Merge branch 'master' of https://github.com/AndreasFMueller/SeminarMatrizen

11 files changed, 956 insertions, 0 deletions

diff --git a/buch/papers/reedsolomon/tikz/codiert.txt b/buch/papers/reedsolomon/tikz/codiert.txt
new file mode 100644
index 0000000..4a481d8
--- /dev/null
+++ b/buch/papers/reedsolomon/tikz/codiert.txt
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diff --git a/buch/papers/reedsolomon/tikz/decodiert.txt b/buch/papers/reedsolomon/tikz/decodiert.txt
new file mode 100644
index 0000000..f6221e6
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diff --git a/buch/papers/reedsolomon/tikz/empfangen.txt b/buch/papers/reedsolomon/tikz/empfangen.txt
new file mode 100644
index 0000000..38c13b0
--- /dev/null
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diff --git a/buch/papers/reedsolomon/tikz/fehler.txt b/buch/papers/reedsolomon/tikz/fehler.txt
new file mode 100644
index 0000000..23f1a83
--- /dev/null
+++ b/buch/papers/reedsolomon/tikz/fehler.txt
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diff --git a/buch/papers/reedsolomon/tikz/locator.txt b/buch/papers/reedsolomon/tikz/locator.txt
new file mode 100644
index 0000000..b28988c
--- /dev/null
+++ b/buch/papers/reedsolomon/tikz/locator.txt
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diff --git a/buch/papers/reedsolomon/tikz/plotfft.tex b/buch/papers/reedsolomon/tikz/plotfft.tex
new file mode 100644
index 0000000..bb74dfb
--- /dev/null
+++ b/buch/papers/reedsolomon/tikz/plotfft.tex
@@ -0,0 +1,94 @@
+%
+% Plot der Übertrangungsabfolge ins FFT und zurück mit IFFT
+%
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{pgfplots}
+\usepackage{pgfplotstable}
+\usepackage{csvsimple}
+\usepackage{filecontents}
+
+
+\begin{document}
+\begin{tikzpicture}[]
+
+	%---------------------------------------------------------------
+	%Knote
+	\matrix(m) [draw = none, column sep=25mm, row sep=2mm]{
+
+		\node(signal)  []    {
+		\begin{tikzpicture}
+			\begin{axis}
+				[title = {\Large {Signal}}, 
+				xtick={0,20,40,64,80,98}]
+				\addplot[blue] table[col sep=comma] {tikz/signal.txt};
+			\end{axis}
+		\end{tikzpicture}}; &
+		
+		\node(codiert) []    {
+		\begin{tikzpicture}[]
+			\begin{axis}[ title = {\Large {Codiert \space + \space Fehler}},
+				xtick={0,40,60,100}, axis y line*=left]
+				\addplot[green] table[col sep=comma] {tikz/codiert.txt};
+			\end{axis}
+			\begin{axis}[xtick={7,21,75}, axis y line*=right]
+					\addplot[red] table[col sep=comma] {tikz/fehler.txt};
+			\end{axis}
+		\end{tikzpicture}}; \\
+		
+		\node(decodiert) []    {
+		\begin{tikzpicture}
+			\begin{axis}[title = {\Large {Decodiert}}]
+				\addplot[blue] table[col sep=comma] {tikz/decodiert.txt};
+			\end{axis}
+		\end{tikzpicture}}; &
+	
+		\node(empfangen) []    {
+		\begin{tikzpicture}
+			\begin{axis}[title = {\Large {Empfangen}}]
+				\addplot[green] table[col sep=comma] {tikz/empfangen.txt};
+			\end{axis}
+		\end{tikzpicture}};\\
+	
+		\node(syndrom) []   {
+		\begin{tikzpicture}
+			\begin{axis}[title = {\Large {Syndrom}}]
+				\addplot[black] table[col sep=comma] {tikz/syndrom.txt};
+			\end{axis}
+		\end{tikzpicture}}; &
+	
+		\node(locator) []    {
+		\begin{tikzpicture}
+			\begin{axis}[title = {\Large {Locator}}]
