13 files changed, 557 insertions, 332 deletions

diff --git a/buch/papers/ellfilter/elliptic.tex b/buch/papers/ellfilter/elliptic.tex
index 88bfbfe..96731c8 100644
--- a/buch/papers/ellfilter/elliptic.tex
+++ b/buch/papers/ellfilter/elliptic.tex
@@ -69,7 +69,15 @@ Analog zu Abbildung \ref{ellfilter:fig:arccos2} können wir auch bei den ellipti
     \label{ellfilter:fig:elliptic}
 \end{figure}
 
-\subsection{Degree Equation}
+
+\begin{figure}
+    \centering
+    \input{papers/ellfilter/python/elliptic.pgf}
+    \caption{Die resultierende frequenzantwort eines elliptischs filter.}
+    \label{ellfilter:fig:elliptic_freq}
+\end{figure}
+
+\subsection{Gradgleichung}
 
 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.
@@ -82,6 +90,19 @@ Dies trifft ein wenn die Degree Equation erfüllt ist.
 Leider ist das lösen dieser Gleichung nicht trivial.
 Die Rechnung wird in \ref{ellfilter:bib:orfanidis} im Detail angeschaut.
 
+\begin{figure}
+    \centering
+    \input{papers/ellfilter/python/k.pgf}
+    \caption{Die Periodizitäten in realer und imaginärer Richtung in Abhängigkeit vom elliptischen Modul $k$.}
+\end{figure}
+
+\begin{figure}
+    \centering
+    \input{papers/ellfilter/tikz/elliptic_transform.tikz}
+    \caption{Die Gradgleichung als geometrisches Problem.}
+\end{figure}
+
+
 
 \subsection{Polynome?}
 
diff --git a/buch/papers/ellfilter/presentation/presentation.tex b/buch/papers/ellfilter/presentation/presentation.tex
index 7fdb864..adbf925 100644
--- a/buch/papers/ellfilter/presentation/presentation.tex
+++ b/buch/papers/ellfilter/presentation/presentation.tex
@@ -117,7 +117,7 @@
 		\tableofcontents
 	\end{frame}
 
-	\section{Linear Filter}
+	\section{Lineare Filter}
 
 	\begin{frame}
 		\frametitle{Lineare Filter}
@@ -349,6 +349,23 @@
 
 	\end{frame}
 
+	\section{Elliptisches Filter}
+
+	\begin{frame}
+		\frametitle{Elliptisches Filter}
+
+		\begin{equation*}
+			z_1 = N~\frac{K_1}{K}~\cd^{-1}(w, k)
+		\end{equation*}
+
+		\begin{center}
+			\scalebox{0.75}{
+				\input{../tikz/cd3.tikz.tex}
+			}
+		\end{center}
+
+	\end{frame}
+
 	\begin{frame}
 		\frametitle{Periodizität in realer und imaginärer Richtung}
 
@@ -360,20 +377,39 @@
 	\end{frame}
 
 	\begin{frame}
+		\frametitle{Gradgleichung}
+
+		\begin{equation}
+			N \frac{K^\prime}{K} = \frac{K^\prime_1}{K_1}
+		\end{equation}
+
+		\begin{center}
+			\scalebox{0.95}{
+				\input{../tikz/elliptic_transform.tikz}
+			}
+		\end{center}
+
+
+	\end{frame}
+
+	\begin{frame}
 		\frametitle{Elliptisches Filter}
 
 		\begin{equation*}
+			R_N = \cd(z_1, k_1),
+			\quad
 			z_1 = N~\frac{K_1}{K}~\cd^{-1}(w, k)
 		\end{equation*}
 
 		\begin{center}
-			\scalebox{0.8}{
+			\scalebox{0.75}{
 				\input{../tikz/cd2.tikz.tex}
 			}
 		\end{center}
 
