\pgfpathlineto{\pgfqpoint{4.214949in}{1.696434in}}%
+\pgfpathlineto{\pgfqpoint{4.249685in}{1.647018in}}%
+\pgfpathlineto{\pgfqpoint{4.288763in}{1.585242in}}%
+\pgfpathlineto{\pgfqpoint{4.332184in}{1.510192in}}%
+\pgfpathlineto{\pgfqpoint{4.388631in}{1.405562in}}%
+\pgfpathlineto{\pgfqpoint{4.505866in}{1.185791in}}%
+\pgfpathlineto{\pgfqpoint{4.544944in}{1.120547in}}%
+\pgfpathlineto{\pgfqpoint{4.575339in}{1.075851in}}%
+\pgfpathlineto{\pgfqpoint{4.601391in}{1.043132in}}%
+\pgfpathlineto{\pgfqpoint{4.623101in}{1.020680in}}%
+\pgfpathlineto{\pgfqpoint{4.640469in}{1.006375in}}%
+\pgfpathlineto{\pgfqpoint{4.657838in}{0.995735in}}%
+\pgfpathlineto{\pgfqpoint{4.675206in}{0.989161in}}%
+\pgfpathlineto{\pgfqpoint{4.688232in}{0.987152in}}%
+\pgfpathlineto{\pgfqpoint{4.701258in}{0.987850in}}%
+\pgfpathlineto{\pgfqpoint{4.714284in}{0.991448in}}%
+\pgfpathlineto{\pgfqpoint{4.727310in}{0.998141in}}%
+\pgfpathlineto{\pgfqpoint{4.740337in}{1.008133in}}%
+\pgfpathlineto{\pgfqpoint{4.753363in}{1.021634in}}%
+\pgfpathlineto{\pgfqpoint{4.766389in}{1.038861in}}%
+\pgfpathlineto{\pgfqpoint{4.783757in}{1.068014in}}%
+\pgfpathlineto{\pgfqpoint{4.801125in}{1.104738in}}%
+\pgfpathlineto{\pgfqpoint{4.818494in}{1.149605in}}%
+\pgfpathlineto{\pgfqpoint{4.835862in}{1.203207in}}%
+\pgfpathlineto{\pgfqpoint{4.853230in}{1.266163in}}%
+\pgfpathlineto{\pgfqpoint{4.870598in}{1.339113in}}%
+\pgfpathlineto{\pgfqpoint{4.892308in}{1.445372in}}%
+\pgfpathlineto{\pgfqpoint{4.914019in}{1.569642in}}%
+\pgfpathlineto{\pgfqpoint{4.935729in}{1.713341in}}%
+\pgfpathlineto{\pgfqpoint{4.957439in}{1.877948in}}%
+\pgfpathlineto{\pgfqpoint{4.979149in}{2.065008in}}%
+\pgfpathlineto{\pgfqpoint{5.004669in}{2.315844in}}%
+\pgfpathlineto{\pgfqpoint{5.004669in}{2.315844in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.617954in}{0.548769in}}{\pgfqpoint{4.732046in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{1.505625pt}%
+\definecolor{currentstroke}{rgb}{0.172549,0.627451,0.172549}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.997762in}{0.534880in}}%
+\pgfpathlineto{\pgfqpoint{1.010515in}{0.938420in}}%
+\pgfpathlineto{\pgfqpoint{1.023541in}{1.256633in}}%
+\pgfpathlineto{\pgfqpoint{1.036568in}{1.493946in}}%
+\pgfpathlineto{\pgfqpoint{1.049594in}{1.662731in}}%
+\pgfpathlineto{\pgfqpoint{1.058278in}{1.742696in}}%
+\pgfpathlineto{\pgfqpoint{1.066962in}{1.800120in}}%
+\pgfpathlineto{\pgfqpoint{1.075646in}{1.837754in}}%
+\pgfpathlineto{\pgfqpoint{1.084330in}{1.858134in}}%
+\pgfpathlineto{\pgfqpoint{1.088672in}{1.862591in}}%
+\pgfpathlineto{\pgfqpoint{1.093014in}{1.863596in}}%
+\pgfpathlineto{\pgfqpoint{1.097356in}{1.861410in}}%
+\pgfpathlineto{\pgfqpoint{1.101698in}{1.856284in}}%
+\pgfpathlineto{\pgfqpoint{1.110382in}{1.838165in}}%
+\pgfpathlineto{\pgfqpoint{1.119067in}{1.811034in}}%
+\pgfpathlineto{\pgfqpoint{1.132093in}{1.756980in}}%
+\pgfpathlineto{\pgfqpoint{1.149461in}{1.667415in}}%
+\pgfpathlineto{\pgfqpoint{1.179855in}{1.488530in}}%
+\pgfpathlineto{\pgfqpoint{1.214592in}{1.289910in}}%
+\pgfpathlineto{\pgfqpoint{1.236302in}{1.184400in}}%
+\pgfpathlineto{\pgfqpoint{1.253670in}{1.114719in}}%
+\pgfpathlineto{\pgfqpoint{1.266696in}{1.072074in}}%
+\pgfpathlineto{\pgfqpoint{1.279722in}{1.038054in}}%
+\pgfpathlineto{\pgfqpoint{1.292749in}{1.012779in}}%
+\pgfpathlineto{\pgfqpoint{1.301433in}{1.000762in}}%
+\pgfpathlineto{\pgfqpoint{1.310117in}{0.992549in}}%
+\pgfpathlineto{\pgfqpoint{1.318801in}{0.988057in}}%
+\pgfpathlineto{\pgfqpoint{1.327485in}{0.987177in}}%
+\pgfpathlineto{\pgfqpoint{1.336169in}{0.989782in}}%
+\pgfpathlineto{\pgfqpoint{1.344853in}{0.995723in}}%
+\pgfpathlineto{\pgfqpoint{1.353537in}{1.004838in}}%
+\pgfpathlineto{\pgfqpoint{1.366563in}{1.024074in}}%
+\pgfpathlineto{\pgfqpoint{1.379590in}{1.049416in}}%
+\pgfpathlineto{\pgfqpoint{1.396958in}{1.091524in}}%
+\pgfpathlineto{\pgfqpoint{1.418668in}{1.155158in}}%
+\pgfpathlineto{\pgfqpoint{1.444720in}{1.243239in}}%
+\pgfpathlineto{\pgfqpoint{1.488141in}{1.403898in}}%
+\pgfpathlineto{\pgfqpoint{1.531561in}{1.561511in}}%
+\pgfpathlineto{\pgfqpoint{1.557614in}{1.646386in}}%
+\pgfpathlineto{\pgfqpoint{1.579324in}{1.708574in}}%
+\pgfpathlineto{\pgfqpoint{1.601034in}{1.761436in}}%
+\pgfpathlineto{\pgfqpoint{1.618402in}{1.796276in}}%
+\pgfpathlineto{\pgfqpoint{1.635771in}{1.824067in}}%
+\pgfpathlineto{\pgfqpoint{1.648797in}{1.840132in}}%
+\pgfpathlineto{\pgfqpoint{1.661823in}{1.852039in}}%
+\pgfpathlineto{\pgfqpoint{1.674849in}{1.859776in}}%
+\pgfpathlineto{\pgfqpoint{1.687875in}{1.863368in}}%
+\pgfpathlineto{\pgfqpoint{1.700901in}{1.862878in}}%
+\pgfpathlineto{\pgfqpoint{1.713927in}{1.858401in}}%
+\pgfpathlineto{\pgfqpoint{1.726954in}{1.850065in}}%
+\pgfpathlineto{\pgfqpoint{1.739980in}{1.838024in}}%
+\pgfpathlineto{\pgfqpoint{1.757348in}{1.816524in}}%
+\pgfpathlineto{\pgfqpoint{1.774716in}{1.789256in}}%
+\pgfpathlineto{\pgfqpoint{1.796426in}{1.747911in}}%
+\pgfpathlineto{\pgfqpoint{1.818137in}{1.699616in}}%
+\pgfpathlineto{\pgfqpoint{1.844189in}{1.634299in}}%
+\pgfpathlineto{\pgfqpoint{1.878925in}{1.538536in}}%
+\pgfpathlineto{\pgfqpoint{1.983135in}{1.243956in}}%
+\pgfpathlineto{\pgfqpoint{2.013529in}{1.169800in}}%
+\pgfpathlineto{\pgfqpoint{2.039581in}{1.114392in}}%
+\pgfpathlineto{\pgfqpoint{2.061291in}{1.074988in}}%
+\pgfpathlineto{\pgfqpoint{2.083002in}{1.042391in}}%
+\pgfpathlineto{\pgfqpoint{2.100370in}{1.021533in}}%
+\pgfpathlineto{\pgfqpoint{2.117738in}{1.005506in}}%
+\pgfpathlineto{\pgfqpoint{2.135106in}{0.994424in}}%
+\pgfpathlineto{\pgfqpoint{2.148132in}{0.989394in}}%
+\pgfpathlineto{\pgfqpoint{2.161159in}{0.987181in}}%
+\pgfpathlineto{\pgfqpoint{2.174185in}{0.987773in}}%
+\pgfpathlineto{\pgfqpoint{2.187211in}{0.991136in}}%
+\pgfpathlineto{\pgfqpoint{2.200237in}{0.997224in}}%
+\pgfpathlineto{\pgfqpoint{2.217605in}{1.009467in}}%
+\pgfpathlineto{\pgfqpoint{2.234974in}{1.026248in}}%
+\pgfpathlineto{\pgfqpoint{2.252342in}{1.047331in}}%
+\pgfpathlineto{\pgfqpoint{2.274052in}{1.079308in}}%
+\pgfpathlineto{\pgfqpoint{2.295762in}{1.116953in}}%
+\pgfpathlineto{\pgfqpoint{2.321815in}{1.168623in}}%
+\pgfpathlineto{\pgfqpoint{2.352209in}{1.236174in}}%
+\pgfpathlineto{\pgfqpoint{2.391287in}{1.331016in}}%
+\pgfpathlineto{\pgfqpoint{2.504181in}{1.611124in}}%
+\pgfpathlineto{\pgfqpoint{2.534575in}{1.677221in}}%
+\pgfpathlineto{\pgfqpoint{2.560627in}{1.727693in}}%
+\pgfpathlineto{\pgfqpoint{2.586680in}{1.771344in}}%
+\pgfpathlineto{\pgfqpoint{2.608390in}{1.801859in}}%
+\pgfpathlineto{\pgfqpoint{2.630100in}{1.826589in}}%
+\pgfpathlineto{\pgfqpoint{2.647468in}{1.841982in}}%
+\pgfpathlineto{\pgfqpoint{2.664837in}{1.853327in}}%
+\pgfpathlineto{\pgfqpoint{2.682205in}{1.860536in}}%
+\pgfpathlineto{\pgfqpoint{2.699573in}{1.863558in}}%
+\pgfpathlineto{\pgfqpoint{2.712599in}{1.863067in}}%
+\pgfpathlineto{\pgfqpoint{2.725625in}{1.860222in}}%
+\pgfpathlineto{\pgfqpoint{2.742993in}{1.852807in}}%
+\pgfpathlineto{\pgfqpoint{2.760362in}{1.841331in}}%
+\pgfpathlineto{\pgfqpoint{2.777730in}{1.825916in}}%
+\pgfpathlineto{\pgfqpoint{2.795098in}{1.806716in}}%
+\pgfpathlineto{\pgfqpoint{2.816808in}{1.777690in}}%
+\pgfpathlineto{\pgfqpoint{2.838519in}{1.743493in}}%
+\pgfpathlineto{\pgfqpoint{2.864571in}{1.696359in}}%
+\pgfpathlineto{\pgfqpoint{2.894965in}{1.634247in}}%
+\pgfpathlineto{\pgfqpoint{2.929702in}{1.556076in}}%
+\pgfpathlineto{\pgfqpoint{2.986148in}{1.420053in}}%
+\pgfpathlineto{\pgfqpoint{3.051279in}{1.264602in}}%
+\pgfpathlineto{\pgfqpoint{3.086015in}{1.189019in}}%
+\pgfpathlineto{\pgfqpoint{3.116410in}{1.130020in}}%
+\pgfpathlineto{\pgfqpoint{3.142462in}{1.086119in}}%
+\pgfpathlineto{\pgfqpoint{3.164172in}{1.054967in}}%
+\pgfpathlineto{\pgfqpoint{3.185883in}{1.029260in}}%
+\pgfpathlineto{\pgfqpoint{3.203251in}{1.012882in}}%
+\pgfpathlineto{\pgfqpoint{3.220619in}{1.000409in}}%
+\pgfpathlineto{\pgfqpoint{3.237987in}{0.991969in}}%
+\pgfpathlineto{\pgfqpoint{3.255355in}{0.987657in}}%
+\pgfpathlineto{\pgfqpoint{3.268382in}{0.987166in}}%
+\pgfpathlineto{\pgfqpoint{3.281408in}{0.989038in}}%
+\pgfpathlineto{\pgfqpoint{3.298776in}{0.995204in}}%
+\pgfpathlineto{\pgfqpoint{3.316144in}{1.005522in}}%
+\pgfpathlineto{\pgfqpoint{3.333512in}{1.019913in}}%
+\pgfpathlineto{\pgfqpoint{3.350880in}{1.038258in}}%
+\pgfpathlineto{\pgfqpoint{3.372591in}{1.066505in}}%
+\pgfpathlineto{\pgfqpoint{3.394301in}{1.100293in}}%
+\pgfpathlineto{\pgfqpoint{3.420353in}{1.147476in}}%
+\pgfpathlineto{\pgfqpoint{3.446406in}{1.200975in}}%
+\pgfpathlineto{\pgfqpoint{3.481142in}{1.280166in}}%
+\pgfpathlineto{\pgfqpoint{3.528905in}{1.398487in}}%
+\pgfpathlineto{\pgfqpoint{3.611404in}{1.604382in}}%
+\pgfpathlineto{\pgfqpoint{3.646140in}{1.682101in}}%
+\pgfpathlineto{\pgfqpoint{3.672192in}{1.733770in}}%
+\pgfpathlineto{\pgfqpoint{3.698245in}{1.778285in}}%
+\pgfpathlineto{\pgfqpoint{3.719955in}{1.809052in}}%
+\pgfpathlineto{\pgfqpoint{3.737323in}{1.829084in}}%
+\pgfpathlineto{\pgfqpoint{3.754691in}{1.844751in}}%
+\pgfpathlineto{\pgfqpoint{3.772059in}{1.855828in}}%
+\pgfpathlineto{\pgfqpoint{3.785086in}{1.861014in}}%
+\pgfpathlineto{\pgfqpoint{3.798112in}{1.863458in}}%
+\pgfpathlineto{\pgfqpoint{3.811138in}{1.863117in}}%
+\pgfpathlineto{\pgfqpoint{3.824164in}{1.859967in}}%
+\pgfpathlineto{\pgfqpoint{3.837190in}{1.853997in}}%
+\pgfpathlineto{\pgfqpoint{3.850216in}{1.845218in}}%
+\pgfpathlineto{\pgfqpoint{3.867584in}{1.829191in}}%
+\pgfpathlineto{\pgfqpoint{3.884953in}{1.808333in}}%
+\pgfpathlineto{\pgfqpoint{3.902321in}{1.782817in}}%
+\pgfpathlineto{\pgfqpoint{3.924031in}{1.744730in}}%
+\pgfpathlineto{\pgfqpoint{3.945741in}{1.700309in}}%
+\pgfpathlineto{\pgfqpoint{3.971794in}{1.639665in}}%
+\pgfpathlineto{\pgfqpoint{4.002188in}{1.560701in}}%
+\pgfpathlineto{\pgfqpoint{4.045609in}{1.437971in}}%
+\pgfpathlineto{\pgfqpoint{4.119423in}{1.227942in}}%
+\pgfpathlineto{\pgfqpoint{4.149818in}{1.151107in}}%
+\pgfpathlineto{\pgfqpoint{4.175870in}{1.093948in}}%
+\pgfpathlineto{\pgfqpoint{4.197580in}{1.054139in}}%
+\pgfpathlineto{\pgfqpoint{4.214949in}{1.028264in}}%
+\pgfpathlineto{\pgfqpoint{4.232317in}{1.008285in}}%
+\pgfpathlineto{\pgfqpoint{4.245343in}{0.997460in}}%
+\pgfpathlineto{\pgfqpoint{4.258369in}{0.990394in}}%
+\pgfpathlineto{\pgfqpoint{4.271395in}{0.987234in}}%
+\pgfpathlineto{\pgfqpoint{4.284421in}{0.988096in}}%
+\pgfpathlineto{\pgfqpoint{4.297447in}{0.993064in}}%
+\pgfpathlineto{\pgfqpoint{4.310474in}{1.002190in}}%
+\pgfpathlineto{\pgfqpoint{4.323500in}{1.015487in}}%
+\pgfpathlineto{\pgfqpoint{4.336526in}{1.032928in}}%
+\pgfpathlineto{\pgfqpoint{4.353894in}{1.062510in}}%
+\pgfpathlineto{\pgfqpoint{4.371262in}{1.099057in}}%
+\pgfpathlineto{\pgfqpoint{4.392973in}{1.153882in}}%
+\pgfpathlineto{\pgfqpoint{4.414683in}{1.217773in}}%
+\pgfpathlineto{\pgfqpoint{4.440735in}{1.304246in}}%
+\pgfpathlineto{\pgfqpoint{4.479814in}{1.446826in}}%
+\pgfpathlineto{\pgfqpoint{4.536260in}{1.652803in}}%
+\pgfpathlineto{\pgfqpoint{4.562313in}{1.735052in}}%
+\pgfpathlineto{\pgfqpoint{4.579681in}{1.781356in}}%
+\pgfpathlineto{\pgfqpoint{4.597049in}{1.818848in}}%
+\pgfpathlineto{\pgfqpoint{4.610075in}{1.840192in}}%
+\pgfpathlineto{\pgfqpoint{4.623101in}{1.855001in}}%
+\pgfpathlineto{\pgfqpoint{4.631785in}{1.860942in}}%
+\pgfpathlineto{\pgfqpoint{4.640469in}{1.863546in}}%
+\pgfpathlineto{\pgfqpoint{4.649154in}{1.862667in}}%
+\pgfpathlineto{\pgfqpoint{4.657838in}{1.858175in}}%
+\pgfpathlineto{\pgfqpoint{4.666522in}{1.849962in}}%
+\pgfpathlineto{\pgfqpoint{4.675206in}{1.837945in}}%
+\pgfpathlineto{\pgfqpoint{4.688232in}{1.812669in}}%
+\pgfpathlineto{\pgfqpoint{4.701258in}{1.778650in}}%
+\pgfpathlineto{\pgfqpoint{4.714284in}{1.736005in}}%
+\pgfpathlineto{\pgfqpoint{4.731653in}{1.666324in}}%
+\pgfpathlineto{\pgfqpoint{4.749021in}{1.583371in}}%
+\pgfpathlineto{\pgfqpoint{4.770731in}{1.464716in}}%
+\pgfpathlineto{\pgfqpoint{4.835862in}{1.093743in}}%
+\pgfpathlineto{\pgfqpoint{4.848888in}{1.039690in}}%
+\pgfpathlineto{\pgfqpoint{4.857572in}{1.012559in}}%
+\pgfpathlineto{\pgfqpoint{4.866256in}{0.994439in}}%
+\pgfpathlineto{\pgfqpoint{4.870598in}{0.989314in}}%
+\pgfpathlineto{\pgfqpoint{4.874940in}{0.987128in}}%
+\pgfpathlineto{\pgfqpoint{4.879282in}{0.988132in}}%
+\pgfpathlineto{\pgfqpoint{4.883624in}{0.992590in}}%
+\pgfpathlineto{\pgfqpoint{4.887966in}{1.000774in}}%
+\pgfpathlineto{\pgfqpoint{4.896650in}{1.029477in}}%
+\pgfpathlineto{\pgfqpoint{4.905335in}{1.076675in}}%
+\pgfpathlineto{\pgfqpoint{4.914019in}{1.145012in}}%
+\pgfpathlineto{\pgfqpoint{4.922703in}{1.237348in}}%
+\pgfpathlineto{\pgfqpoint{4.931387in}{1.356777in}}%
+\pgfpathlineto{\pgfqpoint{4.944413in}{1.594091in}}%
+\pgfpathlineto{\pgfqpoint{4.957439in}{1.912304in}}%
+\pgfpathlineto{\pgfqpoint{4.970193in}{2.315844in}}%
+\pgfpathlineto{\pgfqpoint{4.970193in}{2.315844in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetmiterjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.617954in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{0.617954in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetmiterjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{5.350000in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{5.350000in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetmiterjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.617954in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{5.350000in}{0.548769in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetmiterjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.617954in}{2.301955in}}%
+\pgfpathlineto{\pgfqpoint{5.350000in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetmiterjoin%
+\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetfillopacity{0.800000}%
+\pgfsetlinewidth{1.003750pt}%
+\definecolor{currentstroke}{rgb}{0.800000,0.800000,0.800000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetstrokeopacity{0.800000}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.715177in}{1.609825in}}%
+\pgfpathlineto{\pgfqpoint{1.610430in}{1.609825in}}%
+\pgfpathquadraticcurveto{\pgfqpoint{1.638207in}{1.609825in}}{\pgfqpoint{1.638207in}{1.637603in}}%
+\pgfpathlineto{\pgfqpoint{1.638207in}{2.204733in}}%
+\pgfpathquadraticcurveto{\pgfqpoint{1.638207in}{2.232510in}}{\pgfqpoint{1.610430in}{2.232510in}}%
+\pgfpathlineto{\pgfqpoint{0.715177in}{2.232510in}}%
+\pgfpathquadraticcurveto{\pgfqpoint{0.687399in}{2.232510in}}{\pgfqpoint{0.687399in}{2.204733in}}%
+\pgfpathlineto{\pgfqpoint{0.687399in}{1.637603in}}%
+\pgfpathquadraticcurveto{\pgfqpoint{0.687399in}{1.609825in}}{\pgfqpoint{0.715177in}{1.609825in}}%
+\pgfpathlineto{\pgfqpoint{0.715177in}{1.609825in}}%
+\pgfpathclose%
+\pgfusepath{stroke,fill}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{1.505625pt}%
+\definecolor{currentstroke}{rgb}{0.121569,0.466667,0.705882}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.742954in}{2.128344in}}%
+\pgfpathlineto{\pgfqpoint{0.881843in}{2.128344in}}%
+\pgfpathlineto{\pgfqpoint{1.020732in}{2.128344in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=1.131843in,y=2.079733in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle N=3\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{1.505625pt}%
+\definecolor{currentstroke}{rgb}{1.000000,0.498039,0.054902}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.742954in}{1.934671in}}%
+\pgfpathlineto{\pgfqpoint{0.881843in}{1.934671in}}%
+\pgfpathlineto{\pgfqpoint{1.020732in}{1.934671in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=1.131843in,y=1.886060in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle N=6\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{1.505625pt}%
+\definecolor{currentstroke}{rgb}{0.172549,0.627451,0.172549}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.742954in}{1.740998in}}%
+\pgfpathlineto{\pgfqpoint{0.881843in}{1.740998in}}%
+\pgfpathlineto{\pgfqpoint{1.020732in}{1.740998in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=1.131843in,y=1.692387in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle N=11\)}%
+\end{pgfscope}%
+\end{pgfpicture}%
+\makeatother%
+\endgroup%
diff --git a/buch/papers/ellfilter/python/F_N_elliptic.pgf b/buch/papers/ellfilter/python/F_N_elliptic.pgf
new file mode 100644
index 0000000..03084c6
--- /dev/null
+++ b/buch/papers/ellfilter/python/F_N_elliptic.pgf
@@ -0,0 +1,847 @@
+%% Creator: Matplotlib, PGF backend
+%%
+%% To include the figure in your LaTeX document, write
+%% \input{<filename>.pgf}
+%%
+%% Make sure the required packages are loaded in your preamble
+%% \usepackage{pgf}
+%%
+%% Also ensure that all the required font packages are loaded; for instance,
+%% the lmodern package is sometimes necessary when using math font.
