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\ No newline at end of file diff --git a/buch/papers/fm/00_modulation.tex b/buch/papers/fm/00_modulation.tex new file mode 100644 index 0000000..dc99b40 --- /dev/null +++ b/buch/papers/fm/00_modulation.tex @@ -0,0 +1,28 @@ +% +% teil3.tex -- Beispiel-File für Teil 3 +% +% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\subsection{Modulationsarten\label{fm:section:modulation}} + +Das sinusförmige Trägersignal hat die übliche Form: +\(x_c(t) = A_c \cdot \cos(\omega_c(t)+\varphi)\). +Wobei die konstanten Amplitude \(A_c\) und Phase \(\varphi\) vom Nachrichtensignal \(m(t)\) verändert wird. +Der Parameter \(\omega_c\), die Trägerkreisfrequenz bzw. die Trägerfrequenz \(f_c = \frac{\omega_c}{2\pi}\), +steht nicht für die modulation zur verfügung, statt dessen kann durch ihn die Frequenzachse frei gewählt werden. +\newblockpunct +Jedoch ist das für die Vielfalt der Modulationsarten keine Einschrenkung. +Ein Nachrichtensignal kann auch über die Momentanfrequenz (instantenous frequency) \(\omega_i\) eines trägers verändert werden. +Mathematisch wird dann daraus +\[ + \omega_i = \omega_c + \frac{d \varphi(t)}{dt} +\] +mit der Ableitung der Phase\cite{fm:NAT}. +Mit diesen drei parameter ergeben sich auch drei modulationsarten, die Amplitudenmodulation welche \(A_c\) benutzt, +die Phasenmodulation \(\varphi\) und dann noch die Momentankreisfrequenz \(\omega_i\): +\newline +\newline +To do: Bilder jeder Modulationsart + + + diff --git a/buch/papers/fm/01_AM.tex b/buch/papers/fm/01_AM.tex new file mode 100644 index 0000000..921fcf2 --- /dev/null +++ b/buch/papers/fm/01_AM.tex @@ -0,0 +1,29 @@ +% +% einleitung.tex -- Beispiel-File für die Einleitung +% +% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\section{Amplitudenmodulation\label{fm:section:teil0}} +\rhead{AM} + +Das Ziel ist FM zu verstehen doch dazu wird zuerst AM erklärt welches einwenig einfacher zu verstehen ist und erst dann übertragen wir die Ideen in FM. +Nun zur Amplitudenmodulation verwenden wir das bevorzugte Trägersignal +\[ + x_c(t) = A_c \cdot \cos(\omega_ct). +\] +Dies bringt den grossen Vorteil das, dass modulierend Signal sämtliche Anteile im Frequenzspektrum inanspruch nimmt +und das Trägersignal nur zwei komplexe Schwingungen besitzt. +Dies sieht man besonders in der Eulerischen Formel +\[ + x_c(t) = \frac{A_c}{2} \cdot e^{j\omega_ct}\;+\;\frac{A_c}{2} \cdot e^{-j\omega_ct}. +\] +Dabei ist die negative Frequenz der zweiten komplexen Schwingung zwingend erforderlich, damit in der Summe immer ein reelwertiges Trägersignal ergibt. +Nun wird der parameter \(A_c\) durch das Moduierende Signal \(m(t)\) ersetzt, wobei so \(m(t) \leqslant |1|\) normiert wurde. +\newline +\newline +TODO: +Hier beschrieib ich was AmplitudenModulation ist und mache dan den link zu Frequenzmodulation inkl Formel \[\cos( \cos x)\] +so wird beschrieben das daraus eigentlich \(x_c(t) = A_c \cdot \cos(\omega_i)\) wird und somit \(x_c(t) = A_c \cdot \cos(\omega_c + \frac{d \varphi(t)}{dt})\). +Da \(\sin \) abgeleitet \(\cos \) ergibt, so wird aus dem \(m(t)\) ein \( \frac{d \varphi(t)}{dt}\) in der momentan frequenz. \[ \Rightarrow \cos( \cos x) \] + +\subsection{Frequenzspektrum}
