update

14 files changed, 946 insertions, 741 deletions

diff --git a/buch/papers/reedsolomon/RS presentation/images/polynom1 - Kopie.tex b/buch/papers/reedsolomon/RS presentation/images/polynom1 - Kopie.tex
new file mode 100644
index 0000000..038e93e
--- /dev/null
+++ b/buch/papers/reedsolomon/RS presentation/images/polynom1 - Kopie.tex
@@ -0,0 +1,33 @@
+% polynome1
+%-------------------
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{txfonts}
+\usepackage{pgfplots}
+\usepackage{csvsimple}
+\usetikzlibrary{arrows,intersections,math}
+\newcommand{\teiler}{40}
+\begin{document}
+
+
+\begin{tikzpicture}[>=latex,thick]
+
+	\begin{axis}[
+		axis lines = left,
+		xlabel = \(x\),
+		ylabel = {\(f(x)\)},
+		]
+		%Below the red parabola is defined
+		\addplot[
+		color=blue,
+		]
+		coordinates {
+			(0,23.1)(10,27.5)(20,32)(30,37.8)(40,44.6)(60,61.8)(80,83.8)(100,114)
+		};
+		%Here the blue parabola is defined
+		
+	\end{axis}
+\end{tikzpicture}
+\end{document}
+
diff --git a/buch/papers/reedsolomon/dtf.tex b/buch/papers/reedsolomon/dtf.tex
index d276760..f011ac3 100644
--- a/buch/papers/reedsolomon/dtf.tex
+++ b/buch/papers/reedsolomon/dtf.tex
@@ -26,7 +26,9 @@ Kommen nuun drei Fehler... hinzu zu diesem codierten Signal sind diese nicht zu
 Nach dem Empfangen... und decodieren ... erkennt man die fehlerhafte information in den Punkten 64 bis 100.
 Filtert man nur diese Punkte heraus und Transformiert sie mit Fourier erhält man die stellen an denen die Fehler sich eingeschlichen haben.
 
-
-
-
-
+\begin{figure}
+	\centering
+    \input{papers/reedsolomon/images/plotfft.tex}
+	\caption{Übertragungsabfolge \ref{reedsolomon:subsection:Übertragungsabfolge}}
+	\label{fig:sendorder}
+\end{figure}
\ No newline at end of file
diff --git a/buch/papers/reedsolomon/experiments/codiert.txt b/buch/papers/reedsolomon/experiments/codiert.txt
index a57fb3e..4a481d8 100644
--- a/buch/papers/reedsolomon/experiments/codiert.txt
+++ b/buch/papers/reedsolomon/experiments/codiert.txt
@@ -1,96 +1,96 @@
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diff --git a/buch/papers/reedsolomon/experiments/decodiert.txt b/buch/papers/reedsolomon/experiments/decodiert.txt
index 5295e2a..f6221e6 100644
--- a/buch/papers/reedsolomon/experiments/decodiert.txt
+++ b/buch/papers/reedsolomon/experiments/decodiert.txt
@@ -1,96 +1,96 @@
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diff --git a/buch/papers/reedsolomon/experiments/empfangen.txt b/buch/papers/reedsolomon/experiments/empfangen.txt
index 326dd83..38c13b0 100644
--- a/buch/papers/reedsolomon/experiments/empfangen.txt
+++ b/buch/papers/reedsolomon/experiments/empfangen.txt
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diff --git a/buch/papers/reedsolomon/experiments/f.m b/buch/papers/reedsolomon/experiments/f.m
index 5e4da85..bf2587c 100644
--- a/buch/papers/reedsolomon/experiments/f.m
+++ b/buch/papers/reedsolomon/experiments/f.m
@@ -51,6 +51,7 @@ syndrom(1:N,1) = zeros(N,1)
 plot(abs(syndrom));
 xlim([1, l]);
 title("Syndrom");
+
 pause()
 
 locator = abs(fft(syndrom))
@@ -60,14 +61,12 @@ xlim([1, l]);
 title("Locator");
 pause()
 