+%% \usepackage{lmodern}
+%%
+%% Figures using additional raster images can only be included by \input if
+%% they are in the same directory as the main LaTeX file. For loading figures
+%% from other directories you can use the `import` package
+%% \usepackage{import}
+%%
+%% and then include the figures with
+%% \import{<path to file>}{<filename>.pgf}
+%%
+%% Matplotlib used the following preamble
+%%
+\begingroup%
+\makeatletter%
+\begin{pgfpicture}%
+\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{4.000000in}{2.500000in}}%
+\pgfusepath{use as bounding box, clip}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetmiterjoin%
+\pgfsetlinewidth{0.000000pt}%
+\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetstrokeopacity{0.000000}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{4.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{4.000000in}{2.500000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{2.500000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathclose%
+\pgfusepath{}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetmiterjoin%
+\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.000000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetstrokeopacity{0.000000}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.733531in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{3.761597in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{3.761597in}{2.301955in}}%
+\pgfpathlineto{\pgfqpoint{0.733531in}{2.301955in}}%
+\pgfpathlineto{\pgfqpoint{0.733531in}{0.548769in}}%
+\pgfpathclose%
+\pgfusepath{fill}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.733531in}{0.548769in}}{\pgfqpoint{3.028066in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetbuttcap%
+\pgfsetmiterjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.501961,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetfillopacity{0.200000}%
+\pgfsetlinewidth{0.000000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetstrokeopacity{0.200000}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.733531in}{-174.068564in}}%
+\pgfpathlineto{\pgfqpoint{2.247564in}{-174.068564in}}%
+\pgfpathlineto{\pgfqpoint{2.247564in}{1.250043in}}%
+\pgfpathlineto{\pgfqpoint{0.733531in}{1.250043in}}%
+\pgfpathlineto{\pgfqpoint{0.733531in}{-174.068564in}}%
+\pgfpathclose%
+\pgfusepath{fill}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.733531in}{0.548769in}}{\pgfqpoint{3.028066in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetbuttcap%
+\pgfsetmiterjoin%
+\definecolor{currentfill}{rgb}{1.000000,0.647059,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetfillopacity{0.200000}%
+\pgfsetlinewidth{0.000000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetstrokeopacity{0.200000}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{2.247564in}{1.250043in}}%
+\pgfpathlineto{\pgfqpoint{2.262704in}{1.250043in}}%
+\pgfpathlineto{\pgfqpoint{2.262704in}{1.600680in}}%
+\pgfpathlineto{\pgfqpoint{2.247564in}{1.600680in}}%
+\pgfpathlineto{\pgfqpoint{2.247564in}{1.250043in}}%
+\pgfpathclose%
+\pgfusepath{fill}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.733531in}{0.548769in}}{\pgfqpoint{3.028066in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetbuttcap%
+\pgfsetmiterjoin%
+\definecolor{currentfill}{rgb}{1.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetfillopacity{0.200000}%
+\pgfsetlinewidth{0.000000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetstrokeopacity{0.200000}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{2.262704in}{1.600680in}}%
+\pgfpathlineto{\pgfqpoint{3.776737in}{1.600680in}}%
+\pgfpathlineto{\pgfqpoint{3.776737in}{2.301962in}}%
+\pgfpathlineto{\pgfqpoint{2.262704in}{2.301962in}}%
+\pgfpathlineto{\pgfqpoint{2.262704in}{1.600680in}}%
+\pgfpathclose%
+\pgfusepath{fill}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.733531in}{0.548769in}}{\pgfqpoint{3.028066in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.733531in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{0.733531in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{0.733531in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.733531in,y=0.451547in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.0}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.733531in}{0.548769in}}{\pgfqpoint{3.028066in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{1.490547in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{1.490547in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{1.490547in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=1.490547in,y=0.451547in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.5}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.733531in}{0.548769in}}{\pgfqpoint{3.028066in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{2.247564in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{2.247564in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{2.247564in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=2.247564in,y=0.451547in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {1.0}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.733531in}{0.548769in}}{\pgfqpoint{3.028066in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{3.004580in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{3.004580in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{3.004580in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=3.004580in,y=0.451547in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {1.5}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.733531in}{0.548769in}}{\pgfqpoint{3.028066in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{3.761597in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{3.761597in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{3.761597in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=3.761597in,y=0.451547in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {2.0}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=2.247564in,y=0.272534in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle w\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.733531in}{0.548769in}}{\pgfqpoint{3.028066in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.733531in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{3.761597in}{0.548769in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{0.733531in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.348306in, y=0.500544in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-4}}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.733531in}{0.548769in}}{\pgfqpoint{3.028066in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.733531in}{0.899406in}}%
+\pgfpathlineto{\pgfqpoint{3.761597in}{0.899406in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{0.733531in}{0.899406in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.348306in, y=0.851181in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-2}}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.733531in}{0.548769in}}{\pgfqpoint{3.028066in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.733531in}{1.250043in}}%
+\pgfpathlineto{\pgfqpoint{3.761597in}{1.250043in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{0.733531in}{1.250043in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.435112in, y=1.201818in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{0}}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.733531in}{0.548769in}}{\pgfqpoint{3.028066in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.733531in}{1.600680in}}%
+\pgfpathlineto{\pgfqpoint{3.761597in}{1.600680in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{0.733531in}{1.600680in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.435112in, y=1.552455in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{2}}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.733531in}{0.548769in}}{\pgfqpoint{3.028066in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.733531in}{1.951318in}}%
+\pgfpathlineto{\pgfqpoint{3.761597in}{1.951318in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{0.733531in}{1.951318in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.435112in, y=1.903092in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{4}}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.733531in}{0.548769in}}{\pgfqpoint{3.028066in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.733531in}{2.301955in}}%
+\pgfpathlineto{\pgfqpoint{3.761597in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{0.733531in}{2.301955in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.435112in, y=2.253730in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{6}}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.292751in,y=1.425362in,,bottom,rotate=90.000000]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle F^2_N(w)\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.733531in}{0.548769in}}{\pgfqpoint{3.028066in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{1.003750pt}%
+\definecolor{currentstroke}{rgb}{0.121569,0.466667,0.705882}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.739446in}{0.534880in}}%
+\pgfpathlineto{\pgfqpoint{0.744132in}{0.623916in}}%
+\pgfpathlineto{\pgfqpoint{0.750947in}{0.699506in}}%
+\pgfpathlineto{\pgfqpoint{0.759276in}{0.759013in}}%
+\pgfpathlineto{\pgfqpoint{0.769120in}{0.808295in}}%
+\pgfpathlineto{\pgfqpoint{0.781235in}{0.852871in}}%
+\pgfpathlineto{\pgfqpoint{0.794865in}{0.891083in}}%
+\pgfpathlineto{\pgfqpoint{0.810009in}{0.924604in}}%
+\pgfpathlineto{\pgfqpoint{0.827425in}{0.955729in}}%
+\pgfpathlineto{\pgfqpoint{0.847112in}{0.984554in}}%
+\pgfpathlineto{\pgfqpoint{0.869071in}{1.011252in}}%
+\pgfpathlineto{\pgfqpoint{0.894059in}{1.036721in}}%
+\pgfpathlineto{\pgfqpoint{0.922075in}{1.060823in}}%
+\pgfpathlineto{\pgfqpoint{0.953878in}{1.084028in}}%
+\pgfpathlineto{\pgfqpoint{0.989467in}{1.106127in}}%
+\pgfpathlineto{\pgfqpoint{1.029598in}{1.127375in}}%
+\pgfpathlineto{\pgfqpoint{1.075031in}{1.147865in}}%
+\pgfpathlineto{\pgfqpoint{1.125764in}{1.167300in}}%
+\pgfpathlineto{\pgfqpoint{1.182554in}{1.185675in}}%
+\pgfpathlineto{\pgfqpoint{1.244645in}{1.202480in}}%
+\pgfpathlineto{\pgfqpoint{1.312036in}{1.217494in}}%
+\pgfpathlineto{\pgfqpoint{1.383214in}{1.230171in}}%
+\pgfpathlineto{\pgfqpoint{1.455905in}{1.239991in}}%
+\pgfpathlineto{\pgfqpoint{1.527083in}{1.246540in}}%
+\pgfpathlineto{\pgfqpoint{1.594474in}{1.249707in}}%
+\pgfpathlineto{\pgfqpoint{1.655808in}{1.249589in}}%
+\pgfpathlineto{\pgfqpoint{1.711084in}{1.246442in}}%
+\pgfpathlineto{\pgfqpoint{1.758788in}{1.240733in}}%
+\pgfpathlineto{\pgfqpoint{1.800434in}{1.232740in}}%
+\pgfpathlineto{\pgfqpoint{1.836780in}{1.222684in}}%
+\pgfpathlineto{\pgfqpoint{1.867825in}{1.211013in}}%
+\pgfpathlineto{\pgfqpoint{1.895085in}{1.197575in}}%
+\pgfpathlineto{\pgfqpoint{1.919315in}{1.182199in}}%
+\pgfpathlineto{\pgfqpoint{1.940517in}{1.165082in}}%
+\pgfpathlineto{\pgfqpoint{1.959447in}{1.145758in}}%
+\pgfpathlineto{\pgfqpoint{1.976106in}{1.124277in}}%
+\pgfpathlineto{\pgfqpoint{1.991250in}{1.099472in}}%
+\pgfpathlineto{\pgfqpoint{2.004122in}{1.072523in}}%
+\pgfpathlineto{\pgfqpoint{2.015480in}{1.041896in}}%
+\pgfpathlineto{\pgfqpoint{2.026081in}{1.004016in}}%
+\pgfpathlineto{\pgfqpoint{2.035168in}{0.959254in}}%
+\pgfpathlineto{\pgfqpoint{2.042740in}{0.905583in}}%
+\pgfpathlineto{\pgfqpoint{2.048797in}{0.840043in}}%
+\pgfpathlineto{\pgfqpoint{2.053341in}{0.758643in}}%
+\pgfpathlineto{\pgfqpoint{2.056369in}{0.659102in}}%
+\pgfpathlineto{\pgfqpoint{2.058129in}{0.534880in}}%
+\pgfpathmoveto{\pgfqpoint{2.061041in}{0.534880in}}%
+\pgfpathlineto{\pgfqpoint{2.064699in}{0.731366in}}%
+\pgfpathlineto{\pgfqpoint{2.069999in}{0.841854in}}%
+\pgfpathlineto{\pgfqpoint{2.076814in}{0.921040in}}%
+\pgfpathlineto{\pgfqpoint{2.085143in}{0.984050in}}%
+\pgfpathlineto{\pgfqpoint{2.095744in}{1.040507in}}%
+\pgfpathlineto{\pgfqpoint{2.107859in}{1.088435in}}%
+\pgfpathlineto{\pgfqpoint{2.121489in}{1.130355in}}%
+\pgfpathlineto{\pgfqpoint{2.136633in}{1.167522in}}%
+\pgfpathlineto{\pgfqpoint{2.153292in}{1.200289in}}%
+\pgfpathlineto{\pgfqpoint{2.169193in}{1.224889in}}%
+\pgfpathlineto{\pgfqpoint{2.182823in}{1.240496in}}%
+\pgfpathlineto{\pgfqpoint{2.192666in}{1.247725in}}%
+\pgfpathlineto{\pgfqpoint{2.200239in}{1.250017in}}%
+\pgfpathlineto{\pgfqpoint{2.206296in}{1.248902in}}%
+\pgfpathlineto{\pgfqpoint{2.211597in}{1.244804in}}%
+\pgfpathlineto{\pgfqpoint{2.216897in}{1.236352in}}%
+\pgfpathlineto{\pgfqpoint{2.222197in}{1.220917in}}%
+\pgfpathlineto{\pgfqpoint{2.226741in}{1.197982in}}%
+\pgfpathlineto{\pgfqpoint{2.231284in}{1.157051in}}%
+\pgfpathlineto{\pgfqpoint{2.235070in}{1.089329in}}%
+\pgfpathlineto{\pgfqpoint{2.237342in}{1.003949in}}%
+\pgfpathlineto{\pgfqpoint{2.238856in}{0.869518in}}%
+\pgfpathlineto{\pgfqpoint{2.239613in}{0.638914in}}%
+\pgfpathlineto{\pgfqpoint{2.240370in}{0.794881in}}%
+\pgfpathlineto{\pgfqpoint{2.243399in}{1.100517in}}%
+\pgfpathlineto{\pgfqpoint{2.248700in}{1.280424in}}%
+\pgfpathlineto{\pgfqpoint{2.266873in}{1.753784in}}%
+\pgfpathlineto{\pgfqpoint{2.269144in}{1.924021in}}%
+\pgfpathlineto{\pgfqpoint{2.270659in}{2.202839in}}%
+\pgfpathlineto{\pgfqpoint{2.272930in}{1.848446in}}%
+\pgfpathlineto{\pgfqpoint{2.276716in}{1.730165in}}%
+\pgfpathlineto{\pgfqpoint{2.281260in}{1.672036in}}%
+\pgfpathlineto{\pgfqpoint{2.286560in}{1.637950in}}%
+\pgfpathlineto{\pgfqpoint{2.292618in}{1.617444in}}%
+\pgfpathlineto{\pgfqpoint{2.298675in}{1.606779in}}%
+\pgfpathlineto{\pgfqpoint{2.304733in}{1.601737in}}%
+\pgfpathlineto{\pgfqpoint{2.311548in}{1.600286in}}%
+\pgfpathlineto{\pgfqpoint{2.319120in}{1.602150in}}%
+\pgfpathlineto{\pgfqpoint{2.328206in}{1.607676in}}%
+\pgfpathlineto{\pgfqpoint{2.340322in}{1.618928in}}%
+\pgfpathlineto{\pgfqpoint{2.355466in}{1.637536in}}%
+\pgfpathlineto{\pgfqpoint{2.372881in}{1.664058in}}%
+\pgfpathlineto{\pgfqpoint{2.391054in}{1.697587in}}%
+\pgfpathlineto{\pgfqpoint{2.407713in}{1.734758in}}%
+\pgfpathlineto{\pgfqpoint{2.422857in}{1.776122in}}%
+\pgfpathlineto{\pgfqpoint{2.435729in}{1.820082in}}%
+\pgfpathlineto{\pgfqpoint{2.447088in}{1.870149in}}%
+\pgfpathlineto{\pgfqpoint{2.456174in}{1.923894in}}%
+\pgfpathlineto{\pgfqpoint{2.463746in}{1.987030in}}%
+\pgfpathlineto{\pgfqpoint{2.469804in}{2.064340in}}%
+\pgfpathlineto{\pgfqpoint{2.474347in}{2.165039in}}%
+\pgfpathlineto{\pgfqpoint{2.477435in}{2.315844in}}%
+\pgfpathmoveto{\pgfqpoint{2.481180in}{2.315844in}}%
+\pgfpathlineto{\pgfqpoint{2.484948in}{2.149178in}}%
+\pgfpathlineto{\pgfqpoint{2.490248in}{2.050240in}}%
+\pgfpathlineto{\pgfqpoint{2.497063in}{1.978983in}}%
+\pgfpathlineto{\pgfqpoint{2.505392in}{1.923413in}}%
+\pgfpathlineto{\pgfqpoint{2.515236in}{1.878185in}}%
+\pgfpathlineto{\pgfqpoint{2.526594in}{1.840393in}}%
+\pgfpathlineto{\pgfqpoint{2.539467in}{1.808260in}}%
+\pgfpathlineto{\pgfqpoint{2.553854in}{1.780613in}}%
+\pgfpathlineto{\pgfqpoint{2.569755in}{1.756622in}}%
+\pgfpathlineto{\pgfqpoint{2.587928in}{1.734871in}}%
+\pgfpathlineto{\pgfqpoint{2.608372in}{1.715370in}}%
+\pgfpathlineto{\pgfqpoint{2.631089in}{1.698028in}}%
+\pgfpathlineto{\pgfqpoint{2.656834in}{1.682284in}}%
+\pgfpathlineto{\pgfqpoint{2.686365in}{1.667895in}}%
+\pgfpathlineto{\pgfqpoint{2.720439in}{1.654789in}}%
+\pgfpathlineto{\pgfqpoint{2.759814in}{1.642992in}}%
+\pgfpathlineto{\pgfqpoint{2.806760in}{1.632261in}}%
+\pgfpathlineto{\pgfqpoint{2.862036in}{1.622901in}}%
+\pgfpathlineto{\pgfqpoint{2.928670in}{1.614877in}}%
+\pgfpathlineto{\pgfqpoint{3.008934in}{1.608422in}}%
+\pgfpathlineto{\pgfqpoint{3.108128in}{1.603650in}}%
+\pgfpathlineto{\pgfqpoint{3.233824in}{1.600841in}}%
+\pgfpathlineto{\pgfqpoint{3.396624in}{1.600449in}}%
+\pgfpathlineto{\pgfqpoint{3.619242in}{1.603198in}}%
+\pgfpathlineto{\pgfqpoint{3.761597in}{1.606074in}}%
+\pgfpathlineto{\pgfqpoint{3.761597in}{1.606074in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.733531in}{0.548769in}}{\pgfqpoint{3.028066in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetfillopacity{0.000000}%
