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authorJODBaer <JODBaer@github.com>2021-07-27 17:10:19 +0200
committerJODBaer <JODBaer@github.com>2021-07-27 17:10:19 +0200
commitc3c7a6320004974ba56eb98305b5ac9fa13d4a52 (patch)
tree9a3660fe563137b50a7621b79d3227c4615e672d
parentMerge remote-tracking branch 'upstream/master' into Baer (diff)
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-rw-r--r--buch/papers/reedsolomon/dtf.tex20
-rw-r--r--buch/papers/reedsolomon/experiments/codiert.txt96
-rw-r--r--buch/papers/reedsolomon/experiments/decodiert.txt96
-rw-r--r--buch/papers/reedsolomon/experiments/empfangen.txt96
-rw-r--r--buch/papers/reedsolomon/experiments/fehler.txt96
-rw-r--r--buch/papers/reedsolomon/experiments/locator.txt96
-rw-r--r--buch/papers/reedsolomon/experiments/signal.txt96
-rw-r--r--buch/papers/reedsolomon/experiments/syndrom.txt96
-rw-r--r--buch/papers/reedsolomon/figures/plotfft.pdfbin60217 -> 59617 bytes
-rw-r--r--buch/papers/reedsolomon/figures/polynom2.pdfbin20327 -> 20327 bytes
-rw-r--r--buch/papers/reedsolomon/standalone/standalone.pdfbin1782700 -> 1828186 bytes
-rw-r--r--buch/papers/reedsolomon/tikz/plotfft.tex6
12 files changed, 15 insertions, 683 deletions
diff --git a/buch/papers/reedsolomon/dtf.tex b/buch/papers/reedsolomon/dtf.tex
index ffe98f8..73d0d12 100644
--- a/buch/papers/reedsolomon/dtf.tex
+++ b/buch/papers/reedsolomon/dtf.tex
@@ -7,21 +7,21 @@
\label{reedsolomon:section:dtf}}
\rhead{Umwandlung mit DTF}
Um die Polynominterpolation zu umgehen, gehen wir nun über in die Fourientransformation.
-Dies wird weder eine erklärung der Forientransorfmation noch ein genauer gebrauch
-für den Reed-Solomon-Code. Dieser Abschnitt zeigt nur wie die Fourientransformation auf Fehler reagiert.
+Dies wird weder eine erklärung der Forientransorfmation noch ein genauer gebrauchfür den Reed-Solomon-Code.
+Dieser Abschnitt zeigt nur wie die Fourientransformation auf Fehler reagiert.
wobei sie dann bei späteren Berchnungen ganz nützlich ist.
-\subsection{Diskrete Fourientransformation Zusamenhang
+\subsection{Diskrete Fourietransformation Zusamenhang
\label{reedsolomon:subsection:dtfzusamenhang}}
-Die Diskrete Fourientransformation ist definiert als
+Die Diskrete Fourietransformation ist definiert als
\begin{equation}
\hat{c}_{k}
= \frac{1}{N} \sum_{n=0}^{N-1}
{f}_n \cdot e^{-\frac{2\pi j}{N} \cdot kn}
- \label{reedsolomon:DFT}
+ ,\label{reedsolomon:DFT}
\end{equation}
-, wenn man nun
+wenn man nun
\begin{equation}
w =
e^{-\frac{2\pi j}{N} k}
@@ -38,8 +38,12 @@ ersetzte, und $N$ konstantbleibt, erhält man
was überaust ähnlich zu unserem Polynomidee ist.
\subsection{Übertragungsabfolge
\label{reedsolomon:subsection:Übertragungsabfolge}}
-
-\begin{enumerate}[1)]
+Der Auftrag ist nun 64 Daten zu übertragen und nach 16 Fehler abzusicheren,
+16 Fehler erkennen und rekonstruieren.
+Dieser Auftrag soll mittels Fouriertransformation bewerkstelligt werden.
+In der Abbildung \ref{reedsolomon:subsection:Übertragungsabfolge} sieht man dies Schritt für schritt,
+und hier werden die einzelne Schritte erklärt.
+\begin{enumerate}[(1)]
\item Das Signal hat 64 die Daten, Zahlen welche übertragen werden sollen.
Dabei zusätzlich nach 16 Fehler abgesichert, macht insgesamt 96 Übertragungszahlen.