-writematrix(abs(signal), 'signal.txt')
-writematrix(abs(codiert), 'codiert.txt')
-writematrix(fehler, 'fehler.txt')
-writematrix(abs(empfangen), 'empfangen.txt')
-writematrix(abs(decodiert), 'decodiert.txt')
-writematrix(abs(syndrom), 'syndrom.txt')
-writematrix(locator, 'locator.txt')
-
-
 
+writematrix([transpose(counter), abs(signal)], 'signal.txt')
+writematrix([transpose(counter), abs(codiert)], 'codiert.txt')
+writematrix([transpose(counter), fehler], 'fehler.txt')
+writematrix([transpose(counter), abs(empfangen)], 'empfangen.txt')
+writematrix([transpose(counter), abs(decodiert)], 'decodiert.txt')
+writematrix([transpose(counter), abs(syndrom)], 'syndrom.txt')
+writematrix([transpose(counter), locator], 'locator.txt')
 
diff --git a/buch/papers/reedsolomon/experiments/fehler.txt b/buch/papers/reedsolomon/experiments/fehler.txt
index b8f9afb..23f1a83 100644
--- a/buch/papers/reedsolomon/experiments/fehler.txt
+++ b/buch/papers/reedsolomon/experiments/fehler.txt
@@ -1,96 +1,96 @@
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diff --git a/buch/papers/reedsolomon/experiments/locator.txt b/buch/papers/reedsolomon/experiments/locator.txt
index 421d36e..b28988c 100644
--- a/buch/papers/reedsolomon/experiments/locator.txt
+++ b/buch/papers/reedsolomon/experiments/locator.txt
@@ -1,96 +1,96 @@
-0.0301224340566959
-0.141653026854878
-0.138226631799375
-0.0339903276086926
-0.310585462557496
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-0.0190533549944134
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-0.0417536642697542
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diff --git a/buch/papers/reedsolomon/experiments/plot.tex b/buch/papers/reedsolomon/experiments/plot.tex
new file mode 100644
index 0000000..bf9aadc
--- /dev/null
+++ b/buch/papers/reedsolomon/experiments/plot.tex
@@ -0,0 +1,91 @@
+% polynome1
+%-------------------
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{txfonts}
+\usepackage{pgfplots}
+\usepackage{csvsimple}
+\usepackage{pgfplotstable}
+\usepackage{filecontents}
+\usetikzlibrary{arrows,intersections,math}
+\newcommand{\x}{10}
+\newcommand{\y}{-8}
+\begin{document}
+
+\tikzset{
+	node/.style={rectangle, draw=black!100, thick, on grid}, % on grid added
+	dangling node/.style={node, fill=black!30}
+}
+\begin{tikzpicture}[]
+
+\filldraw[red] (0,0) circle (5mm);
+	%Knote
+\matrix[draw = none, column sep=20mm, row sep=20mm]{
+	\node(signal)  []    {
+	\begin{tikzpicture}
+		\begin{axis}[title = {\Large {Signal}}]
+			\addplot[] table[col sep=comma] {signal.txt};
+		\end{axis}
+	\end{tikzpicture}}; &
+	
+	\node(codiert) []    {
+	\begin{tikzpicture}
+		\begin{axis}[title = {\Large {Codiert}}]
+			\addplot[] table[col sep=comma] {codiert.txt};
+		\end{axis}
+	\end{tikzpicture}}; \\
+		
+	&\node(fehler) []    {
+	\begin{tikzpicture}
+		\begin{axis}[scale=0.6, title = {\Large {Fehler}}]
+			\addplot[] table[col sep=comma] {fehler.txt};
+		\end{axis}