+\pgfsetlinewidth{1.003750pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.041667in}{-0.041667in}}{\pgfqpoint{0.041667in}{0.041667in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{-0.041667in}}%
+\pgfpathcurveto{\pgfqpoint{0.011050in}{-0.041667in}}{\pgfqpoint{0.021649in}{-0.037276in}}{\pgfqpoint{0.029463in}{-0.029463in}}%
+\pgfpathcurveto{\pgfqpoint{0.037276in}{-0.021649in}}{\pgfqpoint{0.041667in}{-0.011050in}}{\pgfqpoint{0.041667in}{0.000000in}}%
+\pgfpathcurveto{\pgfqpoint{0.041667in}{0.011050in}}{\pgfqpoint{0.037276in}{0.021649in}}{\pgfqpoint{0.029463in}{0.029463in}}%
+\pgfpathcurveto{\pgfqpoint{0.021649in}{0.037276in}}{\pgfqpoint{0.011050in}{0.041667in}}{\pgfqpoint{0.000000in}{0.041667in}}%
+\pgfpathcurveto{\pgfqpoint{-0.011050in}{0.041667in}}{\pgfqpoint{-0.021649in}{0.037276in}}{\pgfqpoint{-0.029463in}{0.029463in}}%
+\pgfpathcurveto{\pgfqpoint{-0.037276in}{0.021649in}}{\pgfqpoint{-0.041667in}{0.011050in}}{\pgfqpoint{-0.041667in}{0.000000in}}%
+\pgfpathcurveto{\pgfqpoint{-0.041667in}{-0.011050in}}{\pgfqpoint{-0.037276in}{-0.021649in}}{\pgfqpoint{-0.029463in}{-0.029463in}}%
+\pgfpathcurveto{\pgfqpoint{-0.021649in}{-0.037276in}}{\pgfqpoint{-0.011050in}{-0.041667in}}{\pgfqpoint{0.000000in}{-0.041667in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.041667in}}%
+\pgfpathclose%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{0.733531in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsys@transformshift{2.050740in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsys@transformshift{2.247564in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.733531in}{0.548769in}}{\pgfqpoint{3.028066in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetfillopacity{0.000000}%
+\pgfsetlinewidth{1.003750pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.041667in}{-0.041667in}}{\pgfqpoint{0.041667in}{0.041667in}}{%
+\pgfpathmoveto{\pgfqpoint{-0.041667in}{-0.041667in}}%
+\pgfpathlineto{\pgfqpoint{0.041667in}{0.041667in}}%
+\pgfpathmoveto{\pgfqpoint{-0.041667in}{0.041667in}}%
+\pgfpathlineto{\pgfqpoint{0.041667in}{-0.041667in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{2.262704in}{2.301955in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsys@transformshift{2.482239in}{2.301955in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetmiterjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.733531in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{0.733531in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetmiterjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{3.761597in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{3.761597in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetmiterjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.733531in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{3.761597in}{0.548769in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetmiterjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.733531in}{2.301955in}}%
+\pgfpathlineto{\pgfqpoint{3.761597in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetmiterjoin%
+\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetfillopacity{0.800000}%
+\pgfsetlinewidth{1.003750pt}%
+\definecolor{currentstroke}{rgb}{0.800000,0.800000,0.800000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetstrokeopacity{0.800000}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.830753in}{1.997171in}}%
+\pgfpathlineto{\pgfqpoint{2.157621in}{1.997171in}}%
+\pgfpathquadraticcurveto{\pgfqpoint{2.185399in}{1.997171in}}{\pgfqpoint{2.185399in}{2.024949in}}%
+\pgfpathlineto{\pgfqpoint{2.185399in}{2.204733in}}%
+\pgfpathquadraticcurveto{\pgfqpoint{2.185399in}{2.232510in}}{\pgfqpoint{2.157621in}{2.232510in}}%
+\pgfpathlineto{\pgfqpoint{0.830753in}{2.232510in}}%
+\pgfpathquadraticcurveto{\pgfqpoint{0.802975in}{2.232510in}}{\pgfqpoint{0.802975in}{2.204733in}}%
+\pgfpathlineto{\pgfqpoint{0.802975in}{2.024949in}}%
+\pgfpathquadraticcurveto{\pgfqpoint{0.802975in}{1.997171in}}{\pgfqpoint{0.830753in}{1.997171in}}%
+\pgfpathlineto{\pgfqpoint{0.830753in}{1.997171in}}%
+\pgfpathclose%
+\pgfusepath{stroke,fill}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{1.003750pt}%
+\definecolor{currentstroke}{rgb}{0.121569,0.466667,0.705882}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.858531in}{2.128344in}}%
+\pgfpathlineto{\pgfqpoint{0.997420in}{2.128344in}}%
+\pgfpathlineto{\pgfqpoint{1.136309in}{2.128344in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=1.247420in,y=2.079733in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle N=5, k=0.1\)}%
+\end{pgfscope}%
+\end{pgfpicture}%
+\makeatother%
+\endgroup%
diff --git a/buch/papers/ellfilter/python/chebychef.py b/buch/papers/ellfilter/python/chebychef.py
new file mode 100644
index 0000000..254ad4b
--- /dev/null
+++ b/buch/papers/ellfilter/python/chebychef.py
@@ -0,0 +1,66 @@
+# %%
+
+import matplotlib.pyplot as plt
+import scipy.signal
+import numpy as np
+
+
+order = 5
+passband_ripple_db = 1
+omega_c = 1000
+
+a, b = scipy.signal.cheby1(
+ order,
+ passband_ripple_db,
+ omega_c,
+ btype='low',
+ analog=True,
+ output='ba',
+ fs=None,
+)
+
+w, mag, phase = scipy.signal.bode((a, b), w=np.linspace(0,2000,256))
+f, axs = plt.subplots(2,1, sharex=True)
+axs[0].plot(w, 10**(mag/20))
+axs[0].set_ylabel("$|H(\omega)| /$ db")
+axs[0].grid(True, "both")
+axs[1].plot(w, phase)
+axs[1].set_ylabel(r"$arg H (\omega) / $ deg")
+axs[1].grid(True, "both")
+axs[1].set_xlim([0, 2000])
+axs[1].set_xlabel("$\omega$")
+plt.show()
+
+
+# %% Cheychev filter F_N plot
+
+w = np.linspace(-1.1,1.1, 1000)
+plt.figure(figsize=(5.5,2.5))
+for N in [3,6,11]:
+ # F_N = np.cos(N * np.arccos(w))
+ F_N = scipy.special.eval_chebyt(N, w)
+ plt.plot(w, F_N, label=f"$N={N}$")
+plt.xlim([-1.2,1.2])
+plt.ylim([-2,2])
+plt.grid()
+plt.xlabel("$w$")
+plt.ylabel("$T_N(w)$")
+plt.legend()
+plt.tight_layout()
+plt.savefig("F_N_chebychev2.pgf")
+plt.show()
+
+# %% Build Chebychev polynomials
+
+N = 11
+
+zeros = (np.arange(N)+0.5) * np.pi
+zeros = np.cos(zeros/N)
+
+x = np.linspace(-1.2,1.2,1000)
+y = np.prod(x[:, None] - zeros[None, :], axis=-1)*2**(N-1)
+
+plt.plot(x, y)
+plt.ylim([-1,1])
+plt.grid()
+plt.show()
diff --git a/buch/papers/ellfilter/python/elliptic.pgf b/buch/papers/ellfilter/python/elliptic.pgf
new file mode 100644
index 0000000..31b77d4
--- /dev/null
+++ b/buch/papers/ellfilter/python/elliptic.pgf
@@ -0,0 +1,709 @@
+%% Creator: Matplotlib, PGF backend
+%%
+%% To include the figure in your LaTeX document, write
+%% \input{<filename>.pgf}
+%%
+%% Make sure the required packages are loaded in your preamble
+%% \usepackage{pgf}
+%%
+%% Also ensure that all the required font packages are loaded; for instance,
+%% the lmodern package is sometimes necessary when using math font.
+%% \usepackage{lmodern}
+%%
+%% Figures using additional raster images can only be included by \input if
+%% they are in the same directory as the main LaTeX file. For loading figures
+%% from other directories you can use the `import` package
+%% \usepackage{import}
+%%
+%% and then include the figures with
+%% \import{<path to file>}{<filename>.pgf}
+%%
+%% Matplotlib used the following preamble
+%%
+\begingroup%
+\makeatletter%
+\begin{pgfpicture}%
+\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{4.000000in}{2.500000in}}%
+\pgfusepath{use as bounding box, clip}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetmiterjoin%
+\pgfsetlinewidth{0.000000pt}%
+\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetstrokeopacity{0.000000}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{4.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{4.000000in}{2.500000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{2.500000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathclose%
+\pgfusepath{}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetmiterjoin%
+\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.000000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetstrokeopacity{0.000000}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.617954in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{3.761597in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{3.761597in}{2.301955in}}%
+\pgfpathlineto{\pgfqpoint{0.617954in}{2.301955in}}%
+\pgfpathlineto{\pgfqpoint{0.617954in}{0.548769in}}%
+\pgfpathclose%
+\pgfusepath{fill}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.617954in}{0.548769in}}{\pgfqpoint{3.143642in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetbuttcap%
+\pgfsetmiterjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.501961,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetfillopacity{0.200000}%
+\pgfsetlinewidth{0.000000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetstrokeopacity{0.200000}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.617954in}{1.788459in}}%
+\pgfpathlineto{\pgfqpoint{2.189776in}{1.788459in}}%
+\pgfpathlineto{\pgfqpoint{2.189776in}{3.541645in}}%
+\pgfpathlineto{\pgfqpoint{0.617954in}{3.541645in}}%
+\pgfpathlineto{\pgfqpoint{0.617954in}{1.788459in}}%
+\pgfpathclose%
+\pgfusepath{fill}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.617954in}{0.548769in}}{\pgfqpoint{3.143642in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetbuttcap%
+\pgfsetmiterjoin%
+\definecolor{currentfill}{rgb}{1.000000,0.647059,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetfillopacity{0.200000}%
+\pgfsetlinewidth{0.000000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetstrokeopacity{0.200000}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{2.189776in}{0.724087in}}%
+\pgfpathlineto{\pgfqpoint{2.205494in}{0.724087in}}%
+\pgfpathlineto{\pgfqpoint{2.205494in}{1.788459in}}%
+\pgfpathlineto{\pgfqpoint{2.189776in}{1.788459in}}%
+\pgfpathlineto{\pgfqpoint{2.189776in}{0.724087in}}%
+\pgfpathclose%
+\pgfusepath{fill}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.617954in}{0.548769in}}{\pgfqpoint{3.143642in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetbuttcap%
+\pgfsetmiterjoin%
+\definecolor{currentfill}{rgb}{1.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetfillopacity{0.200000}%
+\pgfsetlinewidth{0.000000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetstrokeopacity{0.200000}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{2.205494in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{3.777315in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{3.777315in}{0.724087in}}%
+\pgfpathlineto{\pgfqpoint{2.205494in}{0.724087in}}%
+\pgfpathlineto{\pgfqpoint{2.205494in}{0.548769in}}%
+\pgfpathclose%
+\pgfusepath{fill}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.617954in}{0.548769in}}{\pgfqpoint{3.143642in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.617954in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{0.617954in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{0.617954in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.617954in,y=0.451547in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.0}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.617954in}{0.548769in}}{\pgfqpoint{3.143642in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{1.403865in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{1.403865in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{1.403865in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=1.403865in,y=0.451547in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.5}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.617954in}{0.548769in}}{\pgfqpoint{3.143642in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{2.189776in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{2.189776in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{2.189776in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=2.189776in,y=0.451547in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {1.0}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.617954in}{0.548769in}}{\pgfqpoint{3.143642in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{2.975686in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{2.975686in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{2.975686in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=2.975686in,y=0.451547in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {1.5}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.617954in}{0.548769in}}{\pgfqpoint{3.143642in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{3.761597in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{3.761597in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{3.761597in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=3.761597in,y=0.451547in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {2.0}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=2.189776in,y=0.272534in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle w\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.617954in}{0.548769in}}{\pgfqpoint{3.143642in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.617954in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{3.761597in}{0.548769in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{0.617954in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.343262in, y=0.500544in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.0}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.617954in}{0.548769in}}{\pgfqpoint{3.143642in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.617954in}{0.899406in}}%
+\pgfpathlineto{\pgfqpoint{3.761597in}{0.899406in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{0.617954in}{0.899406in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.343262in, y=0.851181in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.2}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.617954in}{0.548769in}}{\pgfqpoint{3.143642in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.617954in}{1.250043in}}%
+\pgfpathlineto{\pgfqpoint{3.761597in}{1.250043in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{0.617954in}{1.250043in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.343262in, y=1.201818in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.4}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.617954in}{0.548769in}}{\pgfqpoint{3.143642in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.617954in}{1.600680in}}%
+\pgfpathlineto{\pgfqpoint{3.761597in}{1.600680in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{0.617954in}{1.600680in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.343262in, y=1.552455in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.6}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.617954in}{0.548769in}}{\pgfqpoint{3.143642in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.617954in}{1.951318in}}%
+\pgfpathlineto{\pgfqpoint{3.761597in}{1.951318in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{0.617954in}{1.951318in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.343262in, y=1.903092in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.8}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.617954in}{0.548769in}}{\pgfqpoint{3.143642in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.617954in}{2.301955in}}%
+\pgfpathlineto{\pgfqpoint{3.761597in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{0.617954in}{2.301955in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.343262in, y=2.253730in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {1.0}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.287707in,y=1.425362in,,bottom,rotate=90.000000]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle |H(w)|\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.617954in}{0.548769in}}{\pgfqpoint{3.143642in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{1.003750pt}%
+\definecolor{currentstroke}{rgb}{0.121569,0.466667,0.705882}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.617954in}{2.301955in}}%
+\pgfpathlineto{\pgfqpoint{0.646254in}{2.300410in}}%
+\pgfpathlineto{\pgfqpoint{0.674554in}{2.295805in}}%
+\pgfpathlineto{\pgfqpoint{0.703640in}{2.287983in}}%
+\pgfpathlineto{\pgfqpoint{0.734298in}{2.276528in}}%
+\pgfpathlineto{\pgfqpoint{0.767315in}{2.260797in}}%
