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path: root/buch/papers/ellfilter/tikz/elliptic_transform1.tikz.tex
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\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, minimum size=(0.15cm-\pgflinewidth), inner sep=0pt, outer sep=0pt}}

    \begin{scope}[xscale=1, yscale=1.5]

    \begin{scope}[]

        \fill[orange!25] (0,0) rectangle (1.5, 0.75);
        \fill[yellow!50] (0,0) rectangle (0.5, 0.25);

        \draw[gray, ->] (0,-0.75) -- (0,1.25) node[anchor=south]{$\mathrm{Im}~z$};
        \draw[gray, ->] (-1.75,0) -- (1.75,0) node[anchor=west]{$\mathrm{Re}~z$};

        \draw[gray] ( 0.5,0) +(0,0.05) -- +(0, -0.05) node[inner sep=0, anchor=north] {\small $K$};
        \draw[gray]  (0, 0.25) +(0.05, 0) -- +(-0.05, 0) node[inner sep=0, anchor=east]{\small $jK^\prime$};

        % \draw[gray] ( 1.5,0) +(0,0.05) -- +(0, -0.05) node[inner sep=0, anchor=north] {\small $K_1$};
        % \draw[gray]  (0, 0.75) +(0.05, 0) -- +(-0.05, 0) node[inner sep=0, anchor=east]{\small $jK_1^\prime$};

        \clip(-1.6,-0.6) rectangle (1.6,1.6);
        \begin{scope}[xscale=0.5, yscale=0.25, blue]
            \foreach \i in {-1,...,1} {
                \foreach \j in {-1,...,2} {
                    \begin{scope}[xshift=\i*2cm, yshift=\j*2cm]
                        \node[zero] at ( 1, 0) {};
                        \node[zero] at ( -1, 0) {};
                        \node[pole] at ( 1,1) {};
                        \node[pole] at ( -1,1) {};
                    \end{scope}
                }
            }
        \end{scope}

        \node at (0,2) {$\cd \left(N~K_1~z , k_1 \right)$};
        \node at (0,2) {$w= \cd(z K, k)$};

        \draw[scale=0.2, domain=0.02:5,  variable=\x, red] plot ({\x1+3}, {1/\x+2});

    \end{scope}

    \begin{scope}[xshift=5cm]

        \fill[orange!50] (0,0) rectangle (1.5, 0.75);
        \fill[yellow!25] (0,0) rectangle (0.5, 0.25);

        \draw[gray, ->] (0,-0.75) -- (0,1.25) node[anchor=south]{$\mathrm{Im}~z$};
        \draw[gray, ->] (-1.75,0) -- (1.75,0) node[anchor=west]{$\mathrm{Re}~z$};

        % \draw[gray] ( 0.5,0) +(0,0.05) -- +(0, -0.05) node[inner sep=0, anchor=north] {\small $K$};
        % \draw[gray]  (0, 0.25) +(0.05, 0) -- +(-0.05, 0) node[inner sep=0, anchor=east]{\small $jK^\prime$};

        \draw[gray] ( 0.5,0) +(0,0.05) -- +(0, -0.05) node[inner sep=0, anchor=north] {\small $K_1$};
        \draw[gray]  (0, 0.75) +(0.05, 0) -- +(-0.05, 0) node[inner sep=0, anchor=east]{\small $jK_1^\prime$};

        \clip(-1.6,-0.6) rectangle (1.6,1.6);
        \begin{scope}[xscale=0.5, yscale=0.75, red]
            \foreach \i in {-1,...,1} {
                \foreach \j in {-1,...,0} {
                    \begin{scope}[xshift=\i*2cm, yshift=\j*2cm]
                        \node[zero] at ( 1, 0) {};
                        \node[zero] at ( -1, 0) {};
                        \node[pole] at ( 1,1) {};
                        \node[pole] at ( -1,1) {};
                    \end{scope}
                }
            }
        \end{scope}

    \end{scope}

\end{scope}

\end{tikzpicture}