+	\end{tikzpicture}};\\
+	
+	\node(decodiert) []    {
+	\begin{tikzpicture}
+		\begin{axis}[title = {\Large {Decodiert}}]
+			\addplot[] table[col sep=comma] {decodiert.txt};
+		\end{axis}
+	\end{tikzpicture}}; &
+
+	\node(empfangen) []    {
+	\begin{tikzpicture}
+		\begin{axis}[title = {\Large {Empfangen}}]
+			\addplot[] table[col sep=comma] {empfangen.txt};
+		\end{axis}
+	\end{tikzpicture}};\\
+
+	\node(syndrom) []   {
+	\begin{tikzpicture}
+		\begin{axis}[title = {\Large {Syndrom}}]
+			\addplot[] table[col sep=comma] {syndrom.txt};
+		\end{axis}
+	\end{tikzpicture}}; &
+
+	\node(locator) []    {
+	\begin{tikzpicture}
+		\begin{axis}[title = {\Large {Locator}}]
+			\addplot[] table[col sep=comma] {locator.txt};
+		\end{axis}
+	\end{tikzpicture}};\\
+};
+	%FFT & IFFT deskription
+
+	\draw[thin,gray,dashed] (0,15) to (0,-15);
+	\node(FFT)  [ scale=0.7]  at (0,15.3)   {FFT IFFT};
+	
+	%Arrows
+	\draw[ultra thick, ->] (signal.east) to (codiert.west);
+	\draw[ultra thick, ->] (codiert.south) to (fehler.north);
+	\draw[ultra thick, ->] (fehler.south) to (empfangen.north);
+	\draw[ultra thick, ->] (empfangen.west) to (decodiert.east);
+	\draw[ultra thick, ->] (syndrom.east) to (locator.west);
+	\draw(decodiert.south east)++(-1.8,1)  ellipse (1.3cm and 0.8cm) ++(-1.3,0) coordinate(zoom) ;
+	\draw[ultra thick, ->] (zoom) to[out=180, in=90] (syndrom.north);
+	
+	
+ \end{tikzpicture}
+\end{document}
+
diff --git a/buch/papers/reedsolomon/experiments/signal.txt b/buch/papers/reedsolomon/experiments/signal.txt
index 202dd02..c4fa5f8 100644
--- a/buch/papers/reedsolomon/experiments/signal.txt
+++ b/buch/papers/reedsolomon/experiments/signal.txt
@@ -1,96 +1,96 @@
-5
-4
-4
-3
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diff --git a/buch/papers/reedsolomon/experiments/syndrom.txt b/buch/papers/reedsolomon/experiments/syndrom.txt
index 59b9dc4..8ca9eed 100644
--- a/buch/papers/reedsolomon/experiments/syndrom.txt
+++ b/buch/papers/reedsolomon/experiments/syndrom.txt
@@ -1,96 +1,96 @@
-0
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diff --git a/buch/papers/reedsolomon/idee.tex b/buch/papers/reedsolomon/idee.tex
index 08864cf..39adbbf 100644
--- a/buch/papers/reedsolomon/idee.tex
+++ b/buch/papers/reedsolomon/idee.tex
@@ -25,23 +25,20 @@ p(x)
 \end{equation}
 ergeben.
 Übertragen werden nun die Werte an den stellen 1, 2, 3\dots 7 dieses Polynomes.
-Grafisch sieht man dies dann in Abbildung 
+Grafisch sieht man dies dann in Abbildung \ref{fig:polynom}, 
+mit den Punkten, $p(1),p(2),...,p(7) = (\textcolor{green}{8}, 
+\textcolor{green}{15}, \textcolor{green}{26},
+\textcolor{green}{41}, \textcolor{green}{60}, 
+\textcolor{green}{83}, \textcolor{green}{110})$
 Wenn ein Fehler sich in die Übertragung eingeschlichen hatt, muss der Leser/Empfänger diesen erkennen und das Polynom rekonstruieren.
 Der Leser/Empfänger weiss, den Grad des Polynoms und dessen Werte übermittelt wurden. 
 