+\pgfpathlineto{\pgfqpoint{0.802690in}{2.240472in}}%
+\pgfpathlineto{\pgfqpoint{0.842781in}{2.213774in}}%
+\pgfpathlineto{\pgfqpoint{0.889947in}{2.178486in}}%
+\pgfpathlineto{\pgfqpoint{0.952050in}{2.127836in}}%
+\pgfpathlineto{\pgfqpoint{1.147791in}{1.965399in}}%
+\pgfpathlineto{\pgfqpoint{1.205963in}{1.922684in}}%
+\pgfpathlineto{\pgfqpoint{1.257846in}{1.888382in}}%
+\pgfpathlineto{\pgfqpoint{1.305012in}{1.860803in}}%
+\pgfpathlineto{\pgfqpoint{1.349034in}{1.838524in}}%
+\pgfpathlineto{\pgfqpoint{1.390698in}{1.820826in}}%
+\pgfpathlineto{\pgfqpoint{1.430003in}{1.807434in}}%
+\pgfpathlineto{\pgfqpoint{1.466950in}{1.798051in}}%
+\pgfpathlineto{\pgfqpoint{1.501539in}{1.792361in}}%
+\pgfpathlineto{\pgfqpoint{1.534555in}{1.790011in}}%
+\pgfpathlineto{\pgfqpoint{1.566000in}{1.790875in}}%
+\pgfpathlineto{\pgfqpoint{1.595872in}{1.794823in}}%
+\pgfpathlineto{\pgfqpoint{1.624172in}{1.801709in}}%
+\pgfpathlineto{\pgfqpoint{1.650899in}{1.811365in}}%
+\pgfpathlineto{\pgfqpoint{1.676841in}{1.824030in}}%
+\pgfpathlineto{\pgfqpoint{1.701996in}{1.839797in}}%
+\pgfpathlineto{\pgfqpoint{1.726365in}{1.858757in}}%
+\pgfpathlineto{\pgfqpoint{1.749949in}{1.880985in}}%
+\pgfpathlineto{\pgfqpoint{1.773532in}{1.907483in}}%
+\pgfpathlineto{\pgfqpoint{1.797115in}{1.938719in}}%
+\pgfpathlineto{\pgfqpoint{1.820698in}{1.975139in}}%
+\pgfpathlineto{\pgfqpoint{1.845068in}{2.018557in}}%
+\pgfpathlineto{\pgfqpoint{1.871009in}{2.071217in}}%
+\pgfpathlineto{\pgfqpoint{1.903240in}{2.144258in}}%
+\pgfpathlineto{\pgfqpoint{1.949620in}{2.249449in}}%
+\pgfpathlineto{\pgfqpoint{1.965342in}{2.277408in}}%
+\pgfpathlineto{\pgfqpoint{1.977134in}{2.292569in}}%
+\pgfpathlineto{\pgfqpoint{1.986567in}{2.299856in}}%
+\pgfpathlineto{\pgfqpoint{1.993642in}{2.301922in}}%
+\pgfpathlineto{\pgfqpoint{2.000717in}{2.300685in}}%
+\pgfpathlineto{\pgfqpoint{2.007792in}{2.295839in}}%
+\pgfpathlineto{\pgfqpoint{2.014867in}{2.287135in}}%
+\pgfpathlineto{\pgfqpoint{2.023514in}{2.271025in}}%
+\pgfpathlineto{\pgfqpoint{2.032947in}{2.246492in}}%
+\pgfpathlineto{\pgfqpoint{2.043953in}{2.209014in}}%
+\pgfpathlineto{\pgfqpoint{2.057317in}{2.152165in}}%
+\pgfpathlineto{\pgfqpoint{2.076183in}{2.056775in}}%
+\pgfpathlineto{\pgfqpoint{2.114702in}{1.858945in}}%
+\pgfpathlineto{\pgfqpoint{2.126494in}{1.815249in}}%
+\pgfpathlineto{\pgfqpoint{2.134355in}{1.796399in}}%
+\pgfpathlineto{\pgfqpoint{2.139858in}{1.790308in}}%
+\pgfpathlineto{\pgfqpoint{2.143002in}{1.790254in}}%
+\pgfpathlineto{\pgfqpoint{2.146147in}{1.793264in}}%
+\pgfpathlineto{\pgfqpoint{2.150077in}{1.802263in}}%
+\pgfpathlineto{\pgfqpoint{2.154794in}{1.822852in}}%
+\pgfpathlineto{\pgfqpoint{2.159510in}{1.857784in}}%
+\pgfpathlineto{\pgfqpoint{2.165013in}{1.924261in}}%
+\pgfpathlineto{\pgfqpoint{2.170516in}{2.030210in}}%
+\pgfpathlineto{\pgfqpoint{2.181521in}{2.301670in}}%
+\pgfpathlineto{\pgfqpoint{2.182308in}{2.299748in}}%
+\pgfpathlineto{\pgfqpoint{2.183880in}{2.267565in}}%
+\pgfpathlineto{\pgfqpoint{2.186238in}{2.135783in}}%
+\pgfpathlineto{\pgfqpoint{2.192527in}{1.496420in}}%
+\pgfpathlineto{\pgfqpoint{2.198816in}{1.001269in}}%
+\pgfpathlineto{\pgfqpoint{2.205105in}{0.731898in}}%
+\pgfpathlineto{\pgfqpoint{2.211393in}{0.583247in}}%
+\pgfpathlineto{\pgfqpoint{2.213752in}{0.552138in}}%
+\pgfpathlineto{\pgfqpoint{2.220827in}{0.630495in}}%
+\pgfpathlineto{\pgfqpoint{2.227902in}{0.675607in}}%
+\pgfpathlineto{\pgfqpoint{2.234977in}{0.701566in}}%
+\pgfpathlineto{\pgfqpoint{2.241266in}{0.714626in}}%
+\pgfpathlineto{\pgfqpoint{2.247554in}{0.721456in}}%
+\pgfpathlineto{\pgfqpoint{2.253843in}{0.723972in}}%
+\pgfpathlineto{\pgfqpoint{2.260918in}{0.723210in}}%
+\pgfpathlineto{\pgfqpoint{2.269565in}{0.718770in}}%
+\pgfpathlineto{\pgfqpoint{2.281357in}{0.708826in}}%
+\pgfpathlineto{\pgfqpoint{2.300224in}{0.688160in}}%
+\pgfpathlineto{\pgfqpoint{2.385123in}{0.590361in}}%
+\pgfpathlineto{\pgfqpoint{2.417354in}{0.559882in}}%
+\pgfpathlineto{\pgfqpoint{2.430717in}{0.549063in}}%
+\pgfpathlineto{\pgfqpoint{2.463734in}{0.574407in}}%
+\pgfpathlineto{\pgfqpoint{2.498323in}{0.597083in}}%
+\pgfpathlineto{\pgfqpoint{2.535270in}{0.617584in}}%
+\pgfpathlineto{\pgfqpoint{2.574575in}{0.635868in}}%
+\pgfpathlineto{\pgfqpoint{2.617811in}{0.652529in}}%
+\pgfpathlineto{\pgfqpoint{2.664977in}{0.667359in}}%
+\pgfpathlineto{\pgfqpoint{2.717646in}{0.680619in}}%
+\pgfpathlineto{\pgfqpoint{2.776604in}{0.692216in}}%
+\pgfpathlineto{\pgfqpoint{2.843424in}{0.702155in}}%
+\pgfpathlineto{\pgfqpoint{2.920462in}{0.710422in}}%
+\pgfpathlineto{\pgfqpoint{3.010864in}{0.716921in}}%
+\pgfpathlineto{\pgfqpoint{3.118561in}{0.721464in}}%
+\pgfpathlineto{\pgfqpoint{3.250627in}{0.723829in}}%
+\pgfpathlineto{\pgfqpoint{3.419640in}{0.723619in}}%
+\pgfpathlineto{\pgfqpoint{3.651542in}{0.720038in}}%
+\pgfpathlineto{\pgfqpoint{3.761597in}{0.717600in}}%
+\pgfpathlineto{\pgfqpoint{3.761597in}{0.717600in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetmiterjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.617954in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{0.617954in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetmiterjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{3.761597in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{3.761597in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetmiterjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.617954in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{3.761597in}{0.548769in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetmiterjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.617954in}{2.301955in}}%
+\pgfpathlineto{\pgfqpoint{3.761597in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\end{pgfpicture}%
+\makeatother%
+\endgroup%
diff --git a/buch/papers/ellfilter/python/elliptic.py b/buch/papers/ellfilter/python/elliptic.py
new file mode 100644
index 0000000..b3336a1
--- /dev/null
+++ b/buch/papers/ellfilter/python/elliptic.py
@@ -0,0 +1,356 @@
+
+# %%
+
+import scipy.special
+import scipyx as spx
+import numpy as np
+import matplotlib.pyplot as plt
+from matplotlib.patches import Rectangle
+
+import plot_params
+
+def last_color():
+ return plt.gca().lines[-1].get_color()
+
+# define elliptic functions
+
+def ell_int(k):
+ """ Calculate K(k) """
+ m = k**2
+ return scipy.special.ellipk(m)
+
+def sn(z, k):
+ return spx.ellipj(z, k**2)[0]
+
+def cn(z, k):
+ return spx.ellipj(z, k**2)[1]
+
+def dn(z, k):
+ return spx.ellipj(z, k**2)[2]
+
+def cd(z, k):
+ sn, cn, dn, ph = spx.ellipj(z, k**2)
+ return cn / dn
+
+# https://mathworld.wolfram.com/JacobiEllipticFunctions.html eq 3-8
+
+def sn_inv(z, k):
+ m = k**2
+ return scipy.special.ellipkinc(np.arcsin(z), m)
+
+def cn_inv(z, k):
+ m = k**2
+ return scipy.special.ellipkinc(np.arccos(z), m)
+
+def dn_inv(z, k):
+ m = k**2
+ x = np.sqrt((1-z**2) / k**2)
+ return scipy.special.ellipkinc(np.arcsin(x), m)
+
+def cd_inv(z, k):
+ m = k**2
+ x = np.sqrt(((m - 1) * z**2) / (m*z**2 - 1))
+ return scipy.special.ellipkinc(np.arccos(x), m)
+
+
+k = 0.8
+z = 0.5
+
+assert np.allclose(sn_inv(sn(z ,k), k), z)
+assert np.allclose(cn_inv(cn(z ,k), k), z)
+assert np.allclose(dn_inv(dn(z ,k), k), z)
+assert np.allclose(cd_inv(cd(z ,k), k), z)
+
+
+# %% Buttwerworth filter F_N plot
+
+w = np.linspace(0,1.5, 100)
+plt.figure(figsize=(4,2.5))
+
+for N in range(1,5):
+ F_N = w**N
+ plt.plot(w, F_N**2, label=f"$N={N}$")
+plt.gca().add_patch(Rectangle(
+ (0, 0),
+ 1, 1,
+ fc ='green',
+ alpha=0.2,
+ lw = 10,
+))
+plt.gca().add_patch(Rectangle(
+ (1, 1),
+ 0.5, 1,
+ fc ='orange',
+ alpha=0.2,
+ lw = 10,
+))
+plt.xlim([0,1.5])
+plt.ylim([0,2])
+plt.grid()
+plt.xlabel("$w$")
+plt.ylabel("$F^2_N(w)$")
+plt.legend()
+plt.tight_layout()
+plt.savefig("F_N_butterworth.pgf")
+plt.show()
+
+# %% Cheychev filter F_N plot
+
+w = np.linspace(0,1.5, 100)
+
+plt.figure(figsize=(4,2.5))
+for N in range(1,5):
+ # F_N = np.cos(N * np.arccos(w))
+ F_N = scipy.special.eval_chebyt(N, w)
+ plt.plot(w, F_N**2, label=f"$N={N}$")
+plt.gca().add_patch(Rectangle(
+ (0, 0),
+ 1, 1,
+ fc ='green',
+ alpha=0.2,
+ lw = 10,
+))
+plt.gca().add_patch(Rectangle(
+ (1, 1),
+ 0.5, 1,
+ fc ='orange',
+ alpha=0.2,
+ lw = 10,
+))
+plt.xlim([0,1.5])
+plt.ylim([0,2])
+plt.grid()
+plt.xlabel("$w$")
+plt.ylabel("$F^2_N(w)$")
+plt.legend()
+plt.tight_layout()
+plt.savefig("F_N_chebychev.pgf")
+plt.show()
+
+
+# %% plot arcsin
+
+def lattice(a1, b1, c1, a2, b2, c2):
+ r1 = np.logspace(a1, b1, c1)
+ x1 = np.concatenate((-np.flip(r1), [0], r1), axis=0)
+ x1 = x1.astype(np.complex128)
+ r2 = np.logspace(a2, b2, c2)
+ x2 = np.concatenate((-np.flip(r2), [0], r2), axis=0)
+ x2 = x2.astype(np.complex128)
+ x = (x1[:, None] + (x2[None, :] * 1j))
+ return x
+
+plt.figure(figsize=(12,12))
+y = np.arcsin(lattice(-1,6,1000, -1,5,10))
+plt.plot(np.real(y), np.imag(y), "-", color="red", lw=0.5)
+y = np.arcsin(lattice(-1,6,10, -1,5,100)).T
+plt.plot(np.real(y), np.imag(y), "-", color="red", lw=0.5)
+y = np.arcsin(lattice(-1,6,10, -1,5,10))
+plt.plot(np.real(y), np.imag(y), ".", color="red", lw=0.5)
+plt.show()
+
+# %% plot cd^-1 TODO complex cd^-1 missing
+
+
+r = np.logspace(-1,8, 50)
+
+
+
+x = np.concatenate((-np.flip(r), [0], r), axis=0)
+y = cd_inv(x, 0.99)
+
+plt.figure(figsize=(12,12))
+plt.plot(np.real(y), np.imag(y), "-")
+plt.show()
+
+# %%plot cd
+plt.figure(figsize=(10,6))
+z = np.linspace(-4,4, 500)
+for k in [0, 0.9, 0.99, 0.999, 0.99999]:
+ w = cd(z*ell_int(k), k)
+ plt.plot(z, w, label=f"$k={k}$")
+plt.grid()
+plt.legend()
+# plt.xlim([-4,4])
+plt.xlabel("$u$")
+plt.ylabel("$cd(uK, k)$")
+plt.show()
+
+# %% Test ????
+
+N = 5
+k = 0.9
+k1 = k**N
+
+assert np.allclose(k**(-N), k1**(-1))
+
+K = ell_int(k)
+Kp = ell_int(np.sqrt(1-k**2))
+
+K1 = ell_int(k1)
+Kp1 = ell_int(np.sqrt(1-k1**2))
+
+print(Kp * (K1 / K) * N, Kp1)
+
+
+# %%
+
+
+k = 0.9
+k_prim = np.sqrt(1 - k**2)
+K = ell_int(k)
+Kp = ell_int(k_prim)
+
+print(K, Kp)
+
+zs = [
+ 0 + (K + 0j) * np.linspace(0,1,25),
+ K + (Kp*1j) * np.linspace(0,1,25),
+ (K + Kp*1j) + (-K) * np.linspace(0,1,25),
+]
+
+
+for z in zs:
+ plt.plot(np.real(z), np.imag(z))
+plt.show()
+
+
+
+for z in zs:
+ w = cd(z, k)
+ plt.plot(np.real(w), np.imag(w))
+plt.show()
+
+
+
+
+
+# %%
+
+for i in range(10):
+ x = np.linspace(i*1,i*1+1,10, dtype=np.complex64)
+ w = np.arccos(x)
+
+ x2 = np.cos(w)
+ x4 = np.cos(w+ 2*np.pi)
+ x3 = np.cos(np.conj(w))
+
+ assert np.allclose(x2, x4, rtol=0.001, atol=1e-5)
+
+ assert np.allclose(x2, x3)
+ assert np.allclose(x2, x, rtol=0.001, atol=1e-5)
+
+ plt.plot(np.real(w), np.imag(w), ".-")
+
+for i in range(10):
+ x = -np.linspace(i*1,i*1+1,100, dtype=np.complex64)
+ w = np.arccos(x)
+ plt.plot(np.real(w), np.imag(w), ".-")
+
+plt.grid()
+plt.show()
+
+
+
+
+# %%
+
+plt.plot(omega, np.abs(G))
+plt.show()
+
+
+def cd_inv(u, m):
+ return K(1/2) - F(np.arcsin())
+
+def K(m):
+ return scipy.special.ellipk(m)
+
+def L(n, xi):
+ return 1 #TODO
+
+def R(n, xi, x):
+ cn(n*K(1/L(n, xi))/K(1/xi) * cd_inv(x, 1/xi, 1/L(n, xi)))
+
+epsilon = 0.1
+n = 3
+omega = np.linspace(0, np.pi, 1000)
+omega_0 = 1
+xi = 1.1
+
+G = 1 / np.sqrt(1 + epsilon**2 * R(n, xi, omega/omega_0)**2)
+
+
+plt.plot(omega, np.abs(G))
+plt.show()
+
+
+
+# %% Chebychef
+
+epsilon = 0.5
+omega = np.linspace(0, np.pi, 1000)
+omega_0 = 1
+n = 4
+
+def chebychef_poly(n, x):
+ x = x.astype(np.complex64)
+ y = np.cos(n* np.arccos(x))
+ return np.real(y)
+
+F_omega = chebychef_poly
+
+for n in (1,2,3,4):
+ plt.plot(omega, F_omega(n, omega/omega_0)**2)
+plt.ylim([0,5])
+plt.xlim([0,1.5])
+plt.grid()
+plt.show()
+
+for n in (1,2,3,4):
+ G = 1 / np.sqrt(1 + epsilon**2 * F_omega(n, omega/omega_0)**2)
+ plt.plot(omega, np.abs(G))
+plt.grid()
+plt.show()
+
+
+
+
+# %%
+
+
+k = np.concatenate(([0.00001,0.0001,0.001], np.linspace(0,1,101)[1:-1], [0.999,0.9999, 0.99999]), axis=0)
+K = ell_int(k)
+K_prime = ell_int(np.sqrt(1-k**2))
+
+
+f, axs = plt.subplots(1,2, figsize=(5,2.5))
+axs[0].plot(k, K, linewidth=0.1)
+axs[0].text(k[30], K[30]+0.1, f"$K$")
+axs[0].plot(k, K_prime, linewidth=0.1)
+axs[0].text(k[30], K_prime[30]+0.1, f"$K^\prime$")
+axs[0].set_xlim([0,1])
+axs[0].set_ylim([0,4])
+axs[0].set_xlabel("$k$")
+
+axs[1].axvline(x=np.pi/2, color="gray", linewidth=0.5)
+axs[1].axhline(y=np.pi/2, color="gray", linewidth=0.5)
+axs[1].text(0.1, np.pi/2 + 0.1, "$\pi/2$")
+axs[1].text(np.pi/2+0.1, 0.1, "$\pi/2$")
+axs[1].plot(K, K_prime, linewidth=1)
+
+k = np.array([0.1,0.2,0.4,0.6,0.9,0.99])
+K = ell_int(k)
+K_prime = ell_int(np.sqrt(1-k**2))
+
+axs[1].plot(K, K_prime, '.', color=last_color(), markersize=2)
+for x, y, n in zip(K, K_prime, k):
+ axs[1].text(x+0.1, y+0.1, f"$k={n:.2f}$", rotation_mode="anchor")
+axs[1].set_ylabel("$K^\prime$")
+axs[1].set_xlabel("$K$")
+axs[1].set_xlim([0,6])
+axs[1].set_ylim([0,5])
+plt.tight_layout()
+plt.savefig("k.pgf")
+plt.show()
+
+print(K[0], K[-1])
diff --git a/buch/papers/ellfilter/python/elliptic2.py b/buch/papers/ellfilter/python/elliptic2.py
new file mode 100644
index 0000000..29c6f47
--- /dev/null
+++ b/buch/papers/ellfilter/python/elliptic2.py
@@ -0,0 +1,149 @@
+# %%
+
+import matplotlib.pyplot as plt
+import scipy.signal
+import numpy as np
+import matplotlib
+from matplotlib.patches import Rectangle
+
+import plot_params
+
+def ellip_filter(N):
+
+ order = N
+ passband_ripple_db = 3
+ stopband_attenuation_db = 20
+ omega_c = 1
+
+ a, b = scipy.signal.ellip(
+ order,
+ passband_ripple_db,
+ stopband_attenuation_db,
+ omega_c,
+ btype='low',
+ analog=True,
+ output='ba',
+ fs=None
+ )
+
+ w, mag_db, phase = scipy.signal.bode((a, b), w=np.linspace(0*omega_c,2*omega_c, 4000))
+
+ mag = 10**(mag_db/20)
+
+ passband_ripple = 10**(-passband_ripple_db/20)
+ epsilon2 = (1/passband_ripple)**2 - 1
+
+ FN2 = ((1/mag**2) - 1)
+
+ return w/omega_c, FN2 / epsilon2, mag, a, b
+
+
+plt.figure(figsize=(4,2.5))
+
+for N in [5]:
+ w, FN2, mag, a, b = ellip_filter(N)
+ plt.semilogy(w, FN2, label=f"$N={N}, k=0.1$", linewidth=1)
+
+plt.gca().add_patch(Rectangle(
+ (0, 0),
+ 1, 1,
+ fc ='green',
+ alpha=0.2,
+ lw = 10,
+))
+plt.gca().add_patch(Rectangle(
+ (1, 1),
+ 0.01, 1e2-1,
+ fc ='orange',
+ alpha=0.2,
+ lw = 10,
+))
+
+plt.gca().add_patch(Rectangle(
+ (1.01, 100),
+ 1, 1e6,
+ fc ='red',
+ alpha=0.2,
+ lw = 10,
+))
+
+zeros = [0,0.87,1]
+poles = [1.01,1.155]
+
+import matplotlib.transforms
+plt.plot( # mark errors as vertical bars
+ zeros,
+ np.zeros_like(zeros),
+ "o",
+ mfc='none',
+ color='black',
+ transform=matplotlib.transforms.blended_transform_factory(
+ plt.gca().transData,
+ plt.gca().transAxes,
+ ),
+)
+plt.plot( # mark errors as vertical bars
+ poles,
+ np.ones_like(poles),
+ "x",
+ mfc='none',
+ color='black',
+ transform=matplotlib.transforms.blended_transform_factory(
+ plt.gca().transData,
+ plt.gca().transAxes,
+ ),
+)
+
+plt.xlim([0,2])
+plt.ylim([1e-4,1e6])
+plt.grid()
+plt.xlabel("$w$")
+plt.ylabel("$F^2_N(w)$")
+plt.legend()
+plt.tight_layout()
+plt.savefig("F_N_elliptic.pgf")
+plt.show()
+
+
+
+plt.figure(figsize=(4,2.5))
+plt.plot(w, mag, linewidth=1)
+
+plt.gca().add_patch(Rectangle(
+ (0, np.sqrt(2)/2),
+ 1, 1,
+ fc ='green',
+ alpha=0.2,
+ lw = 10,
+))
+plt.gca().add_patch(Rectangle(
+ (1, 0.1),
+ 0.01, np.sqrt(2)/2 - 0.1,
+ fc ='orange',
+ alpha=0.2,
+ lw = 10,
+))
+
+plt.gca().add_patch(Rectangle(
+ (1.01, 0),
+ 1, 0.1,
+ fc ='red',
+ alpha=0.2,
+ lw = 10,
+))
+
+plt.grid()
+plt.xlim([0,2])
+plt.ylim([0,1])
+plt.xlabel("$w$")
+plt.ylabel("$|H(w)|$")
+plt.tight_layout()
+plt.savefig("elliptic.pgf")
+plt.show()
+
+print("zeros", a)
+print("poles", b)
+
+
+
+
diff --git a/buch/papers/ellfilter/python/k.pgf b/buch/papers/ellfilter/python/k.pgf
new file mode 100644
index 0000000..95d61d4
--- /dev/null
+++ b/buch/papers/ellfilter/python/k.pgf
@@ -0,0 +1,1157 @@
+%% Creator: Matplotlib, PGF backend
+%%
+%% To include the figure in your LaTeX document, write
+%% \input{<filename>.pgf}
+%%
+%% Make sure the required packages are loaded in your preamble
+%% \usepackage{pgf}
+%%
+%% Also ensure that all the required font packages are loaded; for instance,
+%% the lmodern package is sometimes necessary when using math font.