\ No newline at end of file diff --git a/buch/papers/fm/02_FM.tex b/buch/papers/fm/02_FM.tex new file mode 100644 index 0000000..fedfaaa --- /dev/null +++ b/buch/papers/fm/02_FM.tex @@ -0,0 +1,56 @@ +% +% teil1.tex -- Beispiel-File für das Paper +% +% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\section{FM +\label{fm:section:teil1}} +\rhead{FM} +\subsection{Frequenzspektrum} +TODO +Hier Beschreiben ich FM und FM im Frequenzspektrum. +%Sed ut perspiciatis unde omnis iste natus error sit voluptatem +%accusantium doloremque laudantium, totam rem aperiam, eaque ipsa +%quae ab illo inventore veritatis et quasi architecto beatae vitae +%dicta sunt explicabo. +%Nemo enim ipsam voluptatem quia voluptas sit aspernatur aut odit +%aut fugit, sed quia consequuntur magni dolores eos qui ratione +%voluptatem sequi nesciunt +%\begin{equation} +%\int_a^b x^2\, dx +%= +%\left[ \frac13 x^3 \right]_a^b +%= +%\frac{b^3-a^3}3. +%\label{fm:equation1} +%\end{equation} +%Neque porro quisquam est, qui dolorem ipsum quia dolor sit amet, +%consectetur, adipisci velit, sed quia non numquam eius modi tempora +%incidunt ut labore et dolore magnam aliquam quaerat voluptatem. +% +%Ut enim ad minima veniam, quis nostrum exercitationem ullam corporis +%suscipit laboriosam, nisi ut aliquid ex ea commodi consequatur? +%Quis autem vel eum iure reprehenderit qui in ea voluptate velit +%esse quam nihil molestiae consequatur, vel illum qui dolorem eum +%fugiat quo voluptas nulla pariatur? +% +%\subsection{De finibus bonorum et malorum +%\label{fm:subsection:finibus}} +%At vero eos et accusamus et iusto odio dignissimos ducimus qui +%blanditiis praesentium voluptatum deleniti atque corrupti quos +%dolores et quas molestias excepturi sint occaecati cupiditate non +%provident, similique sunt in culpa qui officia deserunt mollitia +%animi, id est laborum et dolorum fuga \eqref{000tempmlate:equation1}. +% +%Et harum quidem rerum facilis est et expedita distinctio +%\ref{fm:section:loesung}. +%Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil +%impedit quo minus id quod maxime placeat facere possimus, omnis +%voluptas assumenda est, omnis dolor repellendus +%\ref{fm:section:folgerung}. +%Temporibus autem quibusdam et aut officiis debitis aut rerum +%necessitatibus saepe eveniet ut et voluptates repudiandae sint et +%molestiae non recusandae. +%Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis +%voluptatibus maiores alias consequatur aut perferendis doloribus +%asperiores