 	\end{frame}
 
+
 	\begin{frame}
 		\frametitle{Elliptisches Filter}
 
@@ -401,13 +437,4 @@
 
 	\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_elliptic.pgf b/buch/papers/ellfilter/python/F_N_elliptic.pgf
index 03084c6..50faaaa 100644
--- a/buch/papers/ellfilter/python/F_N_elliptic.pgf
+++ b/buch/papers/ellfilter/python/F_N_elliptic.pgf
@@ -94,8 +94,8 @@
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 \pgfsetdash{}{0pt}%
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 \pgfpathlineto{\pgfqpoint{2.247564in}{1.250043in}}%
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@@ -114,11 +114,11 @@
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 \pgfpathclose%
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@@ -558,133 +558,162 @@
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+\pgfsetroundjoin%
+\pgfsetlinewidth{1.003750pt}%
+\definecolor{currentstroke}{rgb}{1.000000,0.647059,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{2.189776in}{1.789929in}}%
+\pgfpathlineto{\pgfqpoint{2.198207in}{1.037413in}}%
+\pgfpathlineto{\pgfqpoint{2.204331in}{0.756839in}}%
+\pgfpathlineto{\pgfqpoint{2.205368in}{0.723819in}}%
+\pgfpathlineto{\pgfqpoint{2.205368in}{0.723819in}}%
+\pgfusepath{stroke}%
+\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}{1.000000,0.000000,0.000000}%
+\pgfsetstrokecolor{currentstroke}%
+\pgfsetdash{}{0pt}%
+\pgfpathmoveto{\pgfqpoint{2.205368in}{0.723819in}}%
+\pgfpathlineto{\pgfqpoint{2.211596in}{0.579693in}}%
+\pgfpathlineto{\pgfqpoint{2.213153in}{0.554315in}}%
+\pgfpathlineto{\pgfqpoint{2.213932in}{0.554729in}}%
+\pgfpathlineto{\pgfqpoint{2.220938in}{0.631412in}}%
+\pgfpathlineto{\pgfqpoint{2.227945in}{0.675812in}}%
+\pgfpathlineto{\pgfqpoint{2.234951in}{0.701496in}}%
+\pgfpathlineto{\pgfqpoint{2.241958in}{0.715641in}}%
+\pgfpathlineto{\pgfqpoint{2.248186in}{0.721878in}}%
+\pgfpathlineto{\pgfqpoint{2.254414in}{0.724034in}}%
+\pgfpathlineto{\pgfqpoint{2.261420in}{0.723044in}}%
+\pgfpathlineto{\pgfqpoint{2.269984in}{0.718482in}}%
+\pgfpathlineto{\pgfqpoint{2.281661in}{0.708528in}}%
+\pgfpathlineto{\pgfqpoint{2.300345in}{0.688017in}}%
+\pgfpathlineto{\pgfqpoint{2.384424in}{0.591070in}}%
+\pgfpathlineto{\pgfqpoint{2.417121in}{0.560087in}}%
+\pgfpathlineto{\pgfqpoint{2.431134in}{0.549408in}}%
+\pgfpathlineto{\pgfqpoint{2.464610in}{0.575028in}}%
+\pgfpathlineto{\pgfqpoint{2.499642in}{0.597878in}}%
+\pgfpathlineto{\pgfqpoint{2.536232in}{0.618072in}}%
+\pgfpathlineto{\pgfqpoint{2.575936in}{0.636444in}}%
+\pgfpathlineto{\pgfqpoint{2.618753in}{0.652857in}}%
+\pgfpathlineto{\pgfqpoint{2.666242in}{0.667715in}}%
+\pgfpathlineto{\pgfqpoint{2.719180in}{0.680961in}}%
+\pgfpathlineto{\pgfqpoint{2.778347in}{0.692514in}}%
+\pgfpathlineto{\pgfqpoint{2.845298in}{0.702393in}}%
+\pgfpathlineto{\pgfqpoint{2.922370in}{0.710591in}}%
+\pgfpathlineto{\pgfqpoint{3.012676in}{0.717023in}}%
+\pgfpathlineto{\pgfqpoint{3.120888in}{0.721532in}}%
+\pgfpathlineto{\pgfqpoint{3.254012in}{0.723855in}}%
+\pgfpathlineto{\pgfqpoint{3.424505in}{0.723575in}}%
+\pgfpathlineto{\pgfqpoint{3.658834in}{0.719887in}}%
 \pgfpathlineto{\pgfqpoint{3.761597in}{0.717600in}}%
 \pgfpathlineto{\pgfqpoint{3.761597in}{0.717600in}}%
 \pgfusepath{stroke}%
diff --git a/buch/papers/ellfilter/python/elliptic.py b/buch/papers/ellfilter/python/elliptic.py
index b3336a1..c9cf5bd 100644
--- a/buch/papers/ellfilter/python/elliptic.py
+++ b/buch/papers/ellfilter/python/elliptic.py
@@ -324,9 +324,9 @@ 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].plot(k, K, linewidth=1)
 axs[0].text(k[30], K[30]+0.1, f"$K$")
-axs[0].plot(k, K_prime, linewidth=0.1)
+axs[0].plot(k, K_prime, linewidth=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])
diff --git a/buch/papers/ellfilter/python/elliptic2.py b/buch/papers/ellfilter/python/elliptic2.py
index 29c6f47..cfa16ea 100644
--- a/buch/papers/ellfilter/python/elliptic2.py
+++ b/buch/papers/ellfilter/python/elliptic2.py
@@ -1,5 +1,6 @@
 # %%
 