+%% \usepackage{lmodern}
+%%
+%% Figures using additional raster images can only be included by \input if
+%% they are in the same directory as the main LaTeX file. For loading figures
+%% from other directories you can use the `import` package
+%% \usepackage{import}
+%%
+%% and then include the figures with
+%% \import{<path to file>}{<filename>.pgf}
+%%
+%% Matplotlib used the following preamble
+%%
+\begingroup%
+\makeatletter%
+\begin{pgfpicture}%
+\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{5.000000in}{2.500000in}}%
+\pgfusepath{use as bounding box, clip}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetmiterjoin%
+\pgfsetlinewidth{0.000000pt}%
+\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetstrokeopacity{0.000000}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{5.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{5.000000in}{2.500000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{2.500000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathclose%
+\pgfusepath{}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetmiterjoin%
+\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.000000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetstrokeopacity{0.000000}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.316407in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{2.256930in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{2.256930in}{2.301955in}}%
+\pgfpathlineto{\pgfqpoint{0.316407in}{2.301955in}}%
+\pgfpathlineto{\pgfqpoint{0.316407in}{0.548769in}}%
+\pgfpathclose%
+\pgfusepath{fill}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{0.316407in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.316407in,y=0.451547in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.00}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{0.801538in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.801538in,y=0.451547in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.25}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{1.286669in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=1.286669in,y=0.451547in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.50}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{1.771800in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=1.771800in,y=0.451547in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0.75}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{2.256930in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=2.256930in,y=0.451547in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {1.00}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=1.286669in,y=0.272534in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle k\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{0.316407in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.149740in, y=0.500544in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{0.316407in}{0.987065in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.149740in, y=0.938840in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {1}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{0.316407in}{1.425362in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.149740in, y=1.377137in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {2}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{0.316407in}{1.863658in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.149740in, y=1.815433in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {3}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{0.316407in}{2.301955in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.149740in, y=2.253730in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {4}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.316407in}{0.548769in}}{\pgfqpoint{1.940523in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.100375pt}%
+\definecolor{currentstroke}{rgb}{0.121569,0.466667,0.705882}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.316427in}{1.237243in}}%
+\pgfpathlineto{\pgfqpoint{0.316601in}{1.237243in}}%
+\pgfpathlineto{\pgfqpoint{0.318348in}{1.237244in}}%
+\pgfpathlineto{\pgfqpoint{0.335813in}{1.237261in}}%
+\pgfpathlineto{\pgfqpoint{0.355218in}{1.237312in}}%
+\pgfpathlineto{\pgfqpoint{0.374623in}{1.237398in}}%
+\pgfpathlineto{\pgfqpoint{0.394028in}{1.237519in}}%
+\pgfpathlineto{\pgfqpoint{0.413434in}{1.237674in}}%
+\pgfpathlineto{\pgfqpoint{0.432839in}{1.237864in}}%
+\pgfpathlineto{\pgfqpoint{0.452244in}{1.238089in}}%
+\pgfpathlineto{\pgfqpoint{0.471649in}{1.238349in}}%
+\pgfpathlineto{\pgfqpoint{0.491054in}{1.238644in}}%
+\pgfpathlineto{\pgfqpoint{0.510460in}{1.238974in}}%
+\pgfpathlineto{\pgfqpoint{0.529865in}{1.239340in}}%
+\pgfpathlineto{\pgfqpoint{0.549270in}{1.239742in}}%
+\pgfpathlineto{\pgfqpoint{0.568675in}{1.240180in}}%
+\pgfpathlineto{\pgfqpoint{0.588081in}{1.240655in}}%
+\pgfpathlineto{\pgfqpoint{0.607486in}{1.241166in}}%
+\pgfpathlineto{\pgfqpoint{0.626891in}{1.241714in}}%
+\pgfpathlineto{\pgfqpoint{0.646296in}{1.242300in}}%
+\pgfpathlineto{\pgfqpoint{0.665702in}{1.242924in}}%
+\pgfpathlineto{\pgfqpoint{0.685107in}{1.243586in}}%
+\pgfpathlineto{\pgfqpoint{0.704512in}{1.244287in}}%
+\pgfpathlineto{\pgfqpoint{0.723917in}{1.245028in}}%
+\pgfpathlineto{\pgfqpoint{0.743322in}{1.245809in}}%
+\pgfpathlineto{\pgfqpoint{0.762728in}{1.246630in}}%
+\pgfpathlineto{\pgfqpoint{0.782133in}{1.247492in}}%
+\pgfpathlineto{\pgfqpoint{0.801538in}{1.248396in}}%
+\pgfpathlineto{\pgfqpoint{0.820943in}{1.249343in}}%
+\pgfpathlineto{\pgfqpoint{0.840349in}{1.250333in}}%
+\pgfpathlineto{\pgfqpoint{0.859754in}{1.251367in}}%
+\pgfpathlineto{\pgfqpoint{0.879159in}{1.252446in}}%
+\pgfpathlineto{\pgfqpoint{0.898564in}{1.253571in}}%
+\pgfpathlineto{\pgfqpoint{0.917969in}{1.254743in}}%
+\pgfpathlineto{\pgfqpoint{0.937375in}{1.255962in}}%
+\pgfpathlineto{\pgfqpoint{0.956780in}{1.257230in}}%
+\pgfpathlineto{\pgfqpoint{0.976185in}{1.258548in}}%
+\pgfpathlineto{\pgfqpoint{0.995590in}{1.259917in}}%
+\pgfpathlineto{\pgfqpoint{1.014996in}{1.261339in}}%
+\pgfpathlineto{\pgfqpoint{1.034401in}{1.262814in}}%
+\pgfpathlineto{\pgfqpoint{1.053806in}{1.264344in}}%
+\pgfpathlineto{\pgfqpoint{1.073211in}{1.265930in}}%
+\pgfpathlineto{\pgfqpoint{1.092617in}{1.267575in}}%
+\pgfpathlineto{\pgfqpoint{1.112022in}{1.269279in}}%
+\pgfpathlineto{\pgfqpoint{1.131427in}{1.271045in}}%
+\pgfpathlineto{\pgfqpoint{1.150832in}{1.272874in}}%
+\pgfpathlineto{\pgfqpoint{1.170237in}{1.274768in}}%
+\pgfpathlineto{\pgfqpoint{1.189643in}{1.276729in}}%
+\pgfpathlineto{\pgfqpoint{1.209048in}{1.278760in}}%
+\pgfpathlineto{\pgfqpoint{1.228453in}{1.280863in}}%
+\pgfpathlineto{\pgfqpoint{1.247858in}{1.283040in}}%
+\pgfpathlineto{\pgfqpoint{1.267264in}{1.285294in}}%
+\pgfpathlineto{\pgfqpoint{1.286669in}{1.287627in}}%
+\pgfpathlineto{\pgfqpoint{1.306074in}{1.290044in}}%
+\pgfpathlineto{\pgfqpoint{1.325479in}{1.292546in}}%
+\pgfpathlineto{\pgfqpoint{1.344884in}{1.295137in}}%
+\pgfpathlineto{\pgfqpoint{1.364290in}{1.297822in}}%
+\pgfpathlineto{\pgfqpoint{1.383695in}{1.300603in}}%
+\pgfpathlineto{\pgfqpoint{1.403100in}{1.303485in}}%
+\pgfpathlineto{\pgfqpoint{1.422505in}{1.306473in}}%
+\pgfpathlineto{\pgfqpoint{1.441911in}{1.309570in}}%
+\pgfpathlineto{\pgfqpoint{1.461316in}{1.312784in}}%
+\pgfpathlineto{\pgfqpoint{1.480721in}{1.316118in}}%
+\pgfpathlineto{\pgfqpoint{1.500126in}{1.319579in}}%
+\pgfpathlineto{\pgfqpoint{1.519532in}{1.323174in}}%
+\pgfpathlineto{\pgfqpoint{1.538937in}{1.326910in}}%
+\pgfpathlineto{\pgfqpoint{1.558342in}{1.330793in}}%
+\pgfpathlineto{\pgfqpoint{1.577747in}{1.334833in}}%
+\pgfpathlineto{\pgfqpoint{1.597152in}{1.339039in}}%
+\pgfpathlineto{\pgfqpoint{1.616558in}{1.343420in}}%
+\pgfpathlineto{\pgfqpoint{1.635963in}{1.347988in}}%
+\pgfpathlineto{\pgfqpoint{1.655368in}{1.352753in}}%
+\pgfpathlineto{\pgfqpoint{1.674773in}{1.357730in}}%
+\pgfpathlineto{\pgfqpoint{1.694179in}{1.362933in}}%
+\pgfpathlineto{\pgfqpoint{1.713584in}{1.368377in}}%
+\pgfpathlineto{\pgfqpoint{1.732989in}{1.374081in}}%
+\pgfpathlineto{\pgfqpoint{1.752394in}{1.380064in}}%
+\pgfpathlineto{\pgfqpoint{1.771800in}{1.386349in}}%
+\pgfpathlineto{\pgfqpoint{1.791205in}{1.392961in}}%
+\pgfpathlineto{\pgfqpoint{1.810610in}{1.399927in}}%
+\pgfpathlineto{\pgfqpoint{1.830015in}{1.407281in}}%
+\pgfpathlineto{\pgfqpoint{1.849420in}{1.415059in}}%
+\pgfpathlineto{\pgfqpoint{1.868826in}{1.423303in}}%
+\pgfpathlineto{\pgfqpoint{1.888231in}{1.432062in}}%
+\pgfpathlineto{\pgfqpoint{1.907636in}{1.441392in}}%
+\pgfpathlineto{\pgfqpoint{1.927041in}{1.451361in}}%
+\pgfpathlineto{\pgfqpoint{1.946447in}{1.462048in}}%
+\pgfpathlineto{\pgfqpoint{1.965852in}{1.473546in}}%
+\pgfpathlineto{\pgfqpoint{1.985257in}{1.485971in}}%
+\pgfpathlineto{\pgfqpoint{2.004662in}{1.499462in}}%
+\pgfpathlineto{\pgfqpoint{2.024067in}{1.514194in}}%
+\pgfpathlineto{\pgfqpoint{2.043473in}{1.530388in}}%
+\pgfpathlineto{\pgfqpoint{2.062878in}{1.548326in}}%
+\pgfpathlineto{\pgfqpoint{2.082283in}{1.568383in}}%
+\pgfpathlineto{\pgfqpoint{2.101688in}{1.591069in}}%
+\pgfpathlineto{\pgfqpoint{2.121094in}{1.617098in}}%
+\pgfpathlineto{\pgfqpoint{2.140499in}{1.647519in}}%
+\pgfpathlineto{\pgfqpoint{2.159904in}{1.683962in}}%
+\pgfpathlineto{\pgfqpoint{2.179309in}{1.729164in}}%
+\pgfpathlineto{\pgfqpoint{2.198715in}{1.788269in}}%
+\pgfpathlineto{\pgfqpoint{2.218120in}{1.872854in}}%
+\pgfpathlineto{\pgfqpoint{2.237525in}{2.019955in}}%
+\pgfpathlineto{\pgfqpoint{2.247876in}{2.315844in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{0.316407in}{0.548769in}}{\pgfqpoint{1.940523in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.100375pt}%
+\definecolor{currentstroke}{rgb}{1.000000,0.498039,0.054902}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.454821in}{2.315844in}}%
+\pgfpathlineto{\pgfqpoint{0.471649in}{2.265444in}}%
+\pgfpathlineto{\pgfqpoint{0.491054in}{2.214262in}}%
+\pgfpathlineto{\pgfqpoint{0.510460in}{2.168554in}}%
+\pgfpathlineto{\pgfqpoint{0.529865in}{2.127278in}}%
+\pgfpathlineto{\pgfqpoint{0.549270in}{2.089666in}}%
+\pgfpathlineto{\pgfqpoint{0.568675in}{2.055132in}}%
+\pgfpathlineto{\pgfqpoint{0.588081in}{2.023222in}}%
+\pgfpathlineto{\pgfqpoint{0.607486in}{1.993575in}}%
+\pgfpathlineto{\pgfqpoint{0.626891in}{1.965899in}}%
+\pgfpathlineto{\pgfqpoint{0.646296in}{1.939958in}}%
+\pgfpathlineto{\pgfqpoint{0.665702in}{1.915554in}}%
+\pgfpathlineto{\pgfqpoint{0.685107in}{1.892522in}}%
+\pgfpathlineto{\pgfqpoint{0.704512in}{1.870720in}}%
+\pgfpathlineto{\pgfqpoint{0.723917in}{1.850031in}}%
+\pgfpathlineto{\pgfqpoint{0.743322in}{1.830351in}}%
+\pgfpathlineto{\pgfqpoint{0.762728in}{1.811591in}}%
+\pgfpathlineto{\pgfqpoint{0.782133in}{1.793672in}}%
+\pgfpathlineto{\pgfqpoint{0.801538in}{1.776528in}}%
+\pgfpathlineto{\pgfqpoint{0.820943in}{1.760096in}}%
+\pgfpathlineto{\pgfqpoint{0.840349in}{1.744324in}}%
+\pgfpathlineto{\pgfqpoint{0.859754in}{1.729164in}}%
+\pgfpathlineto{\pgfqpoint{0.879159in}{1.714573in}}%
+\pgfpathlineto{\pgfqpoint{0.898564in}{1.700513in}}%
+\pgfpathlineto{\pgfqpoint{0.917969in}{1.686948in}}%
+\pgfpathlineto{\pgfqpoint{0.937375in}{1.673849in}}%
+\pgfpathlineto{\pgfqpoint{0.956780in}{1.661185in}}%
+\pgfpathlineto{\pgfqpoint{0.976185in}{1.648932in}}%
+\pgfpathlineto{\pgfqpoint{0.995590in}{1.637065in}}%
+\pgfpathlineto{\pgfqpoint{1.014996in}{1.625563in}}%
+\pgfpathlineto{\pgfqpoint{1.034401in}{1.614406in}}%
+\pgfpathlineto{\pgfqpoint{1.053806in}{1.603575in}}%
+\pgfpathlineto{\pgfqpoint{1.073211in}{1.593053in}}%
+\pgfpathlineto{\pgfqpoint{1.092617in}{1.582826in}}%
+\pgfpathlineto{\pgfqpoint{1.112022in}{1.572877in}}%
+\pgfpathlineto{\pgfqpoint{1.131427in}{1.563195in}}%
+\pgfpathlineto{\pgfqpoint{1.150832in}{1.553766in}}%
+\pgfpathlineto{\pgfqpoint{1.170237in}{1.544578in}}%
+\pgfpathlineto{\pgfqpoint{1.189643in}{1.535621in}}%
+\pgfpathlineto{\pgfqpoint{1.209048in}{1.526884in}}%
+\pgfpathlineto{\pgfqpoint{1.228453in}{1.518359in}}%
+\pgfpathlineto{\pgfqpoint{1.247858in}{1.510036in}}%
+\pgfpathlineto{\pgfqpoint{1.267264in}{1.501906in}}%
+\pgfpathlineto{\pgfqpoint{1.286669in}{1.493962in}}%
+\pgfpathlineto{\pgfqpoint{1.306074in}{1.486197in}}%
+\pgfpathlineto{\pgfqpoint{1.325479in}{1.478603in}}%
+\pgfpathlineto{\pgfqpoint{1.344884in}{1.471174in}}%
+\pgfpathlineto{\pgfqpoint{1.364290in}{1.463903in}}%
+\pgfpathlineto{\pgfqpoint{1.383695in}{1.456785in}}%
+\pgfpathlineto{\pgfqpoint{1.403100in}{1.449815in}}%
+\pgfpathlineto{\pgfqpoint{1.422505in}{1.442986in}}%
+\pgfpathlineto{\pgfqpoint{1.441911in}{1.436294in}}%
+\pgfpathlineto{\pgfqpoint{1.461316in}{1.429735in}}%
+\pgfpathlineto{\pgfqpoint{1.480721in}{1.423303in}}%
+\pgfpathlineto{\pgfqpoint{1.500126in}{1.416995in}}%
+\pgfpathlineto{\pgfqpoint{1.519532in}{1.410805in}}%
+\pgfpathlineto{\pgfqpoint{1.538937in}{1.404732in}}%
+\pgfpathlineto{\pgfqpoint{1.558342in}{1.398770in}}%
+\pgfpathlineto{\pgfqpoint{1.577747in}{1.392916in}}%
+\pgfpathlineto{\pgfqpoint{1.597152in}{1.387167in}}%
+\pgfpathlineto{\pgfqpoint{1.616558in}{1.381520in}}%
+\pgfpathlineto{\pgfqpoint{1.635963in}{1.375971in}}%
+\pgfpathlineto{\pgfqpoint{1.655368in}{1.370518in}}%
+\pgfpathlineto{\pgfqpoint{1.674773in}{1.365158in}}%
+\pgfpathlineto{\pgfqpoint{1.694179in}{1.359888in}}%
+\pgfpathlineto{\pgfqpoint{1.713584in}{1.354705in}}%
+\pgfpathlineto{\pgfqpoint{1.732989in}{1.349607in}}%
+\pgfpathlineto{\pgfqpoint{1.752394in}{1.344593in}}%
+\pgfpathlineto{\pgfqpoint{1.771800in}{1.339658in}}%
+\pgfpathlineto{\pgfqpoint{1.791205in}{1.334802in}}%
+\pgfpathlineto{\pgfqpoint{1.810610in}{1.330022in}}%
+\pgfpathlineto{\pgfqpoint{1.830015in}{1.325316in}}%
+\pgfpathlineto{\pgfqpoint{1.849420in}{1.320682in}}%
+\pgfpathlineto{\pgfqpoint{1.868826in}{1.316118in}}%
+\pgfpathlineto{\pgfqpoint{1.888231in}{1.311623in}}%
+\pgfpathlineto{\pgfqpoint{1.907636in}{1.307195in}}%
+\pgfpathlineto{\pgfqpoint{1.927041in}{1.302831in}}%
+\pgfpathlineto{\pgfqpoint{1.946447in}{1.298531in}}%
+\pgfpathlineto{\pgfqpoint{1.965852in}{1.294293in}}%
+\pgfpathlineto{\pgfqpoint{1.985257in}{1.290116in}}%
+\pgfpathlineto{\pgfqpoint{2.004662in}{1.285997in}}%
+\pgfpathlineto{\pgfqpoint{2.024067in}{1.281936in}}%
+\pgfpathlineto{\pgfqpoint{2.043473in}{1.277931in}}%
+\pgfpathlineto{\pgfqpoint{2.062878in}{1.273982in}}%
+\pgfpathlineto{\pgfqpoint{2.082283in}{1.270085in}}%
+\pgfpathlineto{\pgfqpoint{2.101688in}{1.266241in}}%
+\pgfpathlineto{\pgfqpoint{2.121094in}{1.262449in}}%
+\pgfpathlineto{\pgfqpoint{2.140499in}{1.258706in}}%
+\pgfpathlineto{\pgfqpoint{2.159904in}{1.255013in}}%
+\pgfpathlineto{\pgfqpoint{2.179309in}{1.251367in}}%
+\pgfpathlineto{\pgfqpoint{2.198715in}{1.247768in}}%
+\pgfpathlineto{\pgfqpoint{2.218120in}{1.244215in}}%
+\pgfpathlineto{\pgfqpoint{2.237525in}{1.240707in}}%
+\pgfpathlineto{\pgfqpoint{2.254990in}{1.237588in}}%
+\pgfpathlineto{\pgfqpoint{2.256736in}{1.237278in}}%
+\pgfpathlineto{\pgfqpoint{2.256911in}{1.237247in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetmiterjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.316407in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{0.316407in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetmiterjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{2.256930in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{2.256930in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetmiterjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.316407in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{2.256930in}{0.548769in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetmiterjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{0.316407in}{2.301955in}}%
+\pgfpathlineto{\pgfqpoint{2.256930in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.859754in,y=1.295197in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle K\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=0.859754in,y=1.772994in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle K^\prime\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetmiterjoin%
+\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.000000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetstrokeopacity{0.000000}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{2.874885in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{4.815407in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{4.815407in}{2.301955in}}%