-\begin{figure}
-	\centering
-	%\includegraphics[width=0.5\textwidth]{papers/reedsolomon/images/polynom2}
-    %\input{papers/reedsolomon/images/polynom2.tex}
-	\caption{Polynom }
-	\label{fig:polynom}
-\end{figure}
-
 \subsection{Beispiel}
 Für das Beispeil aus der Gleichung \eqref{reedsolomon:equation1},
 ist ein Polynome zweiten Grades durch drei Punkte eindeutig bestimmbar.
-Hat es Fehler in der Übertragunge gegeben, kann man diese erkennen,
-da alle Punkte, die korrekt sind, auf dem Polynom liegen müssen.
+Hat es Fehler in der Übertragunge gegeben,(Bei Abbildung \ref{fig:polynom}\textcolor{red}{roten Punkte}) kann man diese erkennen,
+da alle Punkte, die korrekt sind, auf dem Polynom liegen müssen. 
+(Bei Abbildung \ref{fig:polynom}\textcolor{green}{grünen Punkte})
 Ab wie vielen Fehler ist das Polynom nicht mehr erkennbar beim Übertragen von 7 Punkten?
 Bei 2 Fehlern kann man noch eindeutig bestimmen, dass das Polynom mit 4 Punkten,
 gegenüber dem mit 5 Punkten falsch liegt.\ref{fig:polynom}
@@ -49,6 +46,14 @@ Werden es mehr Fehler kann nur erkennt werden, dass das Polynom nicht stimmt.
 Das orginale Polynom kann aber nicht mehr gefunden werden.
 Dafür sind mehr übertragene Werte nötig.
 