+import enum
 import matplotlib.pyplot as plt
 import scipy.signal
 import numpy as np
@@ -8,7 +9,9 @@ from matplotlib.patches import Rectangle
 
 import plot_params
 
-def ellip_filter(N):
+N=5
+
+def ellip_filter(N, mode=-1):
 
     order = N
     passband_ripple_db = 3
@@ -26,7 +29,16 @@ def ellip_filter(N):
         fs=None
     )
 
-    w, mag_db, phase = scipy.signal.bode((a, b), w=np.linspace(0*omega_c,2*omega_c, 4000))
+    if mode == 0:
+        w = np.linspace(0*omega_c,omega_c, 2000)
+    elif mode == 1:
+        w = np.linspace(omega_c,1.00992*omega_c, 2000)
+    elif mode == 2:
+        w = np.linspace(1.00992*omega_c,2*omega_c, 2000)
+    else:
+        w = np.linspace(0*omega_c,2*omega_c, 4000)
+
+    w, mag_db, phase = scipy.signal.bode((a, b), w=w)
 
     mag = 10**(mag_db/20)
 
@@ -40,9 +52,9 @@ def ellip_filter(N):
 
 plt.figure(figsize=(4,2.5))
 
-for N in [5]:
-    w, FN2, mag, a, b = ellip_filter(N)
-    plt.semilogy(w, FN2, label=f"$N={N}, k=0.1$", linewidth=1)
+for mode, c in enumerate(["green", "orange", "red"]):
+    w, FN2, mag, a, b = ellip_filter(N, mode=mode)
+    plt.semilogy(w, FN2, label=f"$N={N}, k=0.1$", linewidth=1, color=c)
 
 plt.gca().add_patch(Rectangle(
     (0, 0),
@@ -53,21 +65,21 @@ plt.gca().add_patch(Rectangle(
 ))
 plt.gca().add_patch(Rectangle(
     (1, 1),
-    0.01, 1e2-1,
+    0.00992, 1e2-1,
     fc ='orange',
     alpha=0.2,
     lw = 10,
 ))
 
 plt.gca().add_patch(Rectangle(
-    (1.01, 100),
+    (1.00992, 100),
     1, 1e6,
     fc ='red',
     alpha=0.2,
     lw = 10,
 ))
 
-zeros = [0,0.87,1]
+zeros = [0,0.87,0.995]
 poles = [1.01,1.155]
 
 import matplotlib.transforms
@@ -99,7 +111,7 @@ plt.ylim([1e-4,1e6])
 plt.grid()
 plt.xlabel("$w$")
 plt.ylabel("$F^2_N(w)$")
-plt.legend()
+# plt.legend()
 plt.tight_layout()
 plt.savefig("F_N_elliptic.pgf")
 plt.show()
@@ -107,7 +119,9 @@ plt.show()
 
 
 plt.figure(figsize=(4,2.5))
-plt.plot(w, mag, linewidth=1)
+for mode, c in enumerate(["green", "orange", "red"]):
+    w, FN2, mag, a, b = ellip_filter(N, mode=mode)
+    plt.plot(w, mag, linewidth=1, color=c)
 
