diff options
Diffstat (limited to 'buch/papers/ellfilter/tikz')
| -rw-r--r-- | buch/papers/ellfilter/tikz/arccos.tikz.tex | 57 | ||||
| -rw-r--r-- | buch/papers/ellfilter/tikz/arccos2.tikz.tex | 5 | ||||
| -rw-r--r-- | buch/papers/ellfilter/tikz/cd.tikz.tex | 21 | ||||
| -rw-r--r-- | buch/papers/ellfilter/tikz/cd2.tikz.tex | 37 | ||||
| -rw-r--r-- | buch/papers/ellfilter/tikz/cd3.tikz.tex | 86 | ||||
| -rw-r--r-- | buch/papers/ellfilter/tikz/elliptic_transform1.tikz.tex | 76 | ||||
| -rw-r--r-- | buch/papers/ellfilter/tikz/elliptic_transform2.tikz.tex | 75 | ||||
| -rw-r--r-- | buch/papers/ellfilter/tikz/filter.tikz.tex | 26 | ||||
| -rw-r--r-- | buch/papers/ellfilter/tikz/sn.tikz.tex | 53 |
9 files changed, 358 insertions, 78 deletions
diff --git a/buch/papers/ellfilter/tikz/arccos.tikz.tex b/buch/papers/ellfilter/tikz/arccos.tikz.tex index 2772620..4211053 100644 --- a/buch/papers/ellfilter/tikz/arccos.tikz.tex +++ b/buch/papers/ellfilter/tikz/arccos.tikz.tex @@ -8,29 +8,6 @@ \begin{scope}[xscale=0.6] - \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); - - \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) {$-\pi$}; @@ -43,9 +20,41 @@ % \node[gray, anchor=south east] at (0, 0) {$0$}; \node[gray, anchor=east] at (0, 1.5) {$\infty$}; + \clip(-7.5,-2) rectangle (7.5,2); + + % \pause + \draw[ultra thick, ->, orange] (1, 0) -- (0,0); + % \pause + \draw[ultra thick, ->, darkgreen] (0, 0) -- (0,1.5); + % \pause + \draw[ultra thick, ->, red] (2, 0) -- (1,0); + \draw[ultra thick, ->, blue] (2,1.5) -- (2, 0); + + % \pause + + \foreach \i in {-2,...,1} { + \begin{scope}[xshift=\i*4cm] + \begin{scope}[opacity=0.5] + \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); + \end{scope} + \node[zero] at (1,0) {}; + \node[zero] at (3,0) {}; + \end{scope} + } + \end{scope} - \begin{scope}[yshift=-2.5cm] + \node[zero] at (4,2) (n) {}; + \node[anchor=west] at (n.east) {Zero}; + + \begin{scope}[yshift=-3cm] \draw[gray, ->] (-5,0) -- (5,0) node[anchor=west]{$w$}; diff --git a/buch/papers/ellfilter/tikz/arccos2.tikz.tex b/buch/papers/ellfilter/tikz/arccos2.tikz.tex index 3fc3cc6..755e8a0 100644 --- a/buch/papers/ellfilter/tikz/arccos2.tikz.tex +++ b/buch/papers/ellfilter/tikz/arccos2.tikz.tex @@ -14,7 +14,6 @@ \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) 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) {}; \node[zero] at (-5,0) {}; \node[zero] at (-3,0) {}; @@ -24,7 +23,6 @@ \node[zero] at (5,0) {}; \node[zero] at (7,0) {}; - \end{scope} \node[gray, anchor=north] at (-8,0) {$-4\pi$}; @@ -42,4 +40,7 @@ \end{scope} + \node[zero] at (4,2) (n) {}; + \node[anchor=west] at (n.east) {Zero}; + \end{tikzpicture}
\ No newline at end of file diff --git a/buch/papers/ellfilter/tikz/cd.tikz.tex b/buch/papers/ellfilter/tikz/cd.tikz.tex index 7155a85..b2b0090 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 +63,12 @@ \end{scope} - \begin{scope}[yshift=-3.5cm, xscale=0.75] + \node[zero] at (4,3) (n) {}; + \node[anchor=west] at (n.east) {Zero}; + \node[pole, below=0.25cm of n] (n) {}; + \node[anchor=west] at (n.east) {Pole}; + + \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..bba5789 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 $K_1$}; @@ -35,18 +35,30 @@ % \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] (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){}; + + \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 $-1$}; + \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 $1/k$}; + \foreach \i in {-2,...,1} { \foreach \j in {-2,...,1} { \begin{scope}[xshift=\i*4cm, yshift=\j*1cm] @@ -60,25 +72,8 @@ } } - - - - \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/cd3.tikz.tex b/buch/papers/ellfilter/tikz/cd3.tikz.tex new file mode 100644 index 0000000..ae18519 --- /dev/null +++ b/buch/papers/ellfilter/tikz/cd3.