+				\addplot[gray] table[col sep=comma] {tikz/locator.txt};
+			\end{axis}
+		\end{tikzpicture}};\\
+	};
+	%-------------------------------------------------------------
+		%FFT & IFFT deskription
+	
+	\draw[thin,gray,dashed] (0,9) to (0,-9);
+	\node(IFFT)  [scale=0.9]  at (0,9.3)   {IFFT};
+	\draw[stealth-](IFFT.south west)--(IFFT.south east);
+	\node(FFT)  [scale=0.9, above of=IFFT]    {FFT};
+	\draw[-stealth](FFT.north west)--(FFT.north east);
+	
+	\draw[thick, ->,] (codiert)++(-1,0) +(0.05,0.5) -- +(-0.1,-0.1) -- +(0.1,0.1) -- +(0,-0.5);
+	%Arrows
+	\draw[thick, ->] (signal.east) to (codiert.west);
+	\draw[thick, ->] (codiert.south) to (empfangen.north);
+	\draw[thick, ->] (empfangen.west) to (decodiert.east);
+	\draw[thick, ->] (syndrom.east) to (locator.west);
+	\draw[thick](decodiert.south east)++(-1.8,1)  ellipse (1.3cm and 0.8cm) ++(-1.3,0) coordinate(zoom) ;
+	\draw[thick, ->] (zoom) to[out=180, in=90] (syndrom.north);
+	
+	%item
+	\node[circle, draw, fill =lightgray] at (signal.north west) {1};
+	\node[circle, draw, fill =lightgray] at (codiert.north west) {2+3};
+	\node[circle, draw, fill =lightgray] at (empfangen.north west) {4};
+	\node[circle, draw, fill =lightgray] at (decodiert.north west) {5};
+	\node[circle, draw, fill =lightgray] at (syndrom.north west) {6};
+	\node[circle, draw, fill =lightgray] at (locator.north west) {7};
+\end{tikzpicture}	
+\end{document}
\ No newline at end of file
diff --git a/buch/papers/reedsolomon/tikz/plotfftraw.tex b/buch/papers/reedsolomon/tikz/plotfftraw.tex
new file mode 100644
index 0000000..141d2ce
--- /dev/null
+++ b/buch/papers/reedsolomon/tikz/plotfftraw.tex
@@ -0,0 +1,80 @@
+\begin{tikzpicture}[]
+
+	%---------------------------------------------------------------
+	%Knote
+	\matrix(m) [draw = none, column sep=25mm, row sep=2mm]{
+
+		\node(signal)  []    {
+		\begin{tikzpicture}
+			\begin{axis}
+				[title = {\Large {Signal}}, 
+				xtick={0,20,40,64,80,98}]
+				\addplot[blue] table[col sep=comma] {tikz/signal.txt};
+			\end{axis}
+		\end{tikzpicture}}; &
+		
+		\node(codiert) []    {
+		\begin{tikzpicture}[]
+			\begin{axis}[ title = {\Large {Codiert \space + \space Fehler}},
+				xtick={0,40,60,100}, axis y line*=left]
+				\addplot[green] table[col sep=comma] {tikz/codiert.txt};
+			\end{axis}
+			\begin{axis}[xtick={7,21,75}, axis y line*=right]
+					\addplot[red] table[col sep=comma] {tikz/fehler.txt};
+			\end{axis}
+		\end{tikzpicture}}; \\
+		
+		\node(decodiert) []    {
+		\begin{tikzpicture}
+			\begin{axis}[title = {\Large {Decodiert}}]
+				\addplot[blue] table[col sep=comma] {tikz/decodiert.txt};
+			\end{axis}
+		\end{tikzpicture}}; &
+	
+		\node(empfangen) []    {
+		\begin{tikzpicture}
+			\begin{axis}[title = {\Large {Empfangen}}]
+				\addplot[green] table[col sep=comma] {tikz/empfangen.txt};
+			\end{axis}
+		\end{tikzpicture}};\\
+	
+		\node(syndrom) []   {
+		\begin{tikzpicture}
+			\begin{axis}[title = {\Large {Syndrom}}]
+				\addplot[black] table[col sep=comma] {tikz/syndrom.txt};
+			\end{axis}
+		\end{tikzpicture}}; &
+	
+		\node(locator) []    {
+		\begin{tikzpicture}
+			\begin{axis}[title = {\Large {Locator}}]
+				\addplot[gray] table[col sep=comma] {tikz/locator.txt};
+			\end{axis}
+		\end{tikzpicture}};\\