 plt.gca().add_patch(Rectangle(
     (0, np.sqrt(2)/2),
@@ -118,14 +132,14 @@ plt.gca().add_patch(Rectangle(
 ))
 plt.gca().add_patch(Rectangle(
     (1, 0.1),
-    0.01, np.sqrt(2)/2 - 0.1,
+    0.00992, np.sqrt(2)/2 - 0.1,
     fc ='orange',
     alpha=0.2,
     lw = 10,
 ))
 
 plt.gca().add_patch(Rectangle(
-    (1.01, 0),
+    (1.00992, 0),
     1, 0.1,
     fc ='red',
     alpha=0.2,
diff --git a/buch/papers/ellfilter/python/k.pgf b/buch/papers/ellfilter/python/k.pgf
index 95d61d4..52dd705 100644
--- a/buch/papers/ellfilter/python/k.pgf
+++ b/buch/papers/ellfilter/python/k.pgf
@@ -320,7 +320,7 @@
 \pgfusepath{clip}%
 \pgfsetrectcap%
 \pgfsetroundjoin%
-\pgfsetlinewidth{0.100375pt}%
+\pgfsetlinewidth{1.003750pt}%
 \definecolor{currentstroke}{rgb}{0.121569,0.466667,0.705882}%
 \pgfsetstrokecolor{currentstroke}%
 \pgfsetdash{}{0pt}%
@@ -434,7 +434,7 @@
 \pgfusepath{clip}%
 \pgfsetrectcap%
 \pgfsetroundjoin%
-\pgfsetlinewidth{0.100375pt}%
+\pgfsetlinewidth{1.003750pt}%
 \definecolor{currentstroke}{rgb}{1.000000,0.498039,0.054902}%
 \pgfsetstrokecolor{currentstroke}%
 \pgfsetdash{}{0pt}%
diff --git a/buch/papers/ellfilter/tikz/arccos.tikz.tex b/buch/papers/ellfilter/tikz/arccos.tikz.tex
index 2772620..987f885 100644
--- a/buch/papers/ellfilter/tikz/arccos.tikz.tex
+++ b/buch/papers/ellfilter/tikz/arccos.tikz.tex
@@ -10,10 +10,10 @@
 
         \clip(-7.5,-2) rectangle (7.5,2);
 
-        \draw[thick, ->, darkgreen] (0, 0) -- (0,1.5);
-        \draw[thick, ->, orange] (1, 0) -- (0,0);
-        \draw[thick, ->, red] (2, 0) -- (1,0);
-        \draw[thick, ->, blue] (2,1.5) -- (2, 0);
+        \draw[ultra thick, ->, darkgreen] (0, 0) -- (0,1.5);
+        \draw[ultra thick, ->, orange] (1, 0) -- (0,0);
+        \draw[ultra thick, ->, red] (2, 0) -- (1,0);
+        \draw[ultra thick, ->, blue] (2,1.5) -- (2, 0);
 
         \foreach \i in {-2,...,1} {
             \begin{scope}[opacity=0.5, xshift=\i*4cm]
@@ -45,7 +45,7 @@
 
     \end{scope}
 
-    \begin{scope}[yshift=-2.5cm]
+    \begin{scope}[yshift=-3cm]
 
         \draw[gray, ->] (-5,0) -- (5,0) node[anchor=west]{$w$};
 
diff --git a/buch/papers/ellfilter/tikz/cd.tikz.tex b/buch/papers/ellfilter/tikz/cd.tikz.tex
index 7155a85..7a2767b 100644
--- a/buch/papers/ellfilter/tikz/cd.tikz.tex
+++ b/buch/papers/ellfilter/tikz/cd.tikz.tex
@@ -4,7 +4,7 @@
 
     \tikzset{pole/.style={cross out, draw=black, minimum size=(0.15cm-\pgflinewidth), inner sep=0pt, outer sep=0pt}}
 
-    \begin{scope}[xscale=1, yscale=2]
+    \begin{scope}[xscale=0.9, yscale=1.8]
 
         \draw[gray, ->] (0,-1.5) -- (0,1.5) node[anchor=south]{$\mathrm{Im}~z$};
         \draw[gray, ->] (-5,0) -- (5,0) node[anchor=west]{$\mathrm{Re}~z$};
@@ -23,12 +23,12 @@
                 \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);
+                \draw[ultra thick, ->, darkgreen] (0, 0) -- (0,0.5);
+                \draw[ultra thick, ->, orange] (1, 0) -- (0,0);
+                \draw[ultra thick, ->, red] (2, 0) -- (1,0);
+                \draw[ultra thick, ->, blue] (2,0.5) -- (2, 0);
+                \draw[ultra thick, ->, purple] (1, 0.5) -- (2,0.5);
+                \draw[ultra thick, ->, cyan] (0, 0.5) -- (1,0.5);
 
