diff options
Diffstat (limited to 'buch/papers')
20 files changed, 7056 insertions, 239 deletions
diff --git a/buch/papers/ellfilter/main.tex b/buch/papers/ellfilter/main.tex index 29ebf7a..e9d6aba 100644 --- a/buch/papers/ellfilter/main.tex +++ b/buch/papers/ellfilter/main.tex @@ -11,16 +11,15 @@ \section{Einleitung} -Lineare filter +% Lineare filter -Filter, Signalverarbeitung +% 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 - +% 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. @@ -39,15 +38,12 @@ Damit das Filter implementierbar und stabil ist, muss $H(\Omega)^2$ eine rationa $N \in \mathbb{N} $ gibt dabei die Ordnung des Filters vor, also die maximale Anzahl Pole oder Nullstellen. -% In \eqref{ellfilter:eq:h_omega} wird $F_N(w)$ so verzogen, dass $F_N(w) \forall |w| < 1$ - - 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 - \includegraphics[scale=1]{papers/ellfilter/python/F_N_butterworth.pdf} + \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} @@ -60,7 +56,7 @@ wenn $F_N(w)$ eine rationale Funktion ist, ist auch $H(\Omega)$ eine rationale F 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) & \text{Elliptisch (Cauer)} \\ + R_N(w, \xi) & \text{Elliptisch (Cauer)} \\ \end{cases} \end{align} @@ -73,9 +69,9 @@ Es scheint so als sind gewisse Eigenschaften dieser speziellen Funktionen verant \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 Fitler ein Spezialfall davon. +Genauer ausgedrückt sind die Tschebyscheff-1 und -2 Filter Spezialfälle davon. -Der Name des Filters deutet schon an, dass die Tschebyschff-Polynome $T_N$ relevant sind für das Filter: +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\\ @@ -83,15 +79,17 @@ Der Name des Filters deutet schon an, dass die Tschebyschff-Polynome $T_N$ relev 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{equation} \label{ellfilter:eq:chebychef_polynomials} - T_N(w) = \cos \left( N \cos^{-1}(w) \right) -\end{equation} +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 - \includegraphics[scale=1]{papers/ellfilter/python/F_N_chebychev2.pdf} + \input{papers/ellfilter/python/F_N_chebychev2.pgf} \caption{Die Tschebyscheff-Polynome $C_N$.} \label{ellfilter:fig:chebychef_polynomials} \end{figure} @@ -101,103 +99,123 @@ 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 - \includegraphics[scale=1]{papers/ellfilter/python/F_N_chebychev.pdf} + \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 zu verstehen. +Die genauere Betrachtung wird uns dann helfen die elliptischen Filter besser zu verstehen. -\begin{equation} +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_{0}^{x} + &= + \int_{x}^{1} \frac{ dz }{ \sqrt{ 1-z^2 } - } -\end{equation} %TOdO is it minus dz? - -\begin{equation} + }\\ + &= + \int_{0}^{x} \frac{ - 1 + -1 }{ \sqrt{ 1-z^2 } } - \in \mathbb{R} - \quad - \forall - \quad - -1 \leq z \leq 1 -\end{equation} -Wenn $|z|$ über 1 hinausgeht, wird der Term unter der Wurzel negativ. -Durch die Quadratwurzel entstehen zwei Reinkomplexe Lösungen + ~dz + + \frac{\pi}{2} +\end{align} +Der Integrand oder auch die Ableitung \begin{equation} \frac{ - 1 + -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} - +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{ - $z$-Ebene der Tschebyscheff-Funktion. - Je grösser die Ordnung $N$ gewählt wird, desto mehr Nullstellen werden hat das Tschebyscheff-Polynom. + $z_1=N \cos^{-1}(w)$-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:arccos} + \label{ellfilter:fig:arccos2} \end{figure} - - - - - -% Analytische Fortsetzung - - +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. \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. +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. - -%TODO $z$ or $u$ for parameter? - -neu zwei parameter -$sn(z, k)$ -$z$ ist das winkelargument +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. -An deren stelle kommt der parameter $k$ zum Einsatz, welcher durch das elliptische Integral erster Art +Das Winkelargument $z$ kann durch das elliptische Integral erster Art \begin{equation} z = @@ -211,12 +229,18 @@ An deren stelle kommt der parameter $k$ zum Einsatz, welcher durch das elliptisc 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} @@ -231,25 +255,75 @@ Beim vollständigen Integral } } \end{equation} -wird über ein viertel Ellipsenbogen integriert also bis $\phi=\pi/2$. - -Die Jacobischen elliptischen