Added content, presentation

6 files changed, 321 insertions, 70 deletions

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