+	};
+	%-------------------------------------------------------------
+		%FFT & IFFT deskription
+	
+	\draw[thin,gray,dashed] (0,9) to (0,-9);
+	\node(IFFT)  [scale=0.9]  at (0,9.3)   {IFFT};
+	\draw[stealth-](IFFT.south west)--(IFFT.south east);
+	\node(FFT)  [scale=0.9, above of=IFFT]    {FFT};
+	\draw[-stealth](FFT.north west)--(FFT.north east);
+	
+	\draw[thick, ->,] (codiert)++(-1,0) +(0.05,0.5) -- +(-0.1,-0.1) -- +(0.1,0.1) -- +(0,-0.5);
+	%Arrows
+	\draw[thick, ->] (signal.east) to (codiert.west);
+	\draw[thick, ->] (codiert.south) to (empfangen.north);
+	\draw[thick, ->] (empfangen.west) to (decodiert.east);
+	\draw[thick, ->] (syndrom.east) to (locator.west);
+	\draw[thick](decodiert.south east)++(-1.8,1)  ellipse (1.3cm and 0.8cm) ++(-1.3,0) coordinate(zoom) ;
+	\draw[thick, ->] (zoom) to[out=180, in=90] (syndrom.north);
+	
+	%item
+	\node[circle, draw, fill =lightgray] at (signal.north west) {1};
+	\node[circle, draw, fill =lightgray] at (codiert.north west) {2+3};
+	\node[circle, draw, fill =lightgray] at (empfangen.north west) {4};
+	\node[circle, draw, fill =lightgray] at (decodiert.north west) {5};
+	\node[circle, draw, fill =lightgray] at (syndrom.north west) {6};
+	\node[circle, draw, fill =lightgray] at (locator.north west) {7};
+\end{tikzpicture}	
\ No newline at end of file
diff --git a/buch/papers/reedsolomon/tikz/polynom2.tex b/buch/papers/reedsolomon/tikz/polynom2.tex
new file mode 100644
index 0000000..80557fb
--- /dev/null
+++ b/buch/papers/reedsolomon/tikz/polynom2.tex
@@ -0,0 +1,60 @@
+% polynome
+%-------------------
+
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{pgfplots}
+
+
+\begin{document}
+% Teiler für das Skalieren der Grafik /40
+\newcommand{\teiler}{40}
+
+
+%//////////////////////////////////////
+
+\begin{tikzpicture}[>=latex,thick,]
+	\draw[color=blue, line width=1.4pt] 
+	plot[domain=0:8, samples=100]
+	({\x},{(2*\x^2+1*\x+5)/\teiler});
+
+	\draw[->] (-0.2,0) -- (8,0) coordinate[label={$x$}];
+	\draw[->] (0,-0.2) -- (0,150/\teiler) coordinate[label={right:$p(x)$}];
+	
+	\def\punkt#1{
+		\fill[color=green] #1 circle[radius=0.08];
+		\draw #1 circle[radius=0.07];
+	}
+
+	\def\hellpunkt#1{
+		\fill[color=lightgray] #1 circle[radius=0.08];
+		\draw[gray] #1 circle[ radius=0.07];
+	}
+	
+	\draw[color=gray,line width=1pt,dashed] 
+	plot[domain=0.5:7, samples=100]
+	({\x},{(7.832*\x^2-51.5*\x+121.668)/\teiler});
+
+
+	\punkt{(1,8/\teiler)}
+	\hellpunkt{(2,15/\teiler)}
+	\hellpunkt{(3,26/\teiler)}
+	\punkt{(4,41/\teiler)}
+	\punkt{(5,60/\teiler)}
+	\punkt{(6,83/\teiler)}
+	\punkt{(7,110/\teiler)}
+	
+
+	
+	\def\erpunkt#1{
+		\fill[color=red] #1 circle[radius=0.08];
+		\draw #1 circle[radius=0.07];
+	}
+	\erpunkt{(2,50/\teiler)}
+	\erpunkt{(3,37.66/\teiler)}
+
+	\draw(0,100/\teiler) -- (-0.1,100/\teiler) coordinate[label={left:$100$}];
+	\draw(1,0) -- (1,-0.1) coordinate[label={below:$1$}];		
+\end{tikzpicture}
+\end{document}
diff --git a/buch/papers/reedsolomon/tikz/polynomraw.tex b/buch/papers/reedsolomon/tikz/polynomraw.tex
new file mode 100644
index 0000000..02968fd
--- /dev/null
+++ b/buch/papers/reedsolomon/tikz/polynomraw.tex
@@ -0,0 +1,50 @@
+% polynomraw
+
+\newcommand{\teiler}{40}
+
+
+%//////////////////////////////////////
+