+\pgfpathlineto{\pgfqpoint{2.874885in}{2.301955in}}%
+\pgfpathlineto{\pgfqpoint{2.874885in}{0.548769in}}%
+\pgfpathclose%
+\pgfusepath{fill}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{2.874885in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=2.874885in,y=0.451547in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{3.521726in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=3.521726in,y=0.451547in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {2}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{4.168566in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=4.168566in,y=0.451547in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {4}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{4.815407in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=4.815407in,y=0.451547in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {6}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=3.845146in,y=0.272534in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle K\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{2.874885in}{0.548769in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=2.708218in, y=0.500544in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {0}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{2.874885in}{0.899406in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=2.708218in, y=0.851181in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {1}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{2.874885in}{1.250043in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=2.708218in, y=1.201818in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {2}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{2.874885in}{1.600680in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=2.708218in, y=1.552455in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {3}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{2.874885in}{1.951318in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=2.708218in, y=1.903092in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {4}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{%
+\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}%
+\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{2.874885in}{2.301955in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=2.708218in, y=2.253730in, left, base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {5}\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=2.652662in,y=1.425362in,,bottom,rotate=90.000000]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle K^\prime\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{2.874885in}{0.548769in}}{\pgfqpoint{1.940523in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.501875pt}%
+\definecolor{currentstroke}{rgb}{0.501961,0.501961,0.501961}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{3.382912in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{3.382912in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{2.874885in}{0.548769in}}{\pgfqpoint{1.940523in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{0.501875pt}%
+\definecolor{currentstroke}{rgb}{0.501961,0.501961,0.501961}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{2.874885in}{1.099548in}}%
+\pgfpathlineto{\pgfqpoint{4.815407in}{1.099548in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{2.874885in}{0.548769in}}{\pgfqpoint{1.940523in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetrectcap%
+\pgfsetroundjoin%
+\pgfsetlinewidth{1.003750pt}%
+\definecolor{currentstroke}{rgb}{0.121569,0.466667,0.705882}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{3.383004in}{2.315844in}}%
+\pgfpathlineto{\pgfqpoint{3.383027in}{2.264692in}}%
+\pgfpathlineto{\pgfqpoint{3.383116in}{2.164019in}}%
+\pgfpathlineto{\pgfqpoint{3.383230in}{2.086013in}}%
+\pgfpathlineto{\pgfqpoint{3.383370in}{2.022353in}}%
+\pgfpathlineto{\pgfqpoint{3.383536in}{1.968602in}}%
+\pgfpathlineto{\pgfqpoint{3.383728in}{1.922109in}}%
+\pgfpathlineto{\pgfqpoint{3.383946in}{1.881163in}}%
+\pgfpathlineto{\pgfqpoint{3.384190in}{1.844597in}}%
+\pgfpathlineto{\pgfqpoint{3.384460in}{1.811577in}}%
+\pgfpathlineto{\pgfqpoint{3.384756in}{1.781487in}}%
+\pgfpathlineto{\pgfqpoint{3.385079in}{1.753859in}}%
+\pgfpathlineto{\pgfqpoint{3.385429in}{1.728331in}}%
+\pgfpathlineto{\pgfqpoint{3.385807in}{1.704613in}}%
+\pgfpathlineto{\pgfqpoint{3.386211in}{1.682473in}}%
+\pgfpathlineto{\pgfqpoint{3.386644in}{1.661720in}}%
+\pgfpathlineto{\pgfqpoint{3.387104in}{1.642197in}}%
+\pgfpathlineto{\pgfqpoint{3.387593in}{1.623771in}}%
+\pgfpathlineto{\pgfqpoint{3.388110in}{1.606330in}}%
+\pgfpathlineto{\pgfqpoint{3.388657in}{1.589779in}}%
+\pgfpathlineto{\pgfqpoint{3.389233in}{1.574035in}}%
+\pgfpathlineto{\pgfqpoint{3.389839in}{1.559026in}}%
+\pgfpathlineto{\pgfqpoint{3.390475in}{1.544692in}}%
+\pgfpathlineto{\pgfqpoint{3.391142in}{1.530976in}}%
+\pgfpathlineto{\pgfqpoint{3.391841in}{1.517831in}}%
+\pgfpathlineto{\pgfqpoint{3.392571in}{1.505213in}}%
+\pgfpathlineto{\pgfqpoint{3.393334in}{1.493085in}}%
+\pgfpathlineto{\pgfqpoint{3.394130in}{1.481412in}}%
+\pgfpathlineto{\pgfqpoint{3.394960in}{1.470164in}}%
+\pgfpathlineto{\pgfqpoint{3.395825in}{1.459313in}}%
+\pgfpathlineto{\pgfqpoint{3.396725in}{1.448833in}}%
+\pgfpathlineto{\pgfqpoint{3.397661in}{1.438702in}}%
+\pgfpathlineto{\pgfqpoint{3.398633in}{1.428899in}}%
+\pgfpathlineto{\pgfqpoint{3.399643in}{1.419406in}}%
+\pgfpathlineto{\pgfqpoint{3.400692in}{1.410204in}}%
+\pgfpathlineto{\pgfqpoint{3.401781in}{1.401278in}}%
+\pgfpathlineto{\pgfqpoint{3.402910in}{1.392614in}}%
+\pgfpathlineto{\pgfqpoint{3.404081in}{1.384197in}}%
+\pgfpathlineto{\pgfqpoint{3.405294in}{1.376014in}}%
+\pgfpathlineto{\pgfqpoint{3.406552in}{1.368056in}}%
+\pgfpathlineto{\pgfqpoint{3.407855in}{1.360310in}}%
+\pgfpathlineto{\pgfqpoint{3.409204in}{1.352766in}}%
+\pgfpathlineto{\pgfqpoint{3.410602in}{1.345416in}}%
+\pgfpathlineto{\pgfqpoint{3.412049in}{1.338250in}}%
+\pgfpathlineto{\pgfqpoint{3.413548in}{1.331261in}}%
+\pgfpathlineto{\pgfqpoint{3.415099in}{1.324441in}}%
+\pgfpathlineto{\pgfqpoint{3.416706in}{1.317782in}}%
+\pgfpathlineto{\pgfqpoint{3.418369in}{1.311279in}}%
+\pgfpathlineto{\pgfqpoint{3.420091in}{1.304923in}}%
+\pgfpathlineto{\pgfqpoint{3.421874in}{1.298711in}}%
+\pgfpathlineto{\pgfqpoint{3.423720in}{1.292636in}}%
+\pgfpathlineto{\pgfqpoint{3.425632in}{1.286693in}}%
+\pgfpathlineto{\pgfqpoint{3.427613in}{1.280876in}}%
+\pgfpathlineto{\pgfqpoint{3.429665in}{1.275182in}}%
+\pgfpathlineto{\pgfqpoint{3.431792in}{1.269606in}}%
+\pgfpathlineto{\pgfqpoint{3.433997in}{1.264143in}}%
+\pgfpathlineto{\pgfqpoint{3.436283in}{1.258789in}}%
+\pgfpathlineto{\pgfqpoint{3.438654in}{1.253542in}}%
+\pgfpathlineto{\pgfqpoint{3.441114in}{1.248396in}}%
+\pgfpathlineto{\pgfqpoint{3.443668in}{1.243349in}}%
+\pgfpathlineto{\pgfqpoint{3.446321in}{1.238398in}}%
+\pgfpathlineto{\pgfqpoint{3.449077in}{1.233539in}}%
+\pgfpathlineto{\pgfqpoint{3.451943in}{1.228770in}}%
+\pgfpathlineto{\pgfqpoint{3.454924in}{1.224087in}}%
+\pgfpathlineto{\pgfqpoint{3.458028in}{1.219487in}}%
+\pgfpathlineto{\pgfqpoint{3.461261in}{1.214970in}}%
+\pgfpathlineto{\pgfqpoint{3.464631in}{1.210531in}}%
+\pgfpathlineto{\pgfqpoint{3.468147in}{1.206168in}}%
+\pgfpathlineto{\pgfqpoint{3.471820in}{1.201880in}}%
+\pgfpathlineto{\pgfqpoint{3.475659in}{1.197664in}}%
+\pgfpathlineto{\pgfqpoint{3.479676in}{1.193518in}}%
+\pgfpathlineto{\pgfqpoint{3.483885in}{1.189440in}}%
+\pgfpathlineto{\pgfqpoint{3.488300in}{1.185428in}}%
+\pgfpathlineto{\pgfqpoint{3.492938in}{1.181480in}}%
+\pgfpathlineto{\pgfqpoint{3.497817in}{1.177595in}}%
+\pgfpathlineto{\pgfqpoint{3.502957in}{1.173771in}}%
+\pgfpathlineto{\pgfqpoint{3.508384in}{1.170006in}}%
+\pgfpathlineto{\pgfqpoint{3.514123in}{1.166299in}}%
+\pgfpathlineto{\pgfqpoint{3.520206in}{1.162648in}}%
+\pgfpathlineto{\pgfqpoint{3.526670in}{1.159052in}}%
+\pgfpathlineto{\pgfqpoint{3.533555in}{1.155509in}}%
+\pgfpathlineto{\pgfqpoint{3.540911in}{1.152019in}}%
+\pgfpathlineto{\pgfqpoint{3.548796in}{1.148579in}}%
+\pgfpathlineto{\pgfqpoint{3.557281in}{1.145189in}}%
+\pgfpathlineto{\pgfqpoint{3.566449in}{1.141846in}}%
+\pgfpathlineto{\pgfqpoint{3.576405in}{1.138552in}}%
+\pgfpathlineto{\pgfqpoint{3.587275in}{1.135303in}}%
+\pgfpathlineto{\pgfqpoint{3.599224in}{1.132099in}}%
+\pgfpathlineto{\pgfqpoint{3.612461in}{1.128939in}}%
+\pgfpathlineto{\pgfqpoint{3.627261in}{1.125822in}}%
+\pgfpathlineto{\pgfqpoint{3.644002in}{1.122747in}}%
+\pgfpathlineto{\pgfqpoint{3.663208in}{1.119713in}}%
+\pgfpathlineto{\pgfqpoint{3.685656in}{1.116719in}}%
+\pgfpathlineto{\pgfqpoint{3.712547in}{1.113764in}}%
+\pgfpathlineto{\pgfqpoint{3.745902in}{1.110847in}}%
+\pgfpathlineto{\pgfqpoint{3.789516in}{1.107968in}}%
+\pgfpathlineto{\pgfqpoint{3.851932in}{1.105126in}}%
+\pgfpathlineto{\pgfqpoint{3.960478in}{1.102320in}}%
+\pgfpathlineto{\pgfqpoint{4.328852in}{1.099824in}}%
+\pgfpathlineto{\pgfqpoint{4.700641in}{1.099576in}}%
+\pgfpathlineto{\pgfqpoint{4.829296in}{1.099567in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfpathrectangle{\pgfqpoint{2.874885in}{0.548769in}}{\pgfqpoint{1.940523in}{1.753186in}}%
+\pgfusepath{clip}%
+\pgfsetbuttcap%
+\pgfsetroundjoin%
+\definecolor{currentfill}{rgb}{0.121569,0.466667,0.705882}%
+\pgfsetfillcolor{currentfill}%
+\pgfsetlinewidth{1.003750pt}%
+\definecolor{currentstroke}{rgb}{0.121569,0.466667,0.705882}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.006944in}{-0.006944in}}{\pgfqpoint{0.006944in}{0.006944in}}{%
+\pgfpathmoveto{\pgfqpoint{0.000000in}{-0.006944in}}%
+\pgfpathcurveto{\pgfqpoint{0.001842in}{-0.006944in}}{\pgfqpoint{0.003608in}{-0.006213in}}{\pgfqpoint{0.004910in}{-0.004910in}}%
+\pgfpathcurveto{\pgfqpoint{0.006213in}{-0.003608in}}{\pgfqpoint{0.006944in}{-0.001842in}}{\pgfqpoint{0.006944in}{0.000000in}}%
+\pgfpathcurveto{\pgfqpoint{0.006944in}{0.001842in}}{\pgfqpoint{0.006213in}{0.003608in}}{\pgfqpoint{0.004910in}{0.004910in}}%
+\pgfpathcurveto{\pgfqpoint{0.003608in}{0.006213in}}{\pgfqpoint{0.001842in}{0.006944in}}{\pgfqpoint{0.000000in}{0.006944in}}%
+\pgfpathcurveto{\pgfqpoint{-0.001842in}{0.006944in}}{\pgfqpoint{-0.003608in}{0.006213in}}{\pgfqpoint{-0.004910in}{0.004910in}}%
+\pgfpathcurveto{\pgfqpoint{-0.006213in}{0.003608in}}{\pgfqpoint{-0.006944in}{0.001842in}}{\pgfqpoint{-0.006944in}{0.000000in}}%
+\pgfpathcurveto{\pgfqpoint{-0.006944in}{-0.001842in}}{\pgfqpoint{-0.006213in}{-0.003608in}}{\pgfqpoint{-0.004910in}{-0.004910in}}%
+\pgfpathcurveto{\pgfqpoint{-0.003608in}{-0.006213in}}{\pgfqpoint{-0.001842in}{-0.006944in}}{\pgfqpoint{0.000000in}{-0.006944in}}%
+\pgfpathlineto{\pgfqpoint{0.000000in}{-0.006944in}}%
+\pgfpathclose%
+\pgfusepath{stroke,fill}%
+}%
+\begin{pgfscope}%
+\pgfsys@transformshift{3.384190in}{1.844597in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsys@transformshift{3.388110in}{1.606330in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsys@transformshift{3.405294in}{1.376014in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsys@transformshift{3.441114in}{1.248396in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsys@transformshift{3.612461in}{1.128939in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsys@transformshift{3.960478in}{1.102320in}%
+\pgfsys@useobject{currentmarker}{}%
+\end{pgfscope}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetmiterjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{2.874885in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{2.874885in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetmiterjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{4.815407in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{4.815407in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetmiterjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{2.874885in}{0.548769in}}%
+\pgfpathlineto{\pgfqpoint{4.815407in}{0.548769in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\pgfsetrectcap%
+\pgfsetmiterjoin%
+\pgfsetlinewidth{0.803000pt}%
+\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{2.874885in}{2.301955in}}%
+\pgfpathlineto{\pgfqpoint{4.815407in}{2.301955in}}%
+\pgfusepath{stroke}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=2.907227in,y=1.134612in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle \pi/2\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=3.415254in,y=0.583833in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle \pi/2\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=3.416532in,y=1.879661in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle k=0.10\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=3.420452in,y=1.641394in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle k=0.20\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=3.437636in,y=1.411078in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle k=0.40\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=3.473456in,y=1.283460in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle k=0.60\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=3.644803in,y=1.164003in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle k=0.90\)}%
+\end{pgfscope}%
+\begin{pgfscope}%
+\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{textcolor}%
+\pgfsetfillcolor{textcolor}%
+\pgftext[x=3.992820in,y=1.137383in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle k=0.99\)}%
+\end{pgfscope}%
+\end{pgfpicture}%
+\makeatother%
+\endgroup%
diff --git a/buch/papers/ellfilter/python/plot_params.py b/buch/papers/ellfilter/python/plot_params.py
new file mode 100644
index 0000000..4ddd1d8
--- /dev/null
+++ b/buch/papers/ellfilter/python/plot_params.py
@@ -0,0 +1,9 @@
+import matplotlib
+
+matplotlib.rcParams.update({
+ "pgf.texsystem": "pdflatex",
+ 'font.family': 'serif',
+ 'font.size': 9,
+ 'text.usetex': True,
+ 'pgf.rcfonts': False,
+})
diff --git a/buch/papers/ellfilter/references.bib b/buch/papers/ellfilter/references.bib
index 81b3577..8f21971 100644
--- a/buch/papers/ellfilter/references.bib
+++ b/buch/papers/ellfilter/references.bib
@@ -4,32 +4,19 @@
% (c) 2020 Autor, Hochschule Rapperswil
%
-@online{ellfilter:bibtex,
- title = {BibTeX},
- url = {https://de.wikipedia.org/wiki/BibTeX},
- date = {2020-02-06},
- year = {2020},
- month = {2},
- day = {6}
-}
-
-@book{ellfilter:numerical-analysis,
- title = {Numerical Analysis},
- author = {David Kincaid and Ward Cheney},
- publisher = {American Mathematical Society},
- year = {2002},
- isbn = {978-8-8218-4788-6},
- inseries = {Pure and applied undegraduate texts},
- volume = {2}
-}
-
-@article{ellfilter:mendezmueller,
- author = { Tabea Méndez and Andreas Müller },
- title = { Noncommutative harmonic analysis and image registration },
- journal = { Appl. Comput. Harmon. Anal.},
- year = 2019,
- volume = 47,
- pages = {607--627},
- url = {https://doi.org/10.1016/j.acha.2017.11.004}
+@online{ellfilter:bib:orfanidis,
+ author = { Sophocles J. Orfanidis},
+ title = { LECTURE NOTES ON ELLIPTIC FILTER DESIGN },
+ year = 2006,
+ url = {https://www.ece.rutgers.edu/~orfanidi/ece521/notes.pdf}
}
+% Schwalm
+% https://en.wikipedia.org/wiki/Elliptic_rational_functions
+% https://en.wikipedia.org/wiki/Rational_function
+% https://en.wikipedia.org/wiki/Jacobi_elliptic_functions
+% https://de.wikipedia.org/wiki/Elliptisches_Integral
+% https://de.wikipedia.org/wiki/Tschebyschow-Polynom
+% https://en.wikipedia.org/wiki/Chebyshev_filter
+% https://mathworld.wolfram.com/JacobiEllipticFunctions.html
+% https://mathworld.wolfram.com/EllipticIntegraloftheFirstKind.html
diff --git a/buch/papers/ellfilter/teil0.tex b/buch/papers/ellfilter/teil0.tex
deleted file mode 100644
index fd04ba9..0000000
--- a/buch/papers/ellfilter/teil0.tex
+++ /dev/null
@@ -1,22 +0,0 @@
-%
-% einleitung.tex -- Beispiel-File für die Einleitung
-%
-% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil
-%
-\section{Teil 0\label{ellfilter:section:teil0}}
-\rhead{Teil 0}
-Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam
-nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam
-erat, sed diam voluptua \cite{ellfilter:bibtex}.
