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authorSamuel Niederer <43746162+samnied@users.noreply.github.com>2022-07-24 12:17:00 +0200
committerGitHub <noreply@github.com>2022-07-24 12:17:00 +0200
commitefe7c35759afb5cbae3c1683873c5159be0be09f (patch)
tree84f2e8510132352f9943bddc577ccf32cd46f2dc /buch/papers/fm/RS presentation
parentadd current work (diff)
parentMerge pull request #26 from p1mueller/master (diff)
downloadSeminarSpezielleFunktionen-efe7c35759afb5cbae3c1683873c5159be0be09f.tar.gz
SeminarSpezielleFunktionen-efe7c35759afb5cbae3c1683873c5159be0be09f.zip
Merge branch 'AndreasFMueller:master' into master
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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
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diff --git a/buch/papers/fm/RS presentation/FM_presentation.pdf b/buch/papers/fm/RS presentation/FM_presentation.pdf
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diff --git a/buch/papers/fm/RS presentation/FM_presentation.tex b/buch/papers/fm/RS presentation/FM_presentation.tex
new file mode 100644
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+++ b/buch/papers/fm/RS presentation/FM_presentation.tex
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+%% !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
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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
new file mode 100644
index 0000000..8a67619
--- /dev/null
+++ b/buch/papers/fm/RS presentation/RS.tex
@@ -0,0 +1,123 @@
+%% !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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