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-rw-r--r--buch/papers/fm/RS presentation/FM_presentation.pdfbin0 -> 357597 bytes
-rw-r--r--buch/papers/fm/RS presentation/FM_presentation.tex125
-rw-r--r--buch/papers/fm/RS presentation/Frequency modulation (FM) and Bessel functions.pdfbin0 -> 159598 bytes
-rw-r--r--buch/papers/fm/RS presentation/README.txt1
-rw-r--r--buch/papers/fm/RS presentation/RS.tex209
-rw-r--r--buch/papers/fm/RS presentation/images/100HZ.pngbin0 -> 8601 bytes
-rw-r--r--buch/papers/fm/RS presentation/images/200HZ.pngbin0 -> 8502 bytes
-rw-r--r--buch/papers/fm/RS presentation/images/300HZ.pngbin0 -> 9059 bytes
-rw-r--r--buch/papers/fm/RS presentation/images/400HZ.pngbin0 -> 9949 bytes
-rw-r--r--buch/papers/fm/RS presentation/images/bessel.pngbin0 -> 40393 bytes
-rw-r--r--buch/papers/fm/RS presentation/images/bessel2.pngbin0 -> 102494 bytes
-rw-r--r--buch/papers/fm/RS presentation/images/bessel_beta1.pngbin0 -> 40696 bytes
-rw-r--r--buch/papers/fm/RS presentation/images/bessel_frequenz.pngbin0 -> 11264 bytes
-rw-r--r--buch/papers/fm/RS presentation/images/beta_0.001.pngbin0 -> 6233 bytes
-rw-r--r--buch/papers/fm/RS presentation/images/beta_0.1.pngbin0 -> 6630 bytes
-rw-r--r--buch/papers/fm/RS presentation/images/beta_0.5.pngbin0 -> 8167 bytes
-rw-r--r--buch/papers/fm/RS presentation/images/beta_1.pngbin0 -> 11303 bytes
-rw-r--r--buch/papers/fm/RS presentation/images/beta_2.pngbin0 -> 14703 bytes
-rw-r--r--buch/papers/fm/RS presentation/images/beta_3.pngbin0 -> 20377 bytes
-rw-r--r--buch/papers/fm/RS presentation/images/fm_10Hz.pngbin0 -> 6781 bytes
-rw-r--r--buch/papers/fm/RS presentation/images/fm_20hz.pngbin0 -> 7834 bytes
-rw-r--r--buch/papers/fm/RS presentation/images/fm_30Hz.pngbin0 -> 8601 bytes
-rw-r--r--buch/papers/fm/RS presentation/images/fm_3Hz.pngbin0 -> 6558 bytes
-rw-r--r--buch/papers/fm/RS presentation/images/fm_40Hz.pngbin0 -> 8795 bytes
-rw-r--r--buch/papers/fm/RS presentation/images/fm_5Hz.pngbin0 -> 5766 bytes
-rw-r--r--buch/papers/fm/RS presentation/images/fm_7Hz.pngbin0 -> 6337 bytes
-rw-r--r--buch/papers/fm/RS presentation/images/fm_frequenz.pngbin0 -> 11042 bytes
-rw-r--r--buch/papers/fm/RS presentation/images/fm_in_time.pngbin0 -> 27400 bytes
28 files changed, 211 insertions, 124 deletions
diff --git a/buch/papers/fm/RS presentation/FM_presentation.pdf b/buch/papers/fm/RS presentation/FM_presentation.pdf
new file mode 100644
index 0000000..496e35e
--- /dev/null
+++ b/buch/papers/fm/RS presentation/FM_presentation.pdf
Binary files differ
diff --git a/buch/papers/fm/RS presentation/FM_presentation.tex b/buch/papers/fm/RS presentation/FM_presentation.tex
new file mode 100644
index 0000000..92cb501
--- /dev/null
+++ b/buch/papers/fm/RS presentation/FM_presentation.tex
@@ -0,0 +1,125 @@
+%% !TeX root = RS.tex
+
+\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}
+
+ \visible<1->{
+ \begin{equation} \cos(\omega_c t+\beta\sin(\omega_mt))
