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authorJoshua Baer <joshua.baer@ost.ch>2022-07-26 15:14:53 +0200
committerJoshua Baer <joshua.baer@ost.ch>2022-07-26 15:14:53 +0200
commit80f1ac88befc8c0471a47f4400dd727cbd47eff4 (patch)
treed61ed14a047a90664f25185e1ca6f047b5adc65d /buch/papers/fm/RS presentation
parentKapitel TODOs (diff)
downloadSeminarSpezielleFunktionen-80f1ac88befc8c0471a47f4400dd727cbd47eff4.tar.gz
SeminarSpezielleFunktionen-80f1ac88befc8c0471a47f4400dd727cbd47eff4.zip
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-rw-r--r--buch/papers/fm/RS presentation/FM_presentation.pdfbin357597 -> 0 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.pdfbin159598 -> 0 bytes
-rw-r--r--buch/papers/fm/RS presentation/README.txt1
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diff --git a/buch/papers/fm/RS presentation/FM_presentation.pdf b/buch/papers/fm/RS presentation/FM_presentation.pdf
deleted file mode 100644
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diff --git a/buch/papers/fm/RS presentation/FM_presentation.tex b/buch/papers/fm/RS presentation/FM_presentation.tex
deleted file mode 100644
index 92cb501..0000000
--- a/buch/papers/fm/RS presentation/FM_presentation.tex
+++ /dev/null
@@ -1,125 +0,0 @@
-%% !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
deleted file mode 100644
index a6e701c..0000000
--- a/buch/papers/fm/RS presentation/Frequency modulation (FM) and Bessel functions.pdf
+++ /dev/null
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diff --git a/buch/papers/fm/RS presentation/README.txt b/buch/papers/fm/RS presentation/README.txt
deleted file mode 100644
index 4d0620f..0000000
--- a/buch/papers/fm/RS presentation/README.txt
+++ /dev/null
@@ -1 +0,0 @@
-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
deleted file mode 100644
index 8a67619..0000000
--- a/buch/papers/fm/RS presentation/RS.tex
+++ /dev/null
@@ -1,123 +0,0 @@
-%% !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- Spezielle Funktionen}
- %\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(\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}
-
-%-------------------------------------------------------------------------------
-\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[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\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}
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