repellat. diff --git a/buch/papers/fm/03_bessel.tex b/buch/papers/fm/03_bessel.tex new file mode 100644 index 0000000..760cdc4 --- /dev/null +++ b/buch/papers/fm/03_bessel.tex @@ -0,0 +1,164 @@ +% +% teil2.tex -- Beispiel-File für teil2 +% +% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\section{FM und Besselfunktion +\label{fm:section:proof}} +\rhead{Herleitung} +Die momentane Trägerkreisfrequenz \(\omega_i\) wie schon in (ref) beschrieben ist, bringt die Vorigen Kapittel beschreiben. (Ableitung \(\frac{d \varphi(t)}{dt}\) mit sich). +Diese wiederum kann durch \(\beta\sin(\omega_mt)\) ausgedrückt werden, wobei es das Modulierende Signal \(m(t)\) ist. +Somit haben wir unser \(x_c\) welches +\[ +\cos(\omega_c t+\beta\sin(\omega_mt)) +\] +ist. + +\subsection{Herleitung} +Das Ziel ist es unser moduliertes Signal mit der Besselfunktion so auszudrücken: +\begin{align} + x_c(t) + = + \cos(\omega_ct+\beta\sin(\omega_mt)) + &= + \sum_{k= -\infty}^\infty J_{k}(\beta) \cos((\omega_c+k\omega_m)t) + \label{fm:eq:proof} +\end{align} +\subsubsection{Hilfsmittel} +Doch dazu brauchen wir die Hilfe der Additionsthoerme +\begin{align} + \cos(A + B) + &= + \cos(A)\cos(B)-\sin(A)\sin(B) + \label{fm:eq:addth1} + \\ + 2\cos (A)\cos (B) + &= + \cos(A-B)+\cos(A+B) + \label{fm:eq:addth2} + \\ + 2\sin(A)\sin(B) + &= + \cos(A-B)-\cos(A+B) + \label{fm:eq:addth3} +\end{align} +und die drei Besselfunktions indentitäten, +\begin{align} + \cos(\beta\sin\phi) + &= + J_0(\beta) + 2\sum_{k=1}^\infty J_{2k}(\beta) \cos(2k\phi) + \label{fm:eq:besselid1} + \\ + \sin(\beta\sin\phi) + &= + J_0(\beta) + 2\sum_{k=1}^\infty J_{2k+1}(\beta) \cos((2k+1)\phi) + \label{fm:eq:besselid2} + \\ + J_{-n}(\beta) &= (-1)^n J_n(\beta) + \label{fm:eq:besselid3} +\end{align} +welche man im Kapitel (ref), ref, ref findet. + +\subsubsection{Anwenden des Additionstheorem} +Mit dem \eqref{fm:eq:addth1} wird aus dem modulierten Signal +\[ + x_c(t) + = + \cos(\omega_c t + \beta\sin(\omega_mt)) + = + \cos(\omega_c t)\cos(\beta\sin(\omega_m t))-\sin(\omega_c)\sin(\beta\sin(\omega_m t)). + \label{fm:eq:start} +\] +\subsubsection{Cos-Teil} +Zu beginn wird der Cos-Teil +\[ + \cos(\omega_c)\cos(\beta\sin(\omega_mt)) +\] +mit hilfe der Besselindentität \eqref{fm:eq:besselid1} zum +\begin{align*} + \cos(\omega_c t) \cdot \bigg[\, J_0(\beta) + 2\sum_{k=1}^\infty J_{2k}(\beta) \cos( 2k \omega_m t)\, \bigg] + &=\\ + J_0(\beta)\cos(\omega_c t) + \sum_{k=1}^\infty J_{2k}(\beta) + \underbrace{2\cos(\omega_c t)\cos(2k\omega_m t)}_{\text{Additionstheorem}} +\end{align*} +wobei mit dem Additionstheorem \eqref{fm:eq:addth2} \(A = \omega_c t\) und \(B = 2k\omega_m t \) zum +\[ + J_0(\beta)\cdot \cos(\omega_c t) + \sum_{k=1}^\infty J_{2k}(\beta) \{ \cos((\omega_c - 2k \omega_m) t)+\cos((\omega_c + 2k \omega_m) t) \} +\] +wird. +Wenn dabei \(2k\) durch alle geraden Zahlen von \(-\infty \to \infty\) mit \(n\) substituiert erhält man den vereinfachten Term +\[ + \sum_{n\, \text{gerade}} J_{n}(\beta) \cos((\omega_c + n\omega_m) t), + \label{fm:eq:gerade} +\] +dabei gehen nun die Terme von \(-\infty \to \infty\), dabei bleibt n Ganzzahlig. + +\subsubsection{Sin-Teil} +Nun zum zweiten Teil des Term \eqref{fm:eq:start}, den Sin-Teil +\[ + \sin(\omega_c)\sin(\beta\sin(\omega_m t)). +\] +Dieser wird mit der \eqref{fm:eq:besselid2} Besselindentität zu +\begin{align*} + \sin(\omega_c t) \cdot \bigg[ J_0(\beta) + 2 \sum_{k=1}^\infty J_{ 2k + 1}(\beta) \cos(( 2k + 1) \omega_m t) \bigg] + &=\\ + J_0(\beta) \cdot \sin(\omega_c t) + \sum_{k=1}^\infty J_{2k+1}(\beta) \underbrace{2\sin(\omega_c t)\cos((2k+1)\omega_m t)}_{\text{Additionstheorem}}. +\end{align*} +Auch hier wird ein Additionstheorem \eqref{fm:eq:addth3} gebraucht, dabei ist \(A = \omega_c t\) und \(B = (2k+1)\omega_m t \), +somit wird daraus +\[ + J_0(\beta) \cdot \sin(\omega_c) + \sum_{k=1}^\infty J_{2k+1}(\beta) \{ \underbrace{\cos((\omega_c-(2k+1)\omega_m) t)}_{\text{neg.Teil}} - \cos((\omega_c+(2k+1)\omega_m) t) \} +\]dieser Term. +Wenn dabei \(2k +1\) durch alle ungeraden Zahlen von \(-\infty \to \infty\) mit \(n\) substituiert. +Zusätzlich dabei noch die letzte Besselindentität \eqref{fm:eq:besselid3} brauchen, ist bei allen ungeraden negativen \(n : J_{-n}(\beta) = -1\cdot J_n(\beta)\). +Somit wird neg.Teil zum Term \(-\cos((\omega_c+(2k+1)\omega_m) t)\) und die Summe vereinfacht sich zu +\[ + \sum_{n\, \text{ungerade}} -1 \cdot J_{n}(\beta) \cos((\omega_c + n\omega_m) t). + \label{fm:eq:ungerade} +\] +Substituiert man nun noch \(n \text{mit} -n \) so fällt das \(-1\) weg. + +\subsubsection{Summe Zusammenführen} +Beide Teile \eqref{fm:eq:gerade} Gerade +\[ + \sum_{n\, \text{gerade}} J_{n}(\beta) \cos((\omega_c + n\omega_m) t) +\]und \eqref{fm:eq:ungerade} Ungerade +\[ + \sum_{n\, \text{ungerade}} J_{n}(\beta) \cos((\omega_c + n\omega_m) t) +\] +ergeben zusammen +\[ + \cos(\omega_ct+\beta\sin(\omega_mt)) + = + \sum_{k= -\infty}^\infty J_{k}(\beta) \cos((\omega_c+k\omega_m)t). +\] +Somit ist \eqref{fm:eq:proof} bewiesen. +\newpage + +%---------------------------------------------------------------------------- +\subsection{Bessel und Frequenzspektrum} +Um sich das ganze noch einwenig Bildlicher vorzustellenhier einmal die Besselfunktion \(J_{k}(\beta)\) in geplottet. +\begin{figure} + \centering +% \input{./PyPython animation/bessel.pgf} + \caption{Bessle Funktion \(J_{k}(\beta)\)} + \label{fig:bessel} +\end{figure} +TODO Grafik einfügen, +\newline +Nun einmal das Modulierte FM signal im Frequenzspektrum mit den einzelen Summen dargestellt + +TODO +Hier wird beschrieben wie die Bessel Funktion der FM im Frequenzspektrum hilft, wieso diese gebrauch wird und ihre Vorteile. +\begin{itemize} + \item Zuerest einmal die Herleitung von FM zu