From 2bba3b1d52604c9f671763927ec592a72b09088e Mon Sep 17 00:00:00 2001
From: Joshua Baer <joshua.baer@ost.ch>
Date: Sun, 15 May 2022 15:36:08 +0200
Subject: a few animations

---
 buch/papers/fm/RS presentation/RS.tex | 162 ++++++++++++++++++++++++++++++++++
 1 file changed, 162 insertions(+)
 create mode 100644 buch/papers/fm/RS presentation/RS.tex

(limited to 'buch/papers/fm/RS presentation/RS.tex')

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}
-- 
cgit v1.2.1


From 5187a5a947c0283e9f3d7fbc2acef96278109939 Mon Sep 17 00:00:00 2001
From: Joshua Baer <joshua.baer@ost.ch>
Date: Fri, 20 May 2022 18:14:40 +0200
Subject: presentation FM-Bessel

---
 buch/papers/fm/RS presentation/RS.tex | 209 ++++++++++++++--------------------
 1 file changed, 85 insertions(+), 124 deletions(-)

(limited to 'buch/papers/fm/RS presentation/RS.tex')

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}
-- 
cgit v1.2.1