+\begin{figure}
+	\centering
+	%\includegraphics[width=0.5\textwidth]{papers/reedsolomon/images/polynom2}
+    \input{papers/reedsolomon/images/polynom2.tex}
+	\caption{Polynom $p(x)$ \eqref{reedsolomon:equation1}}
+	\label{fig:polynom}
+\end{figure}
+
 \section{Fehlerbestimmung
 \label{reedsolomon:section:Fehlerbestimmmung}}
 So wird ein Muster indentifiziert, welches genau vorherbestimmen kann,
diff --git a/buch/papers/reedsolomon/images/plotfft.tex b/buch/papers/reedsolomon/images/plotfft.tex
new file mode 100644
index 0000000..e6d3b47
--- /dev/null
+++ b/buch/papers/reedsolomon/images/plotfft.tex
@@ -0,0 +1,77 @@
+%
+% Plot der èbertrangungsabfolge ins FFT und zurück mit IFFT
+%
+\tikzset{
+	node/.style={rectangle, draw=black!100, thick, on grid}, % on grid added
+	dangling node/.style={node, fill=black!30}
+}
+\begin{tikzpicture}[]
+
+%---------------------------------------------------------------
+	%Knote
+\matrix[draw = none, column sep=20mm, row sep=20mm]{
+	\node(signal)  []    {
+	\begin{tikzpicture}
+		\begin{axis}[title = {\Large {Signal}}]
+			\addplot[] table[col sep=comma] {signal.txt};
+		\end{axis}
+	\end{tikzpicture}}; &
+	
+	\node(codiert) []    {
+	\begin{tikzpicture}
+		\begin{axis}[title = {\Large {Codiert}}]
+			\addplot[] table[col sep=comma] {codiert.txt};
+		\end{axis}
+	\end{tikzpicture}}; \\
+		
+	&\node(fehler) []    {
+	\begin{tikzpicture}
+		\begin{axis}[scale=0.6, title = {\Large {Fehler}}]
+			\addplot[] table[col sep=comma] {fehler.txt};
+		\end{axis}
+	\end{tikzpicture}};\\
+	
+	\node(decodiert) []    {
+	\begin{tikzpicture}
+		\begin{axis}[title = {\Large {Decodiert}}]
+			\addplot[] table[col sep=comma] {decodiert.txt};
+		\end{axis}
+	\end{tikzpicture}}; &
+
+	\node(empfangen) []    {
+	\begin{tikzpicture}
+		\begin{axis}[title = {\Large {Empfangen}}]
+			\addplot[] table[col sep=comma] {empfangen.txt};
+		\end{axis}
+	\end{tikzpicture}};\\
+
+	\node(syndrom) []   {
+	\begin{tikzpicture}
+		\begin{axis}[title = {\Large {Syndrom}}]
+			\addplot[] table[col sep=comma] {syndrom.txt};
+		\end{axis}
+	\end{tikzpicture}}; &
+
+	\node(locator) []    {
+	\begin{tikzpicture}
+		\begin{axis}[title = {\Large {Locator}}]
+			\addplot[] table[col sep=comma] {locator.txt};
+		\end{axis}
+	\end{tikzpicture}};\\
+};
+%-------------------------------------------------------------
+	%FFT & IFFT deskription
+
+	\draw[thin,gray,dashed] (0,15) to (0,-15);
+	\node(FFT)  [ scale=0.7]  at (0,15.3)   {FFT IFFT};
+	
+	%Arrows
+	\draw[ultra thick, ->] (signal.east) to (codiert.west);
+	\draw[ultra thick, ->] (codiert.south) to (fehler.north);
+	\draw[ultra thick, ->] (fehler.south) to (empfangen.north);
+	\draw[ultra thick, ->] (empfangen.west) to (decodiert.east);
+	\draw[ultra thick, ->] (syndrom.east) to (locator.west);
+	\draw(decodiert.south east)++(-1.8,1)  ellipse (1.3cm and 0.8cm) ++(-1.3,0) coordinate(zoom) ;
+	\draw[ultra thick, ->] (zoom) to[out=180, in=90] (syndrom.north);
+	
+ \end{tikzpicture}
\ No newline at end of file
diff --git a/buch/papers/reedsolomon/images/polynom2.tex b/buch/papers/reedsolomon/images/polynom2.tex
index 4fdfc81..288b51c 100644
--- a/buch/papers/reedsolomon/images/polynom2.tex
+++ b/buch/papers/reedsolomon/images/polynom2.tex
@@ -1,51 +1,49 @@
-% polynome2
+% polynome
 %-------------------
-%\documentclass[tikz]{standalone}
-%\usepackage{amsmath}
-%\usepackage{times}
-%\usepackage{txfonts}
-%\usepackage{pgfplots}
-%\usepackage{csvsimple}
-%\usetikzlibrary{arrows,intersections,math}
+% Teiler für das Skalieren der Grafik /40
 \newcommand{\teiler}{40}
-%\begin{document}
-	Übertragen von den Zahlen 
-	\textcolor{blue}{2}, \textcolor{blue}{1}, \textcolor{blue}{5} 
-	als $ p(x) = \textcolor{blue}{2}x^2 + \textcolor{blue}{1}x + \textcolor{blue}{5} $.\newline
-	Versende $ (p(1),p(2),...,p(7)) = (\textcolor{green}{8}, 
-		\textcolor{green}{15}, \textcolor{green}{26},
-		\textcolor{green}{ 41}, \textcolor{green}{60}, 
-		\textcolor{green}{83}, \textcolor{green}{110})$
+
+
+%//////////////////////////////////////
+
+\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 #1 circle[radius=0.07];
+	}
+	
+	\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)}
 	
+	\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});
 	
-	\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];
-		}
-		\punkt{(1,8/\teiler)}
-		%\punkt{(2,15/\teiler)}
-		%\punkt{(3,26/\teiler)}
-		\punkt{(4,41/\teiler)}
-		\punkt{(5,60/\teiler)}
-		\punkt{(6,83/\teiler)}
-		\punkt{(7,110/\teiler)}
-		\draw[color=gray,line width=1pt,dashed] 
-		plot[domain=0.5:7, samples=100]
-		({\x},{(0.1958*\x^2-1.2875*\x+3.0417)});
-		\def\erpunkt#1{
-			\fill[color=red] #1 circle[radius=0.08];
-			\draw #1 circle[radius=0.07];
-		}
-		\erpunkt{(2,50/\teiler)}
-		\erpunkt{(3,0.9414)}
+	\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}
+	\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}