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] + \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); + + + % \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} + } + } + + + + \onslide<2->{ + \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); + \node[] at (2.5, 0.25) {\small $N=5$}; + } + \onslide<1->{ + \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_transform1.tikz.tex b/buch/papers/ellfilter/tikz/elliptic_transform1.tikz.tex new file mode 100644 index 0000000..2a36ee0 --- /dev/null +++ b/buch/papers/ellfilter/tikz/elliptic_transform1.tikz.tex @@ -0,0 +1,76 @@ +\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} diff --git a/buch/papers/ellfilter/tikz/elliptic_transform2.tikz.tex b/buch/papers/ellfilter/tikz/elliptic_transform2.tikz.tex new file mode 100644 index 0000000..20c2d82 --- /dev/null +++ b/buch/papers/ellfilter/tikz/elliptic_transform2.tikz.tex @@ -0,0 +1,75 @@ + +\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, minimum size=(0.15cm-\pgflinewidth), inner sep=0pt, outer sep=0pt}} + + \begin{scope}[xscale=3, yscale=3] + + \begin{scope}[] + % \onslide<4->{ + \fill[orange!30, scale=1.735] (0,0) rectangle (\d*\a+0.5, \d/\a+0.5); + % } + % \onslide<2->{ + \fill[yellow!30] (0,0) rectangle (\d*\a+0.5, \d/\a+0.5); + % } + + \begin{scope}[] + \clip(0,0) rectangle (2,1.25); + \draw[thick, scale=1, domain=0.1:10, variable=\x, smooth, samples=200] plot ({\d*\x1+0.5}, {\d/\x+0.5}); + \node at(1.25,0.7) {$K + jK^\prime$ Ortskurve}; + \end{scope} + + % \onslide<2->{ + \begin{scope}[blue] + \draw[] (0,0) rectangle (\d*\a+0.5, \d/\a+0.5); + + + \node[pole] at ( \d*\a+0.5, \d/\a+0.5) {}; + \node[zero] 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 $jK^\prime$}; + + % \onslide<3->{ + + \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[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} + % } + + % \onslide<4->{ + \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[pole] at ( \d*\a/\n+0.5/\n, \d/\a+0.5) {}; + \node[zero] 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} + % } + + \draw[gray, ->] (0,-0.25) -- (0,1.25) node[anchor=south]{$\mathrm{Im}$}; + \draw[gray, ->] (-0.25,0) -- (2,0) node[anchor=west]{$\mathrm{Re}$}; + + \end{scope} + +\end{scope} + +\end{tikzpicture} diff --git a/buch/papers/ellfilter/tikz/filter.tikz.tex b/buch/papers/ellfilter/tikz/filter.tikz.tex new file mode 100644 index 0000000..05b59b9 --- /dev/null +++ b/buch/papers/ellfilter/tikz/filter.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] + + \fill[ gray!20] (0,0) rectangle (1,0.707); + + \draw[gray, ->] (0,-0.25) -- (0,1.25) node[anchor=south]{$|H(\Omega)|$}; + \draw[gray, ->] (-0.25,0) -- (3,0) node[anchor=west]{$\Omega$}; + + \draw[fill = gray!20] (0,0.707) node[left] {$\sqrt{\frac{1}{1+\varepsilon^2}}$} -| (1,0) node[below] {$\Omega_p$}; + + \draw[fill = gray!20] (0,0.707) node[left] {$\sqrt{\frac{1}{1+\varepsilon^2}}$} -| (1,0) node[below] {$\Omega_p$}; + + \begin{scope}[] + \draw[thick, domain=0:2.5, variable=\x, smooth, samples=200] plot + ({\x}, {sqrt(abs(1/ (1 + \x^10)))}); + + \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..8e4d223 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]{$\mathrm{Re}~z$}; @@ -17,29 +17,33 @@ \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); - + % \pause + \draw[ultra thick, <-, orange] (2, 0) -- (1,0); + % \pause + \draw[ultra thick, <-, darkgreen] (2,0.5) -- (2, 0); + % \pause + \draw[ultra thick, <-, cyan] (1, 0.5) -- (2,0.5); + % \pause + \draw[ultra thick, <-, blue] (0, 0) -- (0,0.5); + \draw[ultra thick, <-, purple] (0, 0.5) -- (1,0.5); + \draw[ultra thick, <-, red] (1, 0) -- (0,0); + % \pause \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); + \draw[opacity=0.5, <-, blue] (0, 0) -- (0,0.5); + \draw[opacity=0.5, <-, red] (1, 0) -- (0,0); + \draw[opacity=0.5, <-, orange] (2, 0) -- (1,0); + \draw[opacity=0.5, <-, darkgreen] (2,0.5) -- (2, 0); + \draw[opacity=0.5, <-, cyan] (1, 0.5) -- (2,0.5); + \draw[opacity=0.5, <-, purple] (0, 0.5) -- (1,0.5); + \draw[opacity=0.5, <-, blue] (0,1) -- (0,0.5); + \draw[opacity=0.5, <-, darkgreen] (2,0.5) -- (2, 1); + \draw[opacity=0.5, <-, cyan] (3, 0.5) -- (2,0.5); + \draw[opacity=0.5, <-, purple] (4, 0.5) -- (3,0.5); + \draw[opacity=0.5, <-, orange] (2, 0) -- (3,0); + \draw[opacity=0.5, <-, red] (3, 0) -- (4,0); \node[zero] at ( 1, 0) {}; \node[zero] at ( 3, 0) {}; @@ -57,11 +61,14 @@ \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] + \node[zero] at (4,3) (n) {}; + \node[anchor=west] at (n.east) {Zero}; + \node[pole, below=0.25cm of n] (n) {}; + \node[anchor=west] at (n.east) {Pole}; + + \begin{scope}[yshift=-4cm, xscale=0.75] \draw[gray, ->] (-6,0) -- (6,0) node[anchor=west]{$w$}; |