aboutsummaryrefslogtreecommitdiffstats
path: root/buch/papers/fm/RS presentation
diff options
context:
space:
mode:
authorJoshua Baer <joshua.baer@ost.ch>2022-05-15 15:36:08 +0200
committerJoshua Baer <joshua.baer@ost.ch>2022-05-15 15:36:08 +0200
commit2bba3b1d52604c9f671763927ec592a72b09088e (patch)
tree710dfd5f365f1b84b00432336f53cf113d71c578 /buch/papers/fm/RS presentation
parentMerge branch 'AndreasFMueller:master' into master (diff)
downloadSeminarSpezielleFunktionen-2bba3b1d52604c9f671763927ec592a72b09088e.tar.gz
SeminarSpezielleFunktionen-2bba3b1d52604c9f671763927ec592a72b09088e.zip
a few animations
Diffstat (limited to 'buch/papers/fm/RS presentation')
-rw-r--r--buch/papers/fm/RS presentation/RS.tex162
1 files changed, 162 insertions, 0 deletions
diff --git a/buch/papers/fm/RS presentation/RS.tex b/buch/papers/fm/RS presentation/RS.tex
new file mode 100644
index 0000000..8e3de17
--- /dev/null
+++ b/buch/papers/fm/RS presentation/RS.tex
@@ -0,0 +1,162 @@
+\documentclass[11pt,aspectratio=169]{beamer}
+\usepackage[utf8]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage{lmodern}
+\usepackage[ngerman]{babel}
+\usepackage{tikz}
+\usetheme{Hannover}
+
+\begin{document}
+ \author{Joshua Bär}
+ \title{FM - Bessel}
+ \subtitle{}
+ \logo{}
+ \institute{OST Ostschweizer Fachhochschule}
+ \date{16.5.2022}
+ \subject{Mathematisches Seminar}
+ %\setbeamercovered{transparent}
+ \setbeamercovered{invisible}
+ \setbeamertemplate{navigation symbols}{}
+ \begin{frame}[plain]
+ \maketitle
+ \end{frame}
+%-------------------------------------------------------------------------------
+\section{Einführung}
+ \begin{frame}
+ \frametitle{Frequenzmodulation}
+ \begin{itemize}
+ \visible<1->{\item Für Übertragung von Daten}
+ \visible<2->{\item Amplituden unabhängig}
+ \end{itemize}
+ \end{frame}
+%-------------------------------------------------------------------------------
+ \begin{frame}
+ \frametitle{Parameter}
+ \begin{center}
+ \begin{tabular}{ c c c }
+ \hline
+ Nutzlas & Fehler & Versenden \\
+ \hline
+ 3 & 2 & 7 Werte eines Polynoms vom Grad 2 \\
+ 4 & 2 & 8 Werte eines Polynoms vom Grad 3 \\
+\visible<1->{3}&
+\visible<1->{3}&
+\visible<1->{9 Werte eines Polynoms vom Grad 2} \\
+ &&\\
+\visible<1->{$k$} &
+\visible<1->{$t$} &
+\visible<1->{$k+2t$ Werte eines Polynoms vom Grad $k-1$} \\
+ \hline
+ &&\\
+ &&\\
+ \multicolumn{3}{l} {
+ \visible<1>{Ausserdem können bis zu $2t$ Fehler erkannt werden!}
+ }
+ \end{tabular}
+ \end{center}
+ \end{frame}
+
+%-------------------------------------------------------------------------------
+
+\section{Diskrete Fourier Transformation}
+ \begin{frame}
+ \frametitle{Idee}
+ \begin{itemize}
+ \item Fourier-transformieren
+ \item Übertragung
+ \item Rücktransformieren
+ \end{itemize}
+ \end{frame}
+%-------------------------------------------------------------------------------
+ \begin{frame}
+ \begin{figure}
+ \only<1>{
+ \includegraphics[width=0.9\linewidth]{images/fig1.pdf}
+ }
+ \only<2>{
+ \includegraphics[width=0.9\linewidth]{images/fig2.pdf}
+ }
+ \only<3>{
+ \includegraphics[width=0.9\linewidth]{images/fig3.pdf}
+ }
+ \only<4>{
+ \includegraphics[width=0.9\linewidth]{images/fig4.pdf}
+ }
+ \only<5>{
+ \includegraphics[width=0.9\linewidth]{images/fig5.pdf}
+ }
+ \only<6>{
+ \includegraphics[width=0.9\linewidth]{images/fig6.pdf}
+ }
+ \only<7>{
+ \includegraphics[width=0.9\linewidth]{images/fig7.pdf}
+ }
+ \end{figure}
+ \end{frame}
+%-------------------------------------------------------------------------------
+ \begin{frame}
+ \frametitle{Diskrete Fourier Transformation}
+ \begin{itemize}
+ \item Diskrete Fourier-Transformation gegeben durch:
+ \visible<1->{
+ \[
+ \label{ft_discrete}
+ \hat{c}_{k}
+ = \frac{1}{N} \sum_{n=0}^{N-1}
+ {f}_n \cdot e^{-\frac{2\pi j}{N} \cdot kn}
+ \]}
+ \visible<2->{
+ \item Ersetzte
+ \[
+ w = e^{-\frac{2\pi j}{N} k}
+ \]}
+ \visible<3->{
+ \item Wenn $N$ konstant:
+ \[
+ \hat{c}_{k}=\frac{1}{N}( {f}_0 w^0 + {f}_1 w^1 + {f}_2 w^2 + \dots + {f}_{N-1} w^N)
+ \]}
+ \end{itemize}
+ \end{frame}
+
+%-------------------------------------------------------------------------------
+
+%-------------------------------------------------------------------------------
+ \begin{frame}
+ \frametitle{Ein Beispiel}
+
+ \begin{itemize}
+
+ \onslide<1->{\item endlicher Körper $q = 11$}
+
+ \onslide<2->{ist eine Primzahl}
+
+ \onslide<3->{beinhaltet die Zahlen $\mathbb{F}_{11} = \{0,1,2,3,4,5,6,7,8,9,10\}$}
+
+ \vspace{10pt}
+
+ \onslide<4->{\item Nachrichtenblock $=$ Nutzlast $+$ Fehlerkorrekturstellen}
+
+ \onslide<5->{$n = q - 1 = 10$ Zahlen}
+
+ \vspace{10pt}
+
+ \onslide<6->{\item Max.~Fehler $t = 2$}
+
+ \onslide<7->{maximale Anzahl von Fehler, die wir noch korrigieren können}
+
+ \vspace{10pt}
+
+ \onslide<8->{\item Nutzlast $k = n -2t = 6$ Zahlen}
+
+ \onslide<9->{Fehlerkorrkturstellen $2t = 4$ Zahlen}
+
+ \onslide<10->{Nachricht $m = [0,0,0,0,4,7,2,5,8,1]$}
+
+ \onslide<11->{als Polynom $m(X) = 4X^5 + 7X^4 + 2X^3 + 5X^2 + 8X + 1$}
+
+ \end{itemize}
+
+ \end{frame}
+
+
+\end{document}