draft

2 files changed, 143 insertions, 0 deletions

diff --git a/buch/papers/ellfilter/tikz/arccos.tikz.tex b/buch/papers/ellfilter/tikz/arccos.tikz.tex
new file mode 100644
index 0000000..2bdcc2d
--- /dev/null
+++ b/buch/papers/ellfilter/tikz/arccos.tikz.tex
@@ -0,0 +1,97 @@
+\begin{tikzpicture}[>=stealth', auto, node distance=2cm, scale=1.2]
+
+
+    \draw[gray, ->] (0,-2) -- (0,2) node[anchor=south]{Im $z$};
+    \draw[gray, ->] (-5,0) -- (5,0) node[anchor=west]{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}[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}
+
+    \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) {$\infty$};
+
+
+
+    \begin{scope}[yshift=-2.5cm]
+
+        \draw[gray, ->] (-5,0) -- (5,0) node[anchor=west]{$w$};
+
+        \draw[thick, ->, blue]      (-4, 0) -- (-2, 0);
+        \draw[thick, ->, red]       (-2, 0) -- (0, 0);
+        \draw[thick, ->, orange]    (0, 0) -- (2, 0);
+        \draw[thick, ->, darkgreen] (2, 0) -- (4, 0);
+
+        \node[anchor=south] at (-4,0) {$-\infty$};
+        \node[anchor=south] at (-2,0) {$-1$};
+        \node[anchor=south] at (0,0) {$0$};
+        \node[anchor=south] at (2,0) {$1$};
+        \node[anchor=south] at (4,0) {$\infty$};
+
+    \end{scope}
+
+\end{tikzpicture}
\ No newline at end of file
diff --git a/buch/papers/ellfilter/tikz/arccos2.tikz.tex b/buch/papers/ellfilter/tikz/arccos2.tikz.tex
new file mode 100644
index 0000000..dcf02fd
--- /dev/null
+++ b/buch/papers/ellfilter/tikz/arccos2.tikz.tex
@@ -0,0 +1,46 @@
+\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 $z$};
+
+        \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);
+
+
+            \node[zero] at (-7,0) {};
+            \node[zero] at (-5,0) {};
+            \node[zero] at (-3,0) {};
+            \node[zero] at (-1,0) {};
+            \node[zero] at (1,0) {};
+            \node[zero] at (3,0) {};
+            \node[zero] at (5,0) {};
+            \node[zero] at (7,0) {};
+
+
+        \end{scope}
+
+        \node[gray, anchor=north] at (-8,0) {$-4\pi$};
+        \node[gray, anchor=north] at (-6,0) {$-3\pi$};
+        \node[gray, anchor=north] at (-4,0) {$-2\pi$};
+        \node[gray, anchor=north] at (-2,0) {$-\pi$};
+        \node[gray, anchor=north] at (2,0) {$\pi$};
+        \node[gray, anchor=north] at (4,0) {$2\pi$};
+        \node[gray, anchor=north] at (6,0) {$3\pi$};
+        \node[gray, anchor=north] at (8,0) {$4\pi$};
+
+
+        \node[gray, anchor=east] at (0,-1.5) {$-\infty$};
+        \node[gray, anchor=east] at (0, 1.5) {$\infty$};
+
+    \end{scope}
+
+\end{tikzpicture}
\ No newline at end of file