 
 
@@ -63,7 +63,7 @@
 
     \end{scope}
 
-    \begin{scope}[yshift=-3.5cm, xscale=0.75]
+    \begin{scope}[yshift=-4cm, xscale=0.75]
 
         \draw[gray, ->] (-6,0) -- (6,0) node[anchor=west]{$w$};
 
diff --git a/buch/papers/ellfilter/tikz/cd2.tikz.tex b/buch/papers/ellfilter/tikz/cd2.tikz.tex
index 0743f7d..425db95 100644
--- a/buch/papers/ellfilter/tikz/cd2.tikz.tex
+++ b/buch/papers/ellfilter/tikz/cd2.tikz.tex
@@ -5,9 +5,9 @@
 
     \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]
+    \begin{scope}[xscale=1.25, yscale=3.5]
 
-        \draw[gray, ->] (0,-0.75) -- (0,1.25) node[anchor=south]{$\mathrm{Im}~z_1$};
+        \draw[gray, ->] (0,-0.55) -- (0,1.05) 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 $K_1$};
@@ -35,12 +35,12 @@
             % \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);
+            % \fill[yellow!30] (0,0) rectangle (1, 0.1);
             \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]{$NK$}
+                (5,0.5) node(t_k_unten){} -- node[above, yshift=0.1cm]{$NK_1$}
                 (0,0.5) node(t_k_opt_unten){};
 
             \draw[decorate,decoration={brace,amplitude=3pt,mirror}, xshift=0.1cm]
@@ -63,9 +63,9 @@
 
 
 
-            \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[ultra thick, ->, darkgreen] (5, 0) -- node[yshift=-0.5cm]{Durchlassbereich} (0,0);
+            \draw[ultra thick, ->, orange] (-0, 0) --  node[align=center]{Übergangs-\\berech} (0,0.5);
+            \draw[ultra thick, ->, red] (0,0.5) -- node[align=center, yshift=0.7cm]{Sperrbereich} (5, 0.5);
 