+ \end{equation}}
+
+ \only<2>{\includegraphics[scale= 0.7]{images/fm_in_time.png}}
+ \only<3>{\includegraphics[scale= 0.7]{images/fm_frequenz.png}}
+ \only<4>{\includegraphics[scale= 0.7]{images/bessel_frequenz.png}}
+
+
+ \end{frame}
+%-------------------------------------------------------------------------------
+\section{Proof}
+\begin{frame}
+ \frametitle{Bessel}
+
+ \visible<1->{\begin{align}
+ \cos(\beta\sin\varphi)
+ &=
+ J_0(\beta) + 2\sum_{m=1}^\infty J_{2m}(\beta) \cos(2m\varphi)
+ \\
+ \sin(\beta\sin\varphi)
+ &=
+ J_0(\beta) + 2\sum_{m=1}^\infty J_{2m}(\beta) \cos(2m\varphi)
+ \\
+ J_{-n}(\beta) &= (-1)^n J_n(\beta)
+ \end{align}}
+ \visible<2->{\begin{align}
+ \cos(A + B)
+ &=
+ \cos(A)\cos(B)-\sin(A)\sin(B)
+ \\
+ 2\cos (A)\cos (B)
+ &=
+ \cos(A-B)+\cos(A+B)
+ \\
+ 2\sin(A)\sin(B)
+ &=
+ \cos(A-B)-\cos(A+B)
+ \end{align}}
+\end{frame}
+
+%-------------------------------------------------------------------------------
+\begin{frame}
+ \frametitle{Prof->Done}
+ \begin{align}
+ \cos(\omega_ct+\beta\sin(\omega_mt))
+ &=
+ \sum_{k= -\infty}^\infty J_{k}(\beta) \cos((\omega_c+k\omega_m)t)
+ \end{align}
+ \end{frame}
+%-------------------------------------------------------------------------------
+ \begin{frame}
+ \begin{figure}
+ \only<1>{\includegraphics[scale = 0.75]{images/fm_frequenz.png}}
+ \only<2>{\includegraphics[scale = 0.75]{images/bessel_frequenz.png}}
+ \end{figure}
+ \end{frame}
+%-------------------------------------------------------------------------------
+\section{Input Parameter}
+ \begin{frame}
+ \frametitle{Träger-Frequenz Parameter}
+ \onslide<1->{\begin{equation}\cos(\omega_ct+\beta\sin(\omega_mt))\end{equation}}
+ \only<1>{\includegraphics[scale=0.75]{images/100HZ.png}}
+ \only<2>{\includegraphics[scale=0.75]{images/200HZ.png}}
+ \only<3>{\includegraphics[scale=0.75]{images/300HZ.png}}
+ \only<4>{\includegraphics[scale=0.75]{images/400HZ.png}}
+ \end{frame}
+%-------------------------------------------------------------------------------
+\begin{frame}
+\frametitle{Modulations-Frequenz Parameter}
+\onslide<1->{\begin{equation}\cos(\omega_ct+\beta\sin(\omega_mt))\end{equation}}
+\only<1>{\includegraphics[scale=0.75]{images/fm_3Hz.png}}
+\only<2>{\includegraphics[scale=0.75]{images/fm_5Hz.png}}
+\only<3>{\includegraphics[scale=0.75]{images/fm_7Hz.png}}
+\only<4>{\includegraphics[scale=0.75]{images/fm_10Hz.png}}
+\only<5>{\includegraphics[scale=0.75]{images/fm_20Hz.png}}
+\only<6>{\includegraphics[scale=0.75]{images/fm_30Hz.png}}
+\end{frame}
+%-------------------------------------------------------------------------------
+\begin{frame}
+\frametitle{Beta Parameter}
+ \onslide<1->{\begin{equation}\sum_{k= -\infty}^\infty J_{k}(\beta) \cos((\omega_c+k\omega_m)t)\end{equation}}
+ \only<1>{\includegraphics[scale=0.7]{images/beta_0.001.png}}
+ \only<2>{\includegraphics[scale=0.7]{images/beta_0.1.png}}