+\begin{tikzpicture}[>=latex,thick,]
+	\draw[color=blue, line width=1.4pt] 
+	plot[domain=0:8, samples=100]
+	({\x},{(2*\x^2+1*\x+5)/\teiler});
+
+	\draw[->] (-0.2,0) -- (8,0) coordinate[label={$x$}];
+	\draw[->] (0,-0.2) -- (0,150/\teiler) coordinate[label={right:$p(x)$}];
+	
+	\def\punkt#1{
+		\fill[color=green] #1 circle[radius=0.08];
+		\draw #1 circle[radius=0.07];
+	}
+
+	\def\hellpunkt#1{
+		\fill[color=lightgray] #1 circle[radius=0.08];
+		\draw[gray] #1 circle[ radius=0.07];
+	}
+	
+	\draw[color=gray,line width=1pt,dashed] 
+	plot[domain=0.5:7, samples=100]
+	({\x},{(7.832*\x^2-51.5*\x+121.668)/\teiler});
+
+
+	\punkt{(1,8/\teiler)}
+	\hellpunkt{(2,15/\teiler)}
+	\hellpunkt{(3,26/\teiler)}
+	\punkt{(4,41/\teiler)}
+	\punkt{(5,60/\teiler)}
+	\punkt{(6,83/\teiler)}
+	\punkt{(7,110/\teiler)}
+	
+
+	
+	\def\erpunkt#1{
+		\fill[color=red] #1 circle[radius=0.08];
+		\draw #1 circle[radius=0.07];
+	}
+	\erpunkt{(2,50/\teiler)}
+	\erpunkt{(3,37.66/\teiler)}
+
+	\draw(0,100/\teiler) -- (-0.1,100/\teiler) coordinate[label={left:$100$}];
+	\draw(1,0) -- (1,-0.1) coordinate[label={below:$1$}];		
+\end{tikzpicture}
\ No newline at end of file
diff --git a/buch/papers/reedsolomon/tikz/signal.txt b/buch/papers/reedsolomon/tikz/signal.txt
new file mode 100644
index 0000000..c4fa5f8
--- /dev/null
+++ b/buch/papers/reedsolomon/tikz/signal.txt
@@ -0,0 +1,96 @@
+0,6
+1,6
+2,0
+3,6
+4,4
+5,0
+6,5
+7,2
+8,1
+9,2
+10,1
+11,2
+12,0
+13,6
+14,3
+15,5
+16,7
+17,5
+18,5
+19,4
+20,1
+21,5
+22,9
+23,9
+24,3
+25,2
+26,6
+27,6
+28,4
+29,2
+30,9
+31,1
+32,1
+33,1
+34,2
+35,6
+36,6
+37,1
+38,9
+39,7
+40,7
+41,1
+42,9
+43,9
+44,10
+45,9
+46,8
+47,5
+48,2
+49,4
+50,1
+51,0
+52,9
+53,3
+54,3
+55,3
+56,5
+57,6
+58,0
+59,8
+60,6
+61,9
+62,3
+63,4
+64,0
+65,0
+66,0
+67,0
+68,0
+69,0
+70,0
+71,0
+72,0
+73,0
+74,0
+75,0
+76,0
+77,0
+78,0
+79,0
+80,0
+81,0
+82,0
+83,0
+84,0
+85,0
+86,0
+87,0
+88,0
+89,0
+90,0
+91,0
+92,0
+93,0
+94,0
+95,0
diff --git a/buch/papers/reedsolomon/tikz/syndrom.txt b/buch/papers/reedsolomon/tikz/syndrom.txt
new file mode 100644
index 0000000..8ca9eed
--- /dev/null
+++ b/buch/papers/reedsolomon/tikz/syndrom.txt
@@ -0,0 +1,96 @@
+0,0
+1,0
+2,0
+3,0
+4,0
+5,0
+6,0
+7,0
+8,0
+9,0
+10,0
+11,0
+12,0
+13,0
+14,0
+15,0
+16,0
+17,0
+18,0
+19,0
+20,0
+21,0
+22,0
+23,0
+24,0
+25,0
+26,0
+27,0
+28,0
+29,0
+30,0
+31,0
+32,0
+33,0
+34,0
+35,0
+36,0
+37,0
+38,0
+39,0
+40,0
+41,0
+42,0
+43,0
+44,0
+45,0
+46,0
+47,0
+48,0
+49,0
+50,0
+51,0
+52,0
+53,0
+54,0
+55,0
+56,0
+57,0
+58,0
+59,0
+60,0
+61,0
+62,0
+63,0
+64,0.0275599094902563
+65,0.0115837187254191
+66,0.025877761014238
+67,0.0224618032819697
+68,0.04410594689944
+69,0.0474504002669341
+70,0.0227694695500626
+71,0.0271436638090525
+72,0.0104166666666667
+73,0.0271436638090523
+74,0.0227694695500608
+75,0.0474504002669343
+76,0.0441059468994397
+77,0.0224618032819701
+78,0.0258777610142379
+79,0.0115837187254183
+80,0.027559909490256
+81,0.0245124379481793
+82,0.0499782237195209
+83,0.0401432022864265
+84,0.0232923747656228
+85,0.0237974288564099
+86,0.0143895905726624
+87,0.0271745729691685
+88,0.0275599094902567
+89,0.0515501672184983
+90,0.0358255004834542
+91,0.024700508366373
+92,0.0210194725405171
+93,0.0177592928994296
+94,0.0261327016093158
+95,0.0314909067039411