             \draw (4,0  )  node[dot]{} node[anchor=south]      {\small $1$};
             \draw (2,0  )  node[dot]{} node[anchor=south]      {\small $-1$};
diff --git a/buch/papers/ellfilter/tikz/cd3.tikz.tex b/buch/papers/ellfilter/tikz/cd3.tikz.tex
new file mode 100644
index 0000000..fa9cc08
--- /dev/null
+++ b/buch/papers/ellfilter/tikz/cd3.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,-0.55) -- (0,1.05) node[anchor=south]{$\mathrm{Im}$};
+        \draw[gray, ->] (-1.5,0) -- (6,0) node[anchor=west]{$\mathrm{Re}$};
+
+        % \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]{$NK_1$}
+            %     (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[ultra thick, ->, darkgreen] (5, 0) -- node[yshift=-0.4cm]{Durchlassbereich} (0,0);
+            \draw[ultra thick, ->, orange] (-0, 0) --  node[align=center]{Übergangs-\\berech} (0,0.5);
+            \draw[ultra thick, ->, red] (0,0.5) -- node[align=center, yshift=0.4cm]{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/elliptic_transform.tikz.tex b/buch/papers/ellfilter/tikz/elliptic_transform.tikz.tex
new file mode 100644
index 0000000..c91ecf1
--- /dev/null
+++ b/buch/papers/ellfilter/tikz/elliptic_transform.tikz.tex
@@ -0,0 +1,64 @@
+
+\def\d{0.2}
+\def\n{3}
+\def\nn{2}
+\def\a{2.5}
+
+\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=3, yscale=3]
+
+    \begin{scope}[]
+
+        \fill[orange!30, scale=1.735] (0,0) rectangle (\d*\a+0.5, \d/\a+0.5);
+        \fill[yellow!30] (0,0) rectangle (\d*\a+0.5, \d/\a+0.5);
+
+        \begin{scope}[scale=1.735, red]
+            \draw (0,0) rectangle (\d*\a/\n+0.5/\n, \d/\a+0.5);
+            \draw[gray] (0,0) -- (\d*\a/\n+0.5/\n, \d/\a+0.5);
+
+            \node[zero] at ( \d*\a/\n+0.5/\n, \d/\a+0.5) {};
+            \node[pole, color=red] at ( \d*\a/\n+0.5/\n, 0) {};
+
+
+            \draw[] ( \d*\a/\n+0.5/\n,0)  node[anchor=north] {\small $K_1$};
+            \draw[]  (0, \d/\a+0.5)  node[anchor=east]{\small $jK_1^\prime$};
+
+        \end{scope}
+
+        \begin{scope}[blue]
+            \draw[] (0,0) rectangle (\d*\a+0.5, \d/\a+0.5);
+            \foreach \i in {1,...,\nn} {
+                \draw[gray, dotted] (\i*\d*\a/\n+\i*0.5/\n, 0) -- (\i*\d*\a/\n+\i*0.5/\n, \d/\a+0.5);
+            }
+
+            \node[zero] at ( \d*\a+0.5, \d/\a+0.5) {};
+            \node[pole, color=blue] at ( \d*\a+0.5, 0) {};
+
+            \draw[] ( \d*\a+0.5,0)  node[anchor=north] {\small $K$};
+            \draw[]  (0, \d/\a+0.5)  node[anchor=east]{\small $jK^\prime$};
+
+            \node[dot, gray] at (\d*\a/\n+0.5/\n, \d/\a+0.5) {};
+            \node[above] at (0.5*\d*\a/\n+0.5*0.5/\n, \d/\a+0.5) {\small $K/N$};
+
+        \end{scope}
+
+        \draw[thick, gray, ->] (0,-0.25) -- (0,1.25) node[anchor=south]{$\mathrm{Im}$};
+        \draw[thick, gray, ->] (-0.25,0) -- (2,0) node[anchor=west]{$\mathrm{Re}$};
+
+        \begin{scope}[]
+            \clip(0,0) rectangle (2,1.25);
+            \draw[scale=1, domain=0.1:10,  variable=\x, smooth, samples=200] plot ({\d*\x1+0.5}, {\d/\x+0.5});
+
+        \end{scope}
+    \end{scope}
+
+
+\end{scope}
+
+\end{tikzpicture}
diff --git a/buch/papers/ellfilter/tikz/sn.tikz.tex b/buch/papers/ellfilter/tikz/sn.tikz.tex
index 87c63c0..6ced3c5 100644
--- a/buch/papers/ellfilter/tikz/sn.tikz.tex
+++ b/buch/papers/ellfilter/tikz/sn.tikz.tex
@@ -4,7 +4,7 @@
 
     \tikzset{pole/.style={cross out, draw=black, minimum size=(0.15cm-\pgflinewidth), inner sep=0pt, outer sep=0pt}}
 
-    \begin{scope}[xscale=1, yscale=2]
+    \begin{scope}[xscale=0.9, yscale=1.8]
 
         \draw[gray, ->] (0,-1.5) -- (0,1.5) node[anchor=south]{$\mathrm{Im}~z$};
         \draw[gray, ->] (-5,0) -- (5,0) node[anchor=west]{$\mathrm{Re}~z$};
@@ -17,12 +17,12 @@
 
             \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);
+                \draw[ultra thick, ->, darkgreen] (0, 0) -- (0,0.5);
+                \draw[ultra thick, ->, orange] (1, 0) -- (0,0);
+                \draw[ultra thick, ->, red] (2, 0) -- (1,0);
+                \draw[ultra thick, ->, blue] (2,0.5) -- (2, 0);
+                \draw[ultra thick, ->, purple] (1, 0.5) -- (2,0.5);
+                \draw[ultra thick, ->, cyan] (0, 0.5) -- (1,0.5);
 
 
                 \foreach \i in {-2,...,2} {
@@ -61,7 +61,7 @@
 
     \end{scope}
 
-    \begin{scope}[yshift=-3.5cm, xscale=0.75]
+    \begin{scope}[yshift=-4cm, xscale=0.75]
 
         \draw[gray, ->] (-6,0) -- (6,0) node[anchor=west]{$w$};