\item Nun wurde mittels der schnellen diskreten Fourientransformation diese 96 codiert.
diff --git a/buch/papers/reedsolomon/experiments/codiert.txt b/buch/papers/reedsolomon/experiments/codiert.txt
deleted file mode 100644
index 4a481d8..0000000
--- a/buch/papers/reedsolomon/experiments/codiert.txt
+++ /dev/null
@@ -1,96 +0,0 @@
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diff --git a/buch/papers/reedsolomon/experiments/decodiert.txt b/buch/papers/reedsolomon/experiments/decodiert.txt
deleted file mode 100644
index f6221e6..0000000
--- a/buch/papers/reedsolomon/experiments/decodiert.txt
+++ /dev/null
@@ -1,96 +0,0 @@
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diff --git a/buch/papers/reedsolomon/experiments/empfangen.txt b/buch/papers/reedsolomon/experiments/empfangen.txt
deleted file mode 100644
index 38c13b0..0000000
--- a/buch/papers/reedsolomon/experiments/empfangen.txt
+++ /dev/null
@@ -1,96 +0,0 @@
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diff --git a/buch/papers/reedsolomon/experiments/fehler.txt b/buch/papers/reedsolomon/experiments/fehler.txt
deleted file mode 100644
index 23f1a83..0000000
--- a/buch/papers/reedsolomon/experiments/fehler.txt
+++ /dev/null
@@ -1,96 +0,0 @@
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diff --git a/buch/papers/reedsolomon/experiments/locator.txt b/buch/papers/reedsolomon/experiments/locator.txt
deleted file mode 100644
index b28988c..0000000
--- a/buch/papers/reedsolomon/experiments/locator.txt
+++ /dev/null
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diff --git a/buch/papers/reedsolomon/experiments/signal.txt b/buch/papers/reedsolomon/experiments/signal.txt
deleted file mode 100644
index c4fa5f8..0000000
--- a/buch/papers/reedsolomon/experiments/signal.txt
+++ /dev/null
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diff --git a/buch/papers/reedsolomon/experiments/syndrom.txt b/buch/papers/reedsolomon/experiments/syndrom.txt
deleted file mode 100644
index 8ca9eed..0000000
--- a/buch/papers/reedsolomon/experiments/syndrom.txt
+++ /dev/null
@@ -1,96 +0,0 @@
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diff --git a/buch/papers/reedsolomon/figures/plotfft.pdf b/buch/papers/reedsolomon/figures/plotfft.pdf
index 27992c9..c5e21e3 100644
--- a/buch/papers/reedsolomon/figures/plotfft.pdf
+++ b/buch/papers/reedsolomon/figures/plotfft.pdf
Binary files differ
diff --git a/buch/papers/reedsolomon/figures/polynom2.pdf b/buch/papers/reedsolomon/figures/polynom2.pdf
index ae68385..dd6cdd3 100644
--- a/buch/papers/reedsolomon/figures/polynom2.pdf
+++ b/buch/papers/reedsolomon/figures/polynom2.pdf
Binary files differ
diff --git a/buch/papers/reedsolomon/standalone/standalone.pdf b/buch/papers/reedsolomon/standalone/standalone.pdf
index 80af280..a984f35 100644
--- a/buch/papers/reedsolomon/standalone/standalone.pdf
+++ b/buch/papers/reedsolomon/standalone/standalone.pdf
Binary files differ
diff --git a/buch/papers/reedsolomon/tikz/plotfft.tex b/buch/papers/reedsolomon/tikz/plotfft.tex
index db141a8..14af683 100644
--- a/buch/papers/reedsolomon/tikz/plotfft.tex
+++ b/buch/papers/reedsolomon/tikz/plotfft.tex
@@ -22,7 +22,7 @@
\begin{axis}
[title = {\Large {Signal}},
xtick={0,20,40,64,80,98}]
- \addplot[black] table[col sep=comma] {tikz/signal.txt};
+ \addplot[blue] table[col sep=comma] {tikz/signal.txt};
\end{axis}
\end{tikzpicture}}; &
@@ -54,14 +54,14 @@
\node(syndrom) [] {
\begin{tikzpicture}
\begin{axis}[title = {\Large {Syndrom}}]
- \addplot[blue] table[col sep=comma] {tikz/syndrom.txt};
+ \addplot[black] table[col sep=comma] {tikz/syndrom.txt};
\end{axis}
\end{tikzpicture}}; &
\node(locator) [] {
\begin{tikzpicture}
\begin{axis}[title = {\Large {Locator}}]
- \addplot[] table[col sep=comma] {tikz/locator.txt};
+ \addplot[gray] table[col sep=comma] {tikz/locator.txt};
\end{axis}
\end{tikzpicture}};\\
};