+ \only<3>{\includegraphics[scale=0.7]{images/beta_0.5.png}}
+ \only<4>{\includegraphics[scale=0.7]{images/beta_1.png}}
+ \only<5>{\includegraphics[scale=0.7]{images/beta_2.png}}
+ \only<6>{\includegraphics[scale=0.7]{images/beta_3.png}}
+ \only<7>{\includegraphics[scale=0.7]{images/bessel.png}}
+\end{frame}
+%-------------------------------------------------------------------------------
+\begin{frame}
+ \includegraphics[scale=0.5]{images/beta_1.png}
+ \includegraphics[scale=0.5]{images/bessel.png}
+\end{frame}
+\end{document}
diff --git a/buch/papers/fm/RS presentation/Frequency modulation (FM) and Bessel functions.pdf b/buch/papers/fm/RS presentation/Frequency modulation (FM) and Bessel functions.pdf
new file mode 100644
index 0000000..a6e701c
--- /dev/null
+++ b/buch/papers/fm/RS presentation/Frequency modulation (FM) and Bessel functions.pdf
Binary files differ
diff --git a/buch/papers/fm/RS presentation/README.txt b/buch/papers/fm/RS presentation/README.txt
new file mode 100644
index 0000000..4d0620f
--- /dev/null
+++ b/buch/papers/fm/RS presentation/README.txt
@@ -0,0 +1 @@
+Dies ist die Presentation des Reed-Solomon-Code \ No newline at end of file
diff --git a/buch/papers/fm/RS presentation/RS.tex b/buch/papers/fm/RS presentation/RS.tex
index 8e3de17..8a67619 100644
--- a/buch/papers/fm/RS presentation/RS.tex
+++ b/buch/papers/fm/RS presentation/RS.tex
@@ -1,3 +1,5 @@
+%% !TeX root = RS.tex
+
\documentclass[11pt,aspectratio=169]{beamer}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
@@ -13,7 +15,7 @@
\logo{}
\institute{OST Ostschweizer Fachhochschule}
\date{16.5.2022}
- \subject{Mathematisches Seminar}
+ \subject{Mathematisches Seminar- Spezielle Funktionen}
%\setbeamercovered{transparent}
\setbeamercovered{invisible}
\setbeamertemplate{navigation symbols}{}
@@ -24,139 +26,98 @@
\section{Einführung}
\begin{frame}
\frametitle{Frequenzmodulation}
- \begin{itemize}
- \visible<1->{\item Für Übertragung von Daten}
- \visible<2->{\item Amplituden unabhängig}
- \end{itemize}
+
+ \visible<1->{\begin{equation} \cos(\omega_c t+\beta\sin(\omega_mt))\end{equation}}
+
+ \only<2>{\includegraphics[scale= 0.7]{images/fm_in_time.png}}
+ \only<3>{\includegraphics[scale= 0.7]{images/fm_frequenz.png}}
+ \only<4>{\includegraphics[scale= 0.7]{images/bessel_frequenz.png}}
+
+
\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{Proof}
+\begin{frame}
+ \frametitle{Bessel}
-%-------------------------------------------------------------------------------
+ \visible<1->{\begin{align}
+ \cos(\beta\sin\varphi)
+ &=
+ J_0(\beat) + 2\sum_{m=1}^\infty J_{2m}(\beta) \cos(2m\varphi)
+ \\
+ \sin(\beta\sin\varphi)
+ &=
+ J_0(\beat) + 2\sum_{m=1}^\infty J_{2m}(\beta) \cos(2m\varphi)
+ \\
+ J_{-n}(\beat) &= (-1)^n J_n(\beta)
+ \end{align}}
+ \visible<2->{\begin{align}
+ \cos(A + B)
+ &=
+ \cos(A)\cos(B)-\sin(A)\sin(B)
+ \\
+ 2\cos (A)\cos (B)
+ &=
+ \cos(A-B)+\cos(A+B)
+ \\
+ 2\sin(A)\sin(B)
+ &=
+ \cos(A-B)-\cos(A+B)