der Besselfunktion + \item Im Frequenzspektrum darstellen mit Farben, ersichtlich machen. + \item Parameter tuing der Trägerfrequenz, Modulierende frequenz und Beta. +\end{itemize} + + +%\subsection{De finibus bonorum et malorum +%\label{fm:subsection:bonorum}} + + + diff --git a/buch/papers/fm/04_fazit.tex b/buch/papers/fm/04_fazit.tex new file mode 100644 index 0000000..8d5eca4 --- /dev/null +++ b/buch/papers/fm/04_fazit.tex @@ -0,0 +1,12 @@ +% +% teil3.tex -- Beispiel-File für Teil 3 +% +% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\section{Fazit +\label{fm:section:fazit}} +\rhead{Zusamenfassend} + +TODO Anwendungen erklären und Sinn des Ganzen. + + diff --git a/buch/papers/fm/FM presentation/FM_presentation.pdf b/buch/papers/fm/FM presentation/FM_presentation.pdf Binary files differnew file mode 100644 index 0000000..496e35e --- /dev/null +++ b/buch/papers/fm/FM presentation/FM_presentation.pdf diff --git a/buch/papers/fm/FM presentation/FM_presentation.tex b/buch/papers/fm/FM presentation/FM_presentation.tex new file mode 100644 index 0000000..2801e69 --- /dev/null +++ b/buch/papers/fm/FM presentation/FM_presentation.tex @@ -0,0 +1,125 @@ +%% !TeX root = .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(\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/FM presentation/README.txt b/buch/papers/fm/FM presentation/README.txt new file mode 100644 index 0000000..65f390d --- /dev/null +++ b/buch/papers/fm/FM presentation/README.txt @@ -0,0 +1 @@ +Dies ist die Presentation des FM - Bessel
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Dr Andreas Mueller # -images: - @echo "no images to be created in fm" +SOURCES := \ + 00_modulation.tex \ + 01_AM.tex \ + 02_FM.tex \ + 03_bessel.tex \ + 04_fazit.tex \ + main.tex +#TIKZFIGURES := \ + tikz/atoms-grid-still.tex \ + +#FIGURES := $(patsubst tikz/%.tex, figures/%.pdf, $(TIKZFIGURES)) + +all: images standalone + +.PHONY: images +images: $(FIGURES) + +#figures/%.pdf: tikz/%.tex +# mkdir -p figures +# pdflatex --output-directory=figures $< + +.PHONY: standalone +standalone: standalone.tex $(SOURCES) $(FIGURES) + mkdir -p standalone + cd ../..; \ + pdflatex \ + --halt-on-error \ + --shell-escape \ + --output-directory=papers/fm/standalone \ + papers/fm/standalone.tex; + cd standalone; \ + bibtex standalone; \ + makeindex standalone;
\ No newline at end of file diff --git a/buch/papers/fm/Makefile.inc b/buch/papers/fm/Makefile.inc index 0f144b6..40f23b1 100644 --- a/buch/papers/fm/Makefile.inc +++ b/buch/papers/fm/Makefile.inc @@ -6,9 +6,10 @@ dependencies-fm = \ papers/fm/packages.tex \ papers/fm/main.tex \ - papers/fm/references.bib \ - papers/fm/teil0.tex \ - papers/fm/teil1.tex \ - papers/fm/teil2.tex \ - papers/fm/teil3.tex + papers/fm/00_modulation.tex \ + papers/fm/01_AM.tex \ + papers/fm/02_FM.tex \ + papers/fm/03_bessel.tex \ + papers/fm/04_fazit.tex \ + papers/fm/references.bib diff --git a/buch/papers/fm/Python animation/Bessel-FM.ipynb b/buch/papers/fm/Python animation/Bessel-FM.ipynb new file mode 100644 index 0000000..6f099a7 --- /dev/null +++ b/buch/papers/fm/Python animation/Bessel-FM.ipynb @@ -0,0 +1,237 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from scipy import signal\n", + "from scipy.fft import fft, ifft, fftfreq\n", + "import scipy.special as sc\n", + "import scipy.fftpack\n", + "import matplotlib as mpl\n", + "# Use the pgf backend (must be set before pyplot imported)\n", + "#mpl.use('pgf')\n", + "import matplotlib.pyplot as plt\n", + "from matplotlib.widgets import Slider\n", + "def fm(beta):\n", + " # Number of samplepoints\n", + " N = 600\n", + " # sample spacing\n", + " T = 1.0 / 1000.0\n", + " fc = 100.0\n", + " fm = 30.0\n", + " x = np.linspace(0.01, N*T, N)\n", + " #beta = 1.0\n", + " y_old = np.sin(fc * 2.0*np.pi*x+beta*np.sin(fm * 2.0*np.pi*x))\n", + " y = 0*x;\n", + " xf = fftfreq(N, 1 / 400)\n", + " for k in range (-4, 4):\n", + " y = sc.jv(k,beta)*np.sin((fc+k*fm) * 2.0*np.pi*x)\n", + " yf = fft(y)/(fc*np.pi)\n", + " plt.plot(xf, np.abs(yf))\n", + " plt.xlim(-150, 150)\n", + " plt.show()\n", + " #yf_old = fft(y_old)\n", + " #plt.plot(xf, np.abs(yf_old))\n", + " #plt.show()\n", + " \n" + ] + }, + { + "cell_type": "code", + "execution_count": 114, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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yUkkiCnSpvVLFlOLSy0D8oGgAid48KferVxih69R/SYECXWqu+PK5pYwYoVe6QVWQH6EPJKkfhdBhqQoFulSdFS17iYXikfqIaYsBBFxTU1RyGRi7hp6neeiSlAJdqs5sZKSPvB566fAaOUIf3mfrG8c4fbY/3QZWwC9eO1II7zjNQ5c0KdCl6kbdiafEmaLDIZZ7MmJ6X7Tt1Nl+PvC1p/nMt5+rUEvTsePAKT7yvzbxJz/YUVhX/JeHrrooaVCgS82NmIdevC1aEa8155929w4CucDMsvxfEDsODrczf1Gu/sJB0bFphC5JKdCl5kpNWyy+CmH/wOiSS09/LtAnN2X7x3hyc659I0ouhRH62CWXwhROjdEloWz/JkiYoppLuZFn78DIkWt/iRF6V3TG5NTmbP8YN0XHDHoH4idHRZc0KJRcxg/toRDOqJKKyvZvgjSEUvPQe6PRd+9A7nEgNpI9G23r7ss9Tsl4oOcPfBbKK+6cHcivy/W4t8QB0/zB41JlJ5FSsv2bIEEbnpo4ekri2SjIu6I6ebw00dOX35YboWc90Pui69D0RX3oGxwqXDY336/uvuHrsxSP1vNLgwp0GUe2fxMkSBbVXPIlhFK3oDvbPzLo4vPQu6J1+ces19DzoZ2voecP5sLw6L0rtm7UaD1fnkkwxVEaW7Z/EyRoA4WbO8RWRs97JzJCz3ig54O4EOj9w+GdH73HR+jFgV7q8gcipWT7N0GCNjg0+jom+WfFI/T4JWO7+0aGfb2UXPJ/ZfTEwvtMb25KY1dfbIQeC3xQDV2Sy/ZvggQpf6JooYxS4sSi/IHPfNAdPdMHQNMkKwR6d72WXKL2N08yjnflAr079oGV/zDLy9fUVUOX8TTXugHSuAbL1tBzodc3MET/4BDHu/uYO2My7sMj3DPRCN2KLw6TMYWSy+DIQF80bzpHu3IfVPERev6A8PA89Jxyc9ZFQCN0qYF8/pYqIXihhj4cXt29gxzt6mP+jCnMmNI0aoSe9aAbebel4WMAbfOmc7y7D3cfWUPvL90fjdBlPAp0qZlSd+uJ19BnTc39AXno9FmOnull/swptExr5mRPrkyRr6tnPdD7itqXb/+S+TMZHHJOdPfz5smztET9zY/Q84Zr6Nnup9SeAl2qrjBro1ByGX3zip6+Aa5c2ALA7iNddBw+w7IFM1k4ZzoHTvYAw9P/ktxouZbiJ0UNDjn7T+Taf9PlFwDw8pun2XushysXzgaGZ+/kFb9fImNRoEvV5eefD5aYtuieu5hVV98g71w6H4CfvdrJkTN9XLlwNovmTefAibPA8Dz0rI/Q4x84Pf2DHDjRw7wZk7n2knkAPLHtAH2DQ7xzWW758KmRt5jzossEiIxFgS