working on presentation

6 files changed, 176 insertions, 28 deletions

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]{$w$};