Funktionen können mit der inversen Funktion +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 +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 $sn^{-1}$ mit dem Elliptischen integral dargestellt werden: +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(u, k) + \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} @@ -306,28 +380,90 @@ In der reellen Richtung ist sie $4K(k)$-periodisch und in der imaginären Richtu %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} \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} + -\begin{equation} - R_N(\xi, w) = \cd \left(N~f_1(\xi)~\cd^{-1}(w, 1/\xi), f_2(\xi)\right) -\end{equation} -\begin{equation} - R_N(\xi, w) = \cd (N~u K_1, k_1), \quad w= \cd(uK, k) -\end{equation} +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} -sieht ähnlich aus wie die trigonometrische darstellung der Tschebyschef-Polynome +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. -der Ordnungszahl $N$ kommt auch als Faktor for -%TODO cd^{-1} grafik mit +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. +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} @@ -345,19 +481,7 @@ Bei den Tschebyscheff-Polynomen haben wir gesehen, dass die Trigonometrische For 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. - - - -\begin{figure} - \centering - \includegraphics[scale=1]{papers/ellfilter/python/F_N_elliptic.pdf} - \caption{$F_N$ für ein elliptischs filter.} - \label{ellfilter:fig:elliptic} -\end{figure} - - - - +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. \input{papers/ellfilter/teil0.tex} \input{papers/ellfilter/teil1.tex} diff --git a/buch/papers/ellfilter/packages.tex b/buch/papers/ellfilter/packages.tex index 8045a1a..9a550e2 100644 --- a/buch/papers/ellfilter/packages.tex +++ b/buch/papers/ellfilter/packages.tex @@ -8,6 +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}} -\DeclareMathOperator{\sn}{\text{sn}} -\DeclareMathOperator{\cd}{\text{cd}} 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 index a278989..254ad4b 100644 --- a/buch/papers/ellfilter/python/chebychef.py +++ b/buch/papers/ellfilter/python/chebychef.py @@ -35,7 +35,7 @@ plt.show() # %% Cheychev filter F_N plot w = np.linspace(-1.1,1.1, 1000) -plt.figure(figsize=(5.5,2)) +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) @@ -44,9 +44,10 @@ plt.xlim([-1.2,1.2]) plt.ylim([-2,2]) plt.grid() plt.xlabel("$w$") -plt.ylabel("$C_N(w)$") +plt.ylabel("$T_N(w)$") plt.legend() -plt.savefig("F_N_chebychev2.pdf") +plt.tight_layout() +plt.savefig("F_N_chebychev2.pgf") plt.show() # %% Build Chebychev polynomials 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 index 9f209e9..b3336a1 100644 --- a/buch/papers/ellfilter/python/elliptic.py +++ b/buch/papers/ellfilter/python/elliptic.py @@ -5,19 +5,62 @@ import scipy.special import scipyx as spx import numpy as np import matplotlib.pyplot as plt -import matplotlib from matplotlib.patches import Rectangle -matplotlib.rcParams.update({ - "pgf.texsystem": "pdflatex", - 'font.family': 'serif', - 'font.size': 9, - 'text.usetex': True, - 'pgf.rcfonts': False, -}) +import plot_params def last_color(): - plt.gca().lines[-1].get_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 @@ -37,7 +80,7 @@ plt.gca().add_patch(Rectangle( plt.gca().add_patch(Rectangle( (1, 1), 0.5, 1, - fc ='green', + fc ='orange', alpha=0.2, lw = 10, )) @@ -47,7 +90,8 @@ plt.grid() plt.xlabel("$w$") plt.ylabel("$F^2_N(w)$") plt.legend() -plt.savefig("F_N_butterworth.pdf") +plt.tight_layout() +plt.savefig("F_N_butterworth.pgf") plt.show() # %% Cheychev filter F_N plot @@ -69,7 +113,7 @@ plt.gca().add_patch(Rectangle( plt.gca().add_patch(Rectangle( (1, 1), 0.5, 1, - fc ='green', + fc ='orange', alpha=0.2, lw = 10, )) @@ -79,57 +123,10 @@ plt.grid() plt.xlabel("$w$") plt.ylabel("$F^2_N(w)$") plt.legend() -plt.savefig("F_N_chebychev.pdf") +plt.tight_layout() +plt.savefig("F_N_chebychev.pgf") plt.show() -# %% 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) # %% plot arcsin @@ -314,3 +311,46 @@ for n in (1,2,3,4): 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 index 92fefd9..29c6f47 100644 --- a/buch/papers/ellfilter/python/elliptic2.py +++ b/buch/papers/ellfilter/python/elliptic2.py @@ -6,13 +6,14 @@ 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 = 1000 + omega_c = 1 a, b = scipy.signal.ellip( order, @@ -34,14 +35,14 @@ def ellip_filter(N): FN2 = ((1/mag**2) - 1) - return w/omega_c, FN2 / epsilon2 + return w/omega_c, FN2 / epsilon2, mag, a, b plt.figure(figsize=(4,2.5)) for N in [5]: - w, FN2 = ellip_filter(N) - plt.semilogy(w, FN2, label=f"$N={N}$") + 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), @@ -53,7 +54,7 @@ plt.gca().add_patch(Rectangle( plt.gca().add_patch(Rectangle( (1, 1), 0.01, 1e2-1, - fc ='green', + fc ='orange', alpha=0.2, lw = 10, )) @@ -61,18 +62,88 @@ plt.gca().add_patch(Rectangle( plt.gca().add_patch(Rectangle( (1.01, 100), 1, 1e6, - fc ='green', + 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.savefig("F_N_elliptic.pdf") +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 2b873af..8f21971 100644 --- a/buch/papers/ellfilter/references.bib +++ b/buch/papers/ellfilter/references.bib @@ -11,3 +11,12 @@ 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/tikz/arccos.tikz.tex b/buch/papers/ellfilter/tikz/arccos.tikz.tex index 2bdcc2d..2772620 100644 --- a/buch/papers/ellfilter/tikz/arccos.tikz.tex +++ b/buch/papers/ellfilter/tikz/arccos.tikz.tex @@ -1,81 +1,49 @@ \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]{Im $z$}; - \draw[gray, ->] (-5,0) -- (5,0) node[anchor=west]{Re $z$}; + \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} - \draw[thick, ->, orange] (-1, 0) -- (0,0); - \draw[thick, ->, darkgreen] (0, 0) -- (0,1.5); - \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); - \draw[thick, ->, blue] (2,-1.5) -- (2, 0); - \draw[thick, ->, red] (2, 0) -- (3,0); - - \node[anchor=south west] at (0,1.5) {$\infty$}; - \node[anchor=south west] at (0,-1.5) {$\infty$}; - \node[anchor=south west] at (0,0) {$1$}; - \node[anchor=south] at (1,0) {$0$}; - \node[anchor=south west] at (2,0) {$-1$}; - \node[anchor=south west] at (2,1.5) {$-\infty$}; - \node[anchor=south west] at (2,-1.5) {$-\infty$}; - \node[anchor=south west] at (3,0) {$0$}; - \end{scope} + \begin{scope}[xscale=0.6] - \begin{scope}[xshift=4cm] - \draw[thick, ->, orange] (-1, 0) -- (0,0); - \draw[thick, ->, darkgreen] (0, 0) -- (0,1.5); - \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); - % \draw[thick, ->, blue] (2,-1.5) -- (2, 0); - % \draw[thick, ->, red] (2, 0) -- (3,0); - - \node[anchor=south west] at (0,1.5) {$\infty$}; - \node[anchor=south west] at (0,-1.5) {$\infty$}; - \node[anchor=south west] at (0,0) {$1$}; - % \node[anchor=south] at (1,0) {$0$}; - % \node[anchor=south west] at (2,0) {$-1$}; - % \node[anchor=south west] at (2,1.5) {$-\infty$}; - % \node[anchor=south west] at (2,-1.5) {$-\infty$}; - % \node[anchor=south west] at (3,0) {$0$}; - \end{scope} + \clip(-7.5,-2) rectangle (7.5,2); - \begin{scope}[xshift=-4cm] - % \draw[thick, ->, orange] (-1, 0) -- (0,0); \draw[thick, ->, darkgreen] (0, 0) -- (0,1.5); - \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); - \draw[thick, ->, blue] (2,-1.5) -- (2, 0); - \draw[thick, ->, red] (2, 0) -- (3,0); - - \node[anchor=south west] at (0,1.5) {$\infty$}; - \node[anchor=south west] at (0,-1.5) {$\infty$}; - \node[anchor=south west] at (0,0) {$1$}; - \node[anchor=south] at (1,0) {$0$}; - \node[anchor=south west] at (2,0) {$-1$}; - \node[anchor=south west] at (2,1.5) {$-\infty$}; - \node[anchor=south west] at (2,-1.5) {$-\infty$}; - \node[anchor=south west] at (3,0) {$0$}; - \end{scope} - - \node[gray, anchor=north west] at (-4,0) {$-2\pi$}; - \node[gray, anchor=north west] at (-2,0) {$-\pi$}; - \node[gray, anchor=north west] at (0,0) {$0$}; - \node[gray, anchor=north west] at (2,0) {$\pi$}; - \node[gray, anchor=north west] at (4,0) {$2\pi$}; - - - \node[gray, anchor=south east] at (0,-1.5) {$-\infty$}; - \node[gray, anchor=south east] at (0, 0) {$0$}; - \node[gray, anchor=south east] at (0, 1.5) {$\infty$}; + \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] @@ -94,4 +62,5 @@ \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 index dcf02fd..3fc3cc6 100644 --- a/buch/papers/ellfilter/tikz/arccos2.tikz.tex +++ b/buch/papers/ellfilter/tikz/arccos2.tikz.tex @@ -1,19 +1,18 @@ \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]{Im $z$}; - \draw[gray, ->] (-10,0) -- (10,0) node[anchor=west]{Re $z$}; + \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) -- (6,-0.05) -- node[anchor=south, pos=0.1666]{$N=3$} (-0.1,-0.05) -- (-0.1,1.5); + \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) {}; 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 |