5Vlx9p9hemLY508GQusN96cQtXtc3hm5v2AHDzFa20zZvOsa4+Tvb0F0ayWQ/0eMmlq3eAN4520zZvBhfPnsZbL2op9O+D1y4GKPwFUkwjdBmPAl2qLj8yH+vCVPmSxFvmTudzv3kFLdOaufvGS7j8wln8m7a5QO7GFnuO9Yx4nayKt29XZxfP7TnOVYvnYGZ84ba30jK1mY//2lKWLZhJa8tUDkT9H3Utl4x/cEntadqiVNwvdx9j4ZxpLJ4/Axg+uHc8mrIXz/OTPf1s23sSM7jiwhbmzJjMi19+b2H71Uvm0TK1mT/5wU6OnMmVJrr7Rh5EzJru/uGa+Jf+8UW6+ga5eXkrALe+7SJe/K/D/XvrRS1s23cSGL6Oev4Yw7Ho/YJc2WrSJGNgcIgNL73J+9+xkEmTMj5/UypOI3SpuA//1dP8xsNPFZbzI9b8SDxu58FTPLnzTVYsnM2cGZNHbZ8+pYnVN1/Ka51dzJjSxO9cs4gDJ3oKZZdXD53m4Bgli2rpGxjiFx1HCst7j3Vz6YKZ/PrlC9jV2cXb3zKbW992Ycl/e+NlF/Dym6d5af9JjpwZ+YGXL0XBcBnnr//fbv79t5/j/247UKHeSD1JFOhmttLMXjGzDjO7r8T2qWb2nWj7JjNbmnpLpS7l51zHy7+vH+0CSgf6/d/fzkv7T3H3jUvHfM17br2cx37/Otbf8+v82mULGBhy9h7rBuC3vvIzbvzTf67pnO17H3+Bj3x9Ey/tz420d3V2sWzBTL720Wt49KPX8K1P3kDzGGe3fujaNqZPbuJDjz49atuB2Pu1J+pv/jEf/tLYxg10M2sCHgFuA1YAd5nZiqLdPgEcd/fLga8AD6bdUKlPxQf4jnX1setIF9MmT2Lf8R46Dp/h8Olc6eQj1y/hyoUtfPbdy/lQe9uYr2lm3HxFa66mvngOABu3H+JU7GbR+Q+NWvjR9jeB3K3xdh/p4pVDp7lq8Vxapk1m5a8sZM700X955F04exprPnYtb3/LbFbffClTmifRebqXoSHnX/71SOFmHlvfOA4MH4+IXx9GGleSGvp1QIe77wIws7XAKmBHbJ9VwJej598Fvmpm5kluwyJ1zd3pHRiiu2+Qnv5BDp06y67OLtovmceBkz08se1gYd/vP7+f72zeC8DXP/ZOPvXNrXz8b37JZa2zAPjMrZezcM70CX3/yy9s4eYrWnlo48s8vnVvYf1TLx+mbd50DOPnrx3hxksvYNrkphR6PJK7s/WN47TNm0Fry1T2HOsunOX64A9fZsidWVOay35AFXvX8lbeFdXYN+0+xhPbDrL3eDc7Dp7ioQ/8Kt/4+W4e+uHLTG6axHN7TgCw4cU3uXLhbJbMn8G+Ez0MDDpXLZ7DrKnNNE0ymidNYpINH2iVMNl4mWtmHwRWuvsfRMu/C1zv7vfE9nkp2mdftPxatM+RUq8J0N7e7lu2bJlwg5/fe4LffuTnE/53ki2XXDCDN452j1i3ZP6Mc7ouy+mzAyMOGGbRJRfMOKd/V+o9ypdZpH798HPv4m0Xzz6nf2tmW929vdS2qs5yMbPVwGqAJUuWnNNrzJ8xJc0mScom2XC9vLVlKpe1zuTi2dPYfuAUB070cONlFxRO6b968Vz6B52ndx3l6sVzaZmWzo/jmd4BfrzzcCqvdS7esWgOl7XOTOW1rmqby6bdR7n8wlm0zpoKwDVL5jLk8Oye4xzv6uPWKy+ip2+QVw+dZt/xbjRdPfvKld3OR5LfoP3A4thyW7Su1D77zKwZmAMcLX4hd18DrIHcCP1cGrzkghm8/mfvO5d/KiIStCSzXDYDy81smZlNAe4E1hftsx64O3r+QeCfVT8XEamucUfo7j5gZvcAG4Em4Bvuvt3MHgC2uPt64K+BvzezDuAYudAXEZEqSlS0dPcNwIaidffHnp8FPpRu00REZCJ0pqiISCAU6CIigVCgi4gEQoEuIhIIBbqISCDGPfW/Yt/YrBN4oybf/PwsAMa8pEGg1OfGoD7Xh0vcvbXUhpoFer0ysy1jXUchVOpzY1Cf659KLiIigVCgi4gEQoE+cWtq3YAaUJ8bg/pc51RDFxEJhEboIiKBUKCPw8zuNTM3swXRspnZX0Q3xN5mZtfE9r3bzP41+rp77FfNJjN72Mxejvr1f8xsbmzbF6M+v2Jm742tL3sD8XoTWn/yzGyxmT1lZjvMbLuZfTZaP9/Mnox+Zp80s3nR+jF/zuuNmTWZ2XNm9kS0vCy6mX1HdHP7KdH6+r/Zvbvra4wvcjft2EhuvvyCaN3twD8BBtwAbIrWzwd2RY/zoufzat2HCfb3t4Dm6PmDwIPR8xXAC8BUYBnwGrlLKTdFzy8FpkT7rKh1P86j/0H1p6hvC4FrouctwKvR/+tDwH3R+vti/+clf87r8Qv4PPAt4IloeR1wZ/T8UeDfRc8/BTwaPb8T+E6t2z7RL43Qy/sK8J+A+IGGVcBjnvMMMNfMFgLvBZ5092Pufhx4ElhZ9RafB3f/kbvnbx//DLm7U0Guz2vdvdfddwMd5G4eXriBuLv3AfkbiNer0PpT4O4H3f3Z6PlpYCewiFz//i7a7e+A346ej/VzXlfMrA14H/D1aNmAW8ndzB5G9zn/XnwXeLfV2V21FehjMLNVwH53f6Fo0yJgb2x5X7RurPX16vfJjdCgcfocWn9KikoJVwObgIvc/WC06U3gouh5KO/Fn5MblA1FyxcAJ2IDl3i/Cn2Otp+M9q8bVb1JdNaY2Y+Bi0ts+hLwh+RKEEEp12d3/360z5eAAeCb1WybVJ6ZzQK+B3zO3U/FB6Du7mYWzLQ3M3s/cNjdt5rZLTVuTlU0dKC7+3tKrTezd