+ \end{align}}
+\end{frame}
-\section{Diskrete Fourier Transformation}
- \begin{frame}
- \frametitle{Idee}
- \begin{itemize}
- \item Fourier-transformieren
- \item Übertragung
- \item Rücktransformieren
- \end{itemize}
+%-------------------------------------------------------------------------------
+\begin{frame}
+ \frametitle{Prof->Done}
+ \begin{align}
+ \cos(\omega_ct+\beta\sin(\omega_mt))
+ &=
+ \sum_{k= -\infty}^\infty J_{k}(\beta) \cos((\omega_c+k\omgea_m)t)
+ \end{align}
\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}
- }
+ \begin{figure}
+ \only<1>{\includegraphics[scale = 0.75]{images/fm_frequenz.png}}
+ \only<2>{\includegraphics[scale = 0.75]{images/bessel_frequenz.png}}
\end{figure}
\end{frame}
%-------------------------------------------------------------------------------
+\section{Input Parameter}
\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}
-
+ \frametitle{Träger-Frequenz Parameter}
+ \onslide<1->{\begin{equation}\cos(\omega_ct+\beta\sin(\omega_mt))\end{equation}}
+ \only<1>{\includegraphics[scale=0.75]{images/100HZ.png}}
+ \only<2>{\includegraphics[scale=0.75]{images/200HZ.png}}
+ \only<3>{\includegraphics[scale=0.75]{images/300HZ.png}}
+ \only<4>{\includegraphics[scale=0.75]{images/400HZ.png}}
\end{frame}
-
-
+%-------------------------------------------------------------------------------
+\begin{frame}
+\frametitle{Modulations-Frequenz Parameter}
+\onslide<1->{\begin{equation}\cos(\omega_ct+\beta\sin(\omega_mt))\end{equation}}
+\only<1>{\includegraphics[scale=0.75]{images/fm_3Hz.png}}
+\only<2>{\includegraphics[scale=0.75]{images/fm_5Hz.png}}
+\only<3>{\includegraphics[scale=0.75]{images/fm_7Hz.png}}
+\only<4>{\includegraphics[scale=0.75]{images/fm_10Hz.png}}
+\only<5>{\includegraphics[scale=0.75]{images/fm_20Hz.png}}
+\only<6>{\includegraphics[scale=0.75]{images/fm_30Hz.png}}
+\end{frame}
+%-------------------------------------------------------------------------------
+\begin{frame}
+\frametitle{Beta Parameter}
+ \onslide<1->{\begin{equation}\sum_{k= -\infty}^\infty J_{k}(\beta) \cos((\omega_c+k\omgea_m)t)\end{equation}}
+ \only<1>{\includegraphics[scale=0.7]{images/beta_0.001.png}}
+ \only<2>{\includegraphics[scale=0.7]{images/beta_0.1.png}}
+ \only<3>{\includegraphics[scale=0.7]{images/beta_0.5.png}}
+ \only<4>{\includegraphics[scale=0.7]{images/beta_1.png}}
+ \only<5>{\includegraphics[scale=0.7]{images/beta_2.png}}
+ \only<6>{\includegraphics[scale=0.7]{images/beta_3.png}}
+ \only<7>{\includegraphics[scale=0.7]{images/bessel.png}}
+\end{frame}
+%-------------------------------------------------------------------------------
+\begin{frame}
+ \includegraphics[scale=0.5]{images/beta_1.png}
+ \includegraphics[scale=0.5]{images/bessel.png}
+\end{frame}
\end{document}
diff --git a/buch/papers/fm/RS presentation/images/100HZ.png b/buch/papers/fm/RS presentation/images/100HZ.png
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