-At vero eos et accusam et justo duo dolores et ea rebum.
-Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum
-dolor sit amet.
-
-Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam
-nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam
-erat, sed diam voluptua.
-At vero eos et accusam et justo duo dolores et ea rebum. Stet clita
-kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit
-amet.
-
-
diff --git a/buch/papers/ellfilter/teil1.tex b/buch/papers/ellfilter/teil1.tex
deleted file mode 100644
index 7e62a2f..0000000
--- a/buch/papers/ellfilter/teil1.tex
+++ /dev/null
@@ -1,55 +0,0 @@
-%
-% teil1.tex -- Beispiel-File für das Paper
-%
-% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil
-%
-\section{Teil 1
-\label{ellfilter:section:teil1}}
-\rhead{Problemstellung}
-Sed ut perspiciatis unde omnis iste natus error sit voluptatem
-accusantium doloremque laudantium, totam rem aperiam, eaque ipsa
-quae ab illo inventore veritatis et quasi architecto beatae vitae
-dicta sunt explicabo.
-Nemo enim ipsam voluptatem quia voluptas sit aspernatur aut odit
-aut fugit, sed quia consequuntur magni dolores eos qui ratione
-voluptatem sequi nesciunt
-\begin{equation}
-\int_a^b x^2\, dx
-=
-\left[ \frac13 x^3 \right]_a^b
-=
-\frac{b^3-a^3}3.
-\label{ellfilter:equation1}
-\end{equation}
-Neque porro quisquam est, qui dolorem ipsum quia dolor sit amet,
-consectetur, adipisci velit, sed quia non numquam eius modi tempora
-incidunt ut labore et dolore magnam aliquam quaerat voluptatem.
-
-Ut enim ad minima veniam, quis nostrum exercitationem ullam corporis
-suscipit laboriosam, nisi ut aliquid ex ea commodi consequatur?
-Quis autem vel eum iure reprehenderit qui in ea voluptate velit
-esse quam nihil molestiae consequatur, vel illum qui dolorem eum
-fugiat quo voluptas nulla pariatur?
-
-\subsection{De finibus bonorum et malorum
-\label{ellfilter:subsection:finibus}}
-At vero eos et accusamus et iusto odio dignissimos ducimus qui
-blanditiis praesentium voluptatum deleniti atque corrupti quos
-dolores et quas molestias excepturi sint occaecati cupiditate non
-provident, similique sunt in culpa qui officia deserunt mollitia
-animi, id est laborum et dolorum fuga \eqref{000tempmlate:equation1}.
-
-Et harum quidem rerum facilis est et expedita distinctio
-\ref{ellfilter:section:loesung}.
-Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil
-impedit quo minus id quod maxime placeat facere possimus, omnis
-voluptas assumenda est, omnis dolor repellendus
-\ref{ellfilter:section:folgerung}.
-Temporibus autem quibusdam et aut officiis debitis aut rerum
-necessitatibus saepe eveniet ut et voluptates repudiandae sint et
-molestiae non recusandae.
-Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis
-voluptatibus maiores alias consequatur aut perferendis doloribus
-asperiores repellat.
-
-
diff --git a/buch/papers/ellfilter/teil2.tex b/buch/papers/ellfilter/teil2.tex
deleted file mode 100644
index 71fdc6d..0000000
--- a/buch/papers/ellfilter/teil2.tex
+++ /dev/null
@@ -1,40 +0,0 @@
-%
-% teil2.tex -- Beispiel-File für teil2
-%
-% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil
-%
-\section{Teil 2
-\label{ellfilter:section:teil2}}
-\rhead{Teil 2}
-Sed ut perspiciatis unde omnis iste natus error sit voluptatem
-accusantium doloremque laudantium, totam rem aperiam, eaque ipsa
-quae ab illo inventore veritatis et quasi architecto beatae vitae
-dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit
-aspernatur aut odit aut fugit, sed quia consequuntur magni dolores
-eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam
-est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci
-velit, sed quia non numquam eius modi tempora incidunt ut labore
-et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima
-veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam,
-nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure
-reprehenderit qui in ea voluptate velit esse quam nihil molestiae
-consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla
-pariatur?
-
-\subsection{De finibus bonorum et malorum
-\label{ellfilter:subsection:bonorum}}
-At vero eos et accusamus et iusto odio dignissimos ducimus qui
-blanditiis praesentium voluptatum deleniti atque corrupti quos
-dolores et quas molestias excepturi sint occaecati cupiditate non
-provident, similique sunt in culpa qui officia deserunt mollitia
-animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis
-est et expedita distinctio. Nam libero tempore, cum soluta nobis
-est eligendi optio cumque nihil impedit quo minus id quod maxime
-placeat facere possimus, omnis voluptas assumenda est, omnis dolor
-repellendus. Temporibus autem quibusdam et aut officiis debitis aut
-rerum necessitatibus saepe eveniet ut et voluptates repudiandae
-sint et molestiae non recusandae. Itaque earum rerum hic tenetur a
-sapiente delectus, ut aut reiciendis voluptatibus maiores alias
-consequatur aut perferendis doloribus asperiores repellat.
-
-
diff --git a/buch/papers/ellfilter/teil3.tex b/buch/papers/ellfilter/teil3.tex
deleted file mode 100644
index 79a5f3d..0000000
--- a/buch/papers/ellfilter/teil3.tex
+++ /dev/null
@@ -1,40 +0,0 @@
-%
-% teil3.tex -- Beispiel-File für Teil 3
-%
-% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil
-%
-\section{Teil 3
-\label{ellfilter:section:teil3}}
-\rhead{Teil 3}
-Sed ut perspiciatis unde omnis iste natus error sit voluptatem
-accusantium doloremque laudantium, totam rem aperiam, eaque ipsa
-quae ab illo inventore veritatis et quasi architecto beatae vitae
-dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit
-aspernatur aut odit aut fugit, sed quia consequuntur magni dolores
-eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam
-est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci
-velit, sed quia non numquam eius modi tempora incidunt ut labore
-et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima
-veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam,
-nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure
-reprehenderit qui in ea voluptate velit esse quam nihil molestiae
-consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla
-pariatur?
-
-\subsection{De finibus bonorum et malorum
-\label{ellfilter:subsection:malorum}}
-At vero eos et accusamus et iusto odio dignissimos ducimus qui
-blanditiis praesentium voluptatum deleniti atque corrupti quos
-dolores et quas molestias excepturi sint occaecati cupiditate non
-provident, similique sunt in culpa qui officia deserunt mollitia
-animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis
-est et expedita distinctio. Nam libero tempore, cum soluta nobis
-est eligendi optio cumque nihil impedit quo minus id quod maxime
-placeat facere possimus, omnis voluptas assumenda est, omnis dolor
-repellendus. Temporibus autem quibusdam et aut officiis debitis aut
-rerum necessitatibus saepe eveniet ut et voluptates repudiandae
-sint et molestiae non recusandae. Itaque earum rerum hic tenetur a
-sapiente delectus, ut aut reiciendis voluptatibus maiores alias
-consequatur aut perferendis doloribus asperiores repellat.
-
-
diff --git a/buch/papers/ellfilter/tikz/arccos.tikz.tex b/buch/papers/ellfilter/tikz/arccos.tikz.tex
new file mode 100644
index 0000000..2772620
--- /dev/null
+++ b/buch/papers/ellfilter/tikz/arccos.tikz.tex
@@ -0,0 +1,66 @@
+\begin{tikzpicture}[>=stealth', auto, node distance=2cm, scale=1.2]
+
+ \tikzstyle{zero} = [draw, circle, inner sep =0, minimum height=0.15cm]
+ \tikzset{pole/.style={cross out, draw=black, minimum size=(0.15cm-\pgflinewidth), inner sep=0pt, outer sep=0pt}}
+
+ \draw[gray, ->] (0,-2) -- (0,2) node[anchor=south]{$\mathrm{Im}~z$};
+ \draw[gray, ->] (-5,0) -- (5,0) node[anchor=west]{$\mathrm{Re}~z$};
+
+ \begin{scope}[xscale=0.6]
+
+ \clip(-7.5,-2) rectangle (7.5,2);
+
+ \draw[thick, ->, darkgreen] (0, 0) -- (0,1.5);
+ \draw[thick, ->, orange] (1, 0) -- (0,0);
+ \draw[thick, ->, red] (2, 0) -- (1,0);
+ \draw[thick, ->, blue] (2,1.5) -- (2, 0);
+
+ \foreach \i in {-2,...,1} {
+ \begin{scope}[opacity=0.5, xshift=\i*4cm]
+ \draw[->, orange] (-1, 0) -- (0,0);
+ \draw[->, darkgreen] (0, 0) -- (0,1.5);
+ \draw[->, darkgreen] (0, 0) -- (0,-1.5);
+ \draw[->, orange] (1, 0) -- (0,0);
+ \draw[->, red] (2, 0) -- (1,0);
+ \draw[->, blue] (2,1.5) -- (2, 0);
+ \draw[->, blue] (2,-1.5) -- (2, 0);
+ \draw[->, red] (2, 0) -- (3,0);
+
+ \node[zero] at (1,0) {};
+ \node[zero] at (3,0) {};
+ \end{scope}
+ }
+
+ \node[gray, anchor=north] at (-6,0) {$-3\pi$};
+ \node[gray, anchor=north] at (-4,0) {$-2\pi$};
+ \node[gray, anchor=north] at (-2,0) {$-\pi$};
+ % \node[gray, anchor=north] at (0,0) {$0$};
+ \node[gray, anchor=north] at (2,0) {$\pi$};
+ \node[gray, anchor=north] at (4,0) {$2\pi$};
+ \node[gray, anchor=north] at (6,0) {$3\pi$};
+
+ \node[gray, anchor=east] at (0,-1.5) {$-\infty$};
+ % \node[gray, anchor=south east] at (0, 0) {$0$};
+ \node[gray, anchor=east] at (0, 1.5) {$\infty$};
+
+ \end{scope}
+
+ \begin{scope}[yshift=-2.5cm]
+
+ \draw[gray, ->] (-5,0) -- (5,0) node[anchor=west]{$w$};
+
+ \draw[thick, ->, blue] (-4, 0) -- (-2, 0);
+ \draw[thick, ->, red] (-2, 0) -- (0, 0);
+ \draw[thick, ->, orange] (0, 0) -- (2, 0);
+ \draw[thick, ->, darkgreen] (2, 0) -- (4, 0);
+
+ \node[anchor=south] at (-4,0) {$-\infty$};
+ \node[anchor=south] at (-2,0) {$-1$};
+ \node[anchor=south] at (0,0) {$0$};
+ \node[anchor=south] at (2,0) {$1$};
+ \node[anchor=south] at (4,0) {$\infty$};
+
+ \end{scope}
+
+
+\end{tikzpicture} \ No newline at end of file
diff --git a/buch/papers/ellfilter/tikz/arccos2.tikz.tex b/buch/papers/ellfilter/tikz/arccos2.tikz.tex
new file mode 100644
index 0000000..3fc3cc6
--- /dev/null
+++ b/buch/papers/ellfilter/tikz/arccos2.tikz.tex
@@ -0,0 +1,45 @@
+\begin{tikzpicture}[>=stealth', auto, node distance=2cm, scale=1.2]
+
+ \tikzstyle{zero} = [draw, circle, inner sep =0, minimum height=0.15cm]
+ \tikzset{pole/.style={cross out, draw=black, minimum size=(0.15cm-\pgflinewidth), inner sep=0pt, outer sep=0pt}}
+
+ \begin{scope}[xscale=0.5]
+
+ \draw[gray, ->] (0,-2) -- (0,2) node[anchor=south]{$\mathrm{Im}~z_1$};
+ \draw[gray, ->] (-10,0) -- (10,0) node[anchor=west]{$\mathrm{Re}~z_1$};
+
+ \begin{scope}
+
+ \draw[>->, line width=0.05, thick, blue] (2, 1.5) -- (2,0.05) -- node[anchor=south, pos=0.5]{$N=1$} (0.1,0.05) -- (0.1,1.5);
+ \draw[>->, line width=0.05, thick, orange] (4, 1.5) -- (4,0) -- node[anchor=south, pos=0.25]{$N=2$} (0,0) -- (0,1.5);
+ \draw[>->, line width=0.05, thick, red] (6, 1.5) node[anchor=north west]{$-\infty$} -- (6,-0.05) node[anchor=west]{$-1$} -- node[anchor=north]{$0$} node[anchor=south, pos=0.1666]{$N=3$} (-0.1,-0.05) node[anchor=east]{$1$} -- (-0.1,1.5) node[anchor=north east]{$\infty$};
+
+
+ \node[zero] at (-7,0) {};
+ \node[zero] at (-5,0) {};
+ \node[zero] at (-3,0) {};
+ \node[zero] at (-1,0) {};
+ \node[zero] at (1,0) {};
+ \node[zero] at (3,0) {};
+ \node[zero] at (5,0) {};
+ \node[zero] at (7,0) {};
+
+
+ \end{scope}
+
+ \node[gray, anchor=north] at (-8,0) {$-4\pi$};
+ \node[gray, anchor=north] at (-6,0) {$-3\pi$};
+ \node[gray, anchor=north] at (-4,0) {$-2\pi$};
+ \node[gray, anchor=north] at (-2,0) {$-\pi$};
+ \node[gray, anchor=north] at (2,0) {$\pi$};
+ \node[gray, anchor=north] at (4,0) {$2\pi$};
+ \node[gray, anchor=north] at (6,0) {$3\pi$};
+ \node[gray, anchor=north] at (8,0) {$4\pi$};
+
+
+ \node[gray, anchor=east] at (0,-1.5) {$-\infty$};
+ \node[gray, anchor=east] at (0, 1.5) {$\infty$};
+
+ \end{scope}
+
+\end{tikzpicture} \ No newline at end of file
diff --git a/buch/papers/ellfilter/tikz/cd.tikz.tex b/buch/papers/ellfilter/tikz/cd.tikz.tex
new file mode 100644
index 0000000..7155a85
--- /dev/null
+++ b/buch/papers/ellfilter/tikz/cd.tikz.tex
@@ -0,0 +1,87 @@
+\begin{tikzpicture}[>=stealth', auto, node distance=2cm, scale=1.2]
+
+ \tikzstyle{zero} = [draw, circle, inner sep =0, minimum height=0.15cm]
+
+ \tikzset{pole/.style={cross out, draw=black, minimum size=(0.15cm-\pgflinewidth), inner sep=0pt, outer sep=0pt}}
+
+ \begin{scope}[xscale=1, yscale=2]
+
+ \draw[gray, ->] (0,-1.5) -- (0,1.5) node[anchor=south]{$\mathrm{Im}~z$};
+ \draw[gray, ->] (-5,0) -- (5,0) node[anchor=west]{$\mathrm{Re}~z$};
+
+ \draw[gray] ( 1,0) +(0,0.1) -- +(0, -0.1) node[inner sep=0, anchor=north] {\small $K$};
+
+ \draw[gray] (0, 0.5) +(0.1, 0) -- +(-0.1, 0) node[inner sep=0, anchor=east]{\small $jK^\prime$};
+
+
+ \begin{scope}
+
+ \begin{scope}[xshift=0cm]
+
+ \clip(-4.5,-1.25) rectangle (4.5,1.25);
+
+ \fill[yellow!30] (0,0) rectangle (1, 0.5);
+
+
+ \draw[thick, ->, darkgreen] (0, 0) -- (0,0.5);
+ \draw[thick, ->, orange] (1, 0) -- (0,0);
+ \draw[thick, ->, red] (2, 0) -- (1,0);
+ \draw[thick, ->, blue] (2,0.5) -- (2, 0);
+ \draw[thick, ->, purple] (1, 0.5) -- (2,0.5);
+ \draw[thick, ->, cyan] (0, 0.5) -- (1,0.5);
+
+
+
+ \foreach \i in {-2,...,1} {
+ \foreach \j in {-2,...,1} {
+ \begin{scope}[xshift=\i*4cm, yshift=\j*1cm]
+ \draw[opacity=0.5, ->, darkgreen] (0, 0) -- (0,0.5);
+ \draw[opacity=0.5, ->, orange] (1, 0) -- (0,0);
+ \draw[opacity=0.5, ->, red] (2, 0) -- (1,0);
+ \draw[opacity=0.5, ->, blue] (2,0.5) -- (2, 0);
+ \draw[opacity=0.5, ->, purple] (1, 0.5) -- (2,0.5);
+ \draw[opacity=0.5, ->, cyan] (0, 0.5) -- (1,0.5);
+ \draw[opacity=0.5, ->, darkgreen] (0,1) -- (0,0.5);
+ \draw[opacity=0.5, ->, blue] (2,0.5) -- (2, 1);
+ \draw[opacity=0.5, ->, purple] (3, 0.5) -- (2,0.5);
+ \draw[opacity=0.5, ->, cyan] (4, 0.5) -- (3,0.5);
+ \draw[opacity=0.5, ->, red] (2, 0) -- (3,0);
+ \draw[opacity=0.5, ->, orange] (3, 0) -- (4,0);
+
+ \node[zero] at ( 1, 0) {};
+ \node[zero] at ( 3, 0) {};
+ \node[pole] at ( 1,0.5) {};
+ \node[pole] at ( 3,0.5) {};
+
+ \end{scope}
+ }
+ }
+
+ \end{scope}
+
+ \end{scope}
+
+ \end{scope}
+
+ \begin{scope}[yshift=-3.5cm, xscale=0.75]
+
+ \draw[gray, ->] (-6,0) -- (6,0) node[anchor=west]{$w$};
+
+ \draw[thick, ->, purple] (-5, 0) -- (-3, 0);
+ \draw[thick, ->, blue] (-3, 0) -- (-2, 0);
+ \draw[thick, ->, red] (-2, 0) -- (0, 0);
+ \draw[thick, ->, orange] (0, 0) -- (2, 0);
+ \draw[thick, ->, darkgreen] (2, 0) -- (3, 0);
+ \draw[thick, ->, cyan] (3, 0) -- (5, 0);
+
+ \node[anchor=south] at (-5,0) {$-\infty$};
+ \node[anchor=south] at (-3,0) {$-1/k$};
+ \node[anchor=south] at (-2,0) {$-1$};
+ \node[anchor=south] at (0,0) {$0$};
+ \node[anchor=south] at (2,0) {$1$};
+ \node[anchor=south] at (3,0) {$1/k$};
+ \node[anchor=south] at (5,0) {$\infty$};
+
+ \end{scope}
+
+\end{tikzpicture} \ No newline at end of file
diff --git a/buch/papers/ellfilter/tikz/cd2.tikz.tex b/buch/papers/ellfilter/tikz/cd2.tikz.tex
new file mode 100644
index 0000000..0743f7d
--- /dev/null
+++ b/buch/papers/ellfilter/tikz/cd2.tikz.tex
@@ -0,0 +1,84 @@
+\begin{tikzpicture}[>=stealth', auto, node distance=2cm, scale=1.2]
+
+ \tikzstyle{zero} = [draw, circle, inner sep =0, minimum height=0.15cm]
+ \tikzstyle{dot} = [fill, circle, inner sep =0, minimum height=0.1cm]
+
+ \tikzset{pole/.style={cross out, draw=black, minimum size=(0.15cm-\pgflinewidth), inner sep=0pt, outer sep=0pt}}
+
+ \begin{scope}[xscale=1.25, yscale=2.5]
+
+ \draw[gray, ->] (0,-0.75) -- (0,1.25) node[anchor=south]{$\mathrm{Im}~z_1$};
+ \draw[gray, ->] (-1.5,0) -- (6,0) node[anchor=west]{$\mathrm{Re}~z_1$};
+
+ \draw[gray] ( 1,0) +(0,0.05) -- +(0, -0.05) node[inner sep=0, anchor=north] {\small $K_1$};
+ \draw[gray] ( 5,0) +(0,0.05) -- +(0, -0.05) node[inner sep=0, anchor=north] {\small $5K_1$};
+ \draw[gray] (0, 0.5) +(0.1, 0) -- +(-0.1, 0) node[inner sep=0, anchor=east]{\small $jK^\prime_1$};
+
+ \begin{scope}
+
+ \clip(-1.5,-0.75) rectangle (6.8,1.25);
+
+ % \draw[>->, line width=0.05, thick, blue] (1, 0.45) -- (2, 0.45) -- (2, 0.05) -- ( 0.1, 0.05) -- ( 0.1,0.45) -- (1, 0.45);
+ % \draw[>->, line width=0.05, thick, orange] (2, 0.5 ) -- (4, 0.5 ) -- (4, 0 ) -- ( 0 , 0 ) -- ( 0 ,0.5 ) -- (2, 0.5 );
+ % \draw[>->, line width=0.05, thick, red] (3, 0.55) -- (6, 0.55) -- (6,-0.05) -- (-0.1,-0.05) -- (-0.1,0.55) -- (3, 0.55);
+ % \node[blue] at (1, 0.25) {$N=1$};
+ % \node[orange] at (3, 0.25) {$N=2$};
+ % \node[red] at (5, 0.25) {$N=3$};
+
+
+
+ % \draw[line width=0.1cm, fill, red!50] (0,0) rectangle (3, 0.5);
+ % \draw[line width=0.05cm, fill, orange!50] (0,0) rectangle (2, 0.5);
+ % \fill[yellow!50] (0,0) rectangle (1, 0.5);
+ % \node[] at (0.5, 0.25) {\small $N=1$};
+ % \node[] at (1.5, 0.25) {\small $N=2$};
+ % \node[] at (2.5, 0.25) {\small $N=3$};
+
+ \fill[orange!30] (0,0) rectangle (5, 0.5);
+ \fill[yellow!30] (0,0) rectangle (1, 0.5);
+ \node[] at (2.5, 0.25) {\small $N=5$};
+
+
+ \draw[decorate,decoration={brace,amplitude=3pt,mirror}, yshift=0.05cm]
+ (5,0.5) node(t_k_unten){} -- node[above, yshift=0.1cm]{$NK$}
+ (0,0.5) node(t_k_opt_unten){};
+
+ \draw[decorate,decoration={brace,amplitude=3pt,mirror}, xshift=0.1cm]
+ (5,0) node(t_k_unten){} -- node[right, xshift=0.1cm]{$K^\prime \frac{K_1N}{K} = K^\prime_1$}
+ (5,0.5) node(t_k_opt_unten){};
+
+ \foreach \i in {-2,...,1} {
+ \foreach \j in {-2,...,1} {
+ \begin{scope}[xshift=\i*4cm, yshift=\j*1cm]
+
+ \node[zero] at ( 1, 0) {};
+ \node[zero] at ( 3, 0) {};
+ \node[pole] at ( 1,0.5) {};
+ \node[pole] at ( 3,0.5) {};
+
+ \end{scope}
+ }
+ }
+
+
+
+
+ \draw[thick, ->, darkgreen] (5, 0) -- node[yshift=-0.5cm]{Durchlassbereich} (0,0);
+ \draw[thick, ->, orange] (-0, 0) -- node[align=center]{Übergangs-\\berech} (0,0.5);
+ \draw[thick, ->, red] (0,0.5) -- node[align=center, yshift=0.5cm]{Sperrbereich} (5, 0.5);
+
+ \draw (4,0 ) node[dot]{} node[anchor=south] {\small $1$};
+ \draw (2,0 ) node[dot]{} node[anchor=south] {\small $-1$};
+ \draw (0,0 ) node[dot]{} node[anchor=south west] {\small $1$};
+ \draw (0,0.5) node[dot]{} node[anchor=north west] {\small $1/k$};
+ \draw (2,0.5) node[dot]{} node[anchor=north] {\small $-1/k$};
+ \draw (4,0.5) node[dot]{} node[anchor=north] {\small $1/k$};
+
+
+
+ \end{scope}
+
+
+ \end{scope}
+
+\end{tikzpicture} \ No newline at end of file
diff --git a/buch/papers/ellfilter/tikz/fundamental_rectangle.tikz.tex b/buch/papers/ellfilter/tikz/fundamental_rectangle.tikz.tex
new file mode 100644
index 0000000..921dbfa
--- /dev/null
+++ b/buch/papers/ellfilter/tikz/fundamental_rectangle.tikz.tex
@@ -0,0 +1,26 @@
+\begin{tikzpicture}[>=stealth', auto, node distance=2cm, scale=1.2]
+
+ \tikzstyle{zero} = [draw, circle, inner sep =0, minimum height=0.15cm]
+
+ \tikzset{pole/.style={cross out, draw=black, minimum size=(0.15cm-\pgflinewidth), inner sep=0pt, outer sep=0pt}}
+
+ \begin{scope}[xscale=2, yscale=2]
+
+ \draw[gray, ->] (0,-0.25) -- (0,1.25) node[anchor=south]{$\mathrm{Im}~z$};
+ \draw[gray, ->] (-0.25,0) -- (1.5,0) node[anchor=west]{$\mathrm{Re}~z$};
+
+ \draw[gray] ( 1,0) +(0,0.05) -- +(0, -0.05) node[inner sep=0, anchor=north] {\small $K$};
+
+ \draw[gray] (0, 1) +(0.05, 0) -- +(-0.05, 0) node[inner sep=0, anchor=east]{\small $jK^\prime$};
+
+ \fill[yellow!50] (0,0) rectangle (1, 1);
+
+ \node[anchor=south east] at ( 1,0) {$c$};
+ \node[anchor=north east] at ( 1,1) {$d$};
+ \node[anchor=north west] at ( 0,1) {$n$};
+ \node[anchor=south west] at ( 0,0) {$s$};
+
+ \end{scope}
+
+
+\end{tikzpicture} \ No newline at end of file
diff --git a/buch/papers/ellfilter/tikz/sn.tikz.tex b/buch/papers/ellfilter/tikz/sn.tikz.tex
new file mode 100644
index 0000000..87c63c0
--- /dev/null
+++ b/buch/papers/ellfilter/tikz/sn.tikz.tex
@@ -0,0 +1,86 @@
+\begin{tikzpicture}[>=stealth', auto, node distance=2cm, scale=1.2]
+
+ \tikzstyle{zero} = [draw, circle, inner sep =0, minimum height=0.15cm]
+
+ \tikzset{pole/.style={cross out, draw=black, minimum size=(0.15cm-\pgflinewidth), inner sep=0pt, outer sep=0pt}}
+
+ \begin{scope}[xscale=1, yscale=2]
+
+ \draw[gray, ->] (0,-1.5) -- (0,1.5) node[anchor=south]{$\mathrm{Im}~z$};
+ \draw[gray, ->] (-5,0) -- (5,0) node[anchor=west]{$\mathrm{Re}~z$};
+
+ \begin{scope}
+
+ \clip(-4.5,-1.25) rectangle (4.5,1.25);
+
+ \fill[yellow!30] (0,0) rectangle (1, 0.5);
+
+ \begin{scope}[xshift=-1cm]
+
+ \draw[thick, ->, darkgreen] (0, 0) -- (0,0.5);
+ \draw[thick, ->, orange] (1, 0) -- (0,0);
+ \draw[thick, ->, red] (2, 0) -- (1,0);
+ \draw[thick, ->, blue] (2,0.5) -- (2, 0);
+ \draw[thick, ->, purple] (1, 0.5) -- (2,0.5);
+ \draw[thick, ->, cyan] (0, 0.5) -- (1,0.5);
+
+
+ \foreach \i in {-2,...,2} {
+ \foreach \j in {-2,...,1} {
+ \begin{scope}[xshift=\i*4cm, yshift=\j*1cm]
+ \draw[opacity=0.5, ->, darkgreen] (0, 0) -- (0,0.5);
+ \draw[opacity=0.5, ->, orange] (1, 0) -- (0,0);
+ \draw[opacity=0.5, ->, red] (2, 0) -- (1,0);
+ \draw[opacity=0.5, ->, blue] (2,0.5) -- (2, 0);
+ \draw[opacity=0.5, ->, purple] (1, 0.5) -- (2,0.5);
+ \draw[opacity=0.5, ->, cyan] (0, 0.5) -- (1,0.5);
+ \draw[opacity=0.5, ->, darkgreen] (0,1) -- (0,0.5);
+ \draw[opacity=0.5, ->, blue] (2,0.5) -- (2, 1);
+ \draw[opacity=0.5, ->, purple] (3, 0.5) -- (2,0.5);
+ \draw[opacity=0.5, ->, cyan] (4, 0.5) -- (3,0.5);
+ \draw[opacity=0.5, ->, red] (2, 0) -- (3,0);
+ \draw[opacity=0.5, ->, orange] (3, 0) -- (4,0);
+
+ \node[zero] at ( 1, 0) {};
+ \node[zero] at ( 3, 0) {};
+ \node[pole] at ( 1,0.5) {};
+ \node[pole] at ( 3,0.5) {};
+
+ \end{scope}
+ }
+ }
+
+ \end{scope}
+
+ \end{scope}
+
+ \draw[gray] ( 1,0) +(0,0.1) -- +(0, -0.1) node[inner sep=0, anchor=north] {\small $K$};
+ \draw[gray] (0, 0.5) +(0.1, 0) -- +(-0.1, 0) node[inner sep=0, anchor=east]{\small $jK^\prime$};
+
+
+
+ \end{scope}
+
+ \begin{scope}[yshift=-3.5cm, xscale=0.75]
+
+ \draw[gray, ->] (-6,0) -- (6,0) node[anchor=west]{$w$};
+
+ \draw[thick, ->, purple] (-5, 0) -- (-3, 0);
+ \draw[thick, ->, blue] (-3, 0) -- (-2, 0);
+ \draw[thick, ->, red] (-2, 0) -- (0, 0);
+ \draw[thick, ->, orange] (0, 0) -- (2, 0);
+ \draw[thick, ->, darkgreen] (2, 0) -- (3, 0);
+ \draw[thick, ->, cyan] (3, 0) -- (5, 0);
+
+ \node[anchor=south] at (-5,0) {$-\infty$};
+ \node[anchor=south] at (-3,0) {$-1/k$};
+ \node[anchor=south] at (-2,0) {$-1$};
+ \node[anchor=south] at (0,0) {$0$};
+ \node[anchor=south] at (2,0) {$1$};
+ \node[anchor=south] at (3,0) {$1/k$};
+ \node[anchor=south] at (5,0) {$\infty$};
+
+ \end{scope}
+
+
+\end{tikzpicture} \ No newline at end of file
diff --git a/buch/papers/ellfilter/tschebyscheff.tex b/buch/papers/ellfilter/tschebyscheff.tex
new file mode 100644
index 0000000..7d426b6
--- /dev/null
+++ b/buch/papers/ellfilter/tschebyscheff.tex
@@ -0,0 +1,133 @@
+\section{Tschebyscheff-Filter}
+
+Als Einstieg betrachent Wir das Tschebyscheff-Filter, welches sehr verwand ist mit dem elliptischen Filter.
+Genauer ausgedrückt sind die Tschebyscheff-1 und -2 Filter Spezialfälle davon.
+
+Der Name des Filters deutet schon an, dass die Tschebyscheff-Polynome $T_N$ für das Filter relevant sind:
+\begin{align}
+ T_{0}(x)&=1\\
+ T_{1}(x)&=x\\
+ T_{2}(x)&=2x^{2}-1\\
+ T_{3}(x)&=4x^{3}-3x\\
+ T_{n+1}(x)&=2x~T_{n}(x)-T_{n-1}(x).
+\end{align}
+Bemerkenswert ist, dass die Polynome im Intervall $[-1, 1]$ mit der trigonometrischen Funktion
+\begin{align} \label{ellfilter:eq:chebychef_polynomials}
+ T_N(w) &= \cos \left( N \cos^{-1}(w) \right) \\
+ &= \cos \left(N~z \right), \quad w= \cos(z)
+\end{align}
+übereinstimmt.
+Der Zusammenhang lässt sich mit den Doppel- und Mehrfachwinkelfunktionen der trigonometrischen Funktionen erklären.
+Abbildung \ref{ellfilter:fig:chebychef_polynomials} zeigt einige Tschebyscheff-Polynome.
+\begin{figure}
+ \centering
+ \input{papers/ellfilter/python/F_N_chebychev2.pgf}
+ \caption{Die Tschebyscheff-Polynome $C_N$.}
+ \label{ellfilter:fig:chebychef_polynomials}
+\end{figure}
+Da der Kosinus begrenzt zwischen $-1$ und $1$ ist, sind auch die Tschebyscheff-Polynome begrenzt.
+Geht man aber über das Intervall $[-1, 1]$ hinaus, divergieren die Funktionen mit zunehmender Ordnung immer steiler gegen $\pm \infty$.
+Diese Eigenschaft ist sehr nützlich für ein Filter.
+Wenn wir die Tschebyscheff-Polynome quadrieren, passen sie perfekt in die Voraussetzungen für Filterfunktionen, wie es Abbildung \ref{ellfiter:fig:chebychef} demonstriert.
+\begin{figure}
+ \centering
+ \input{papers/ellfilter/python/F_N_chebychev.pgf}
+ \caption{Die Tschebyscheff-Polynome füllen den erlaubten Bereich besser, und erhalten dadurch eine steilere Flanke im Sperrbereich.}
+ \label{ellfiter:fig:chebychef}
+\end{figure}
+
+
+Die analytische Fortsetzung von \eqref{ellfilter:eq:chebychef_polynomials} über das Intervall $[-1,1]$ hinaus stimmt mit den Polynomen überein, wie es zu erwarten ist.
+Die genauere Betrachtung wird uns dann helfen die elliptischen Filter besser zu verstehen.
+
+Starten wir mit der Funktion, die als erstes auf $w$ angewendet wird, dem Arcuscosinus.
+Die invertierte Funktion des Kosinus kann als definites Integral dargestellt werden:
+\begin{align}
+ \cos^{-1}(x)
+ &=
+ \int_{x}^{1}
+ \frac{
+ dz
+ }{
+ \sqrt{
+ 1-z^2
+ }
+ }\\
+ &=
+ \int_{0}^{x}
+ \frac{
+ -1
+ }{
+ \sqrt{
+ 1-z^2
+ }
+ }
+ ~dz
+ + \frac{\pi}{2}
+\end{align}
+Der Integrand oder auch die Ableitung
+\begin{equation}
+ \frac{
+ -1
+ }{
+ \sqrt{
+ 1-z^2
+ }
+ }
+\end{equation}
+bestimmt dabei die Richtung, in der die Funktion verläuft.
+Der reelle Arcuscosinus is bekanntlich nur für $|z| \leq 1$ definiert.
+Hier bleibt der Wert unter der Wurzel positiv und das Integral liefert reelle Werte.
+Doch wenn $|z|$ über 1 hinausgeht, wird der Term unter der Wurzel negativ.
+Durch die Quadratwurzel entstehen für den Integranden zwei rein komplexe Lösungen.
+Der Wert des Arcuscosinus verlässt also bei $z= \pm 1$ den reellen Zahlenstrahl und knickt in die komplexe Ebene ab.
+Abbildung \ref{ellfilter:fig:arccos} zeigt den $\arccos$ in der komplexen Ebene.
+\begin{figure}
+ \centering
+ \input{papers/ellfilter/tikz/arccos.tikz.tex}
+ \caption{Die Funktion $z = \cos^{-1}(w)$ dargestellt in der komplexen ebene.}
+ \label{ellfilter:fig:arccos}
+\end{figure}
+Wegen der Periodizität des Kosinus ist auch der Arcuscosinus $2\pi$-periodisch und es entstehen periodische Nullstellen.
+% \begin{equation}
+% \frac{
+% 1
+% }{
+% \sqrt{
+% 1-z^2
+% }
+% }
+% \in \mathbb{R}
+% \quad
+% \forall
+% \quad
+% -1 \leq z \leq 1
+% \end{equation}
+% \begin{equation}
+% \frac{
+% 1
+% }{
+% \sqrt{
+% 1-z^2
+% }
+% }
+% = i \xi \quad | \quad \xi \in \mathbb{R}
+% \quad
+% \forall
+% \quad
+% z \leq -1 \cup z \geq 1
+% \end{equation}
+
+Die Tschebyscheff-Polynome skalieren diese Nullstellen mit dem Ordnungsfaktor $N$, wie dargestellt in Abbildung \ref{ellfilter:fig:arccos2}.
+\begin{figure}
+ \centering
+ \input{papers/ellfilter/tikz/arccos2.tikz.tex}
+ \caption{
+ $z_1=N \cos^{-1}(w)$-Ebene der Tschebyscheff-Funktion.
+ Die eingefärbten Pfade sind Verläufe von $w~\forall~[-\infty, \infty]$ für verschiedene Ordnungen $N$.
+ Je grösser die Ordnung $N$ gewählt wird, desto mehr Nullstellen werden passiert.
+ }
+ \label{ellfilter:fig:arccos2}
+\end{figure}
+Somit passert $\cos( N~\cos^{-1}(w))$ im Intervall $[-1, 1]$ $N$ Nullstellen.
+Durch die spezielle Anordnung der Nullstellen hat die Funktion Equirippel-Verhalten und ist dennoch ein Polynom, was sich perfekt für linear Filter eignet.