5CrFb8Q/cC3Ac+a2XWMfdPs/cAtRet/mnqjz9NYfc4zs48D7wfe7VExkfI3Ch/vBuL1JMkN0euWmU0mF+bfdPf/Ha0+ZGYL3f1gVFI5HK0P4b24CbjDzG4HpgGzgf9JrnzUHI3C4/1KdLP7TKt1Eb8evoDXGT4o+j5GHiz6ZbR+PrCb3AHRedHz+bVu+wT7uRLYAbQWrX87Iw+K7iJ3ALE5er6M4YOIb691P86j/0H1p6hvBjwG/HnR+ocZeVD0oeh5yZ/zev0iN9jKHxR9nJEHRT8VPf80Iw+Krqt1uyf61dAj9HO0gdwMgA6gG/g9AHc/ZmZ/BGyO9nvA3Y/Vponn7KvkQvvJ6C+TZ9z933rupuDryIX9APBpdx8EKHUD8do0/fz5GDdEr3Gz0nIT8LvAi2b2fLTuD4E/A9aZ2SfIzeb6cLSt5M95IL4ArDWzPwaeI3eTewjgZvc6U1REJBCa5SIiEggFuohIIBToIiKBUKCLiARCgS4iEggFuohIIBToIiKBUKCLiATi/wO3Cq7Lzsky6gAAAABJRU5ErkJggg==", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Number of samplepoints\n", + "N = 800\n", + "# sample spacing\n", + "T = 1.0 / 1000.0\n", + "x = np.linspace(0.01, N*T, N)\n", + "\n", + "y_old = np.sin(100* 2.0*np.pi*x+1*np.sin(15* 2.0*np.pi*x))\n", + "yf_old = fft(y_old)/(100*np.pi)\n", + "xf = fftfreq(N, 1 / 1000)\n", + "plt.plot(xf, np.abs(yf_old))\n", + "#plt.xlim(-150, 150)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 118, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fm(1)" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.7651976865579666\n" + ] + } + ], + "source": [ + "\n", + "for n in range (-2,4):\n", + " x = np.linspace(-11,11,1000)\n", + " y = sc.jv(n,x)\n", + " plt.plot(x, y, '-',label='n='+str(n))\n", + "#plt.plot([1,1],[sc.jv(0,1),sc.jv(-1,1)],)\n", + "plt.xlim(-10,10)\n", + "plt.grid(True)\n", + "plt.ylabel('Bessel $J_n(\\\\beta)$')\n", + "plt.xlabel(' $ \\\\beta $ ')\n", + "plt.plot(x, y)\n", + "plt.legend()\n", + "plt.show()\n", + "#plt.savefig('bessel.pgf', format='pgf')\n", + "print(sc.jv(0,1))" + ] + }, + { + "cell_type": "code", + "execution_count": 85, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "from scipy import special\n", + "\n", + "def drumhead_height(n, k, distance, angle, t):\n", + " kth_zero = special.jn_zeros(n, k)[-1]\n", + " return np.cos(t) * np.cos(n*angle) * special.jn(n, distance*kth_zero)\n", + "\n", + "theta = np.r_[0:2*np.pi:50j]\n", + "radius = np.r_[0:1:50j]\n", + "x = np.array([r * np.cos(theta) for r in radius])\n", + "y = np.array([r * np.sin(theta) for r in radius])\n", + "z = np.array([drumhead_height(1, 1, r, theta, 0.5) for r in radius])\n", + "\n", + "import matplotlib.pyplot as plt\n", + "fig = plt.figure()\n", + "ax = fig.add_axes(rect=(0, 0.05, 0.95, 0.95), projection='3d')\n", + "ax.plot_surface(x, y, z, rstride=1, cstride=1, cmap='RdBu_r', vmin=-0.5, vmax=0.5)\n", + "ax.set_xlabel('X')\n", + "ax.set_ylabel('Y')\n", + "ax.set_xticks(np.arange(-1, 1.1, 0.5))\n", + "ax.set_yticks(np.arange(-1, 1.1, 0.5))\n", + "ax.set_zlabel('Z')\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "x = np.linspace(0,0.1,1000)\n", + "y = np.sin(100 * 2.0*np.pi*x+1.5*np.sin(30 * 2.0*np.pi*x))\n", + "plt.plot(x, y, '-')\n", + "plt.show()" + ] + } + ], + "metadata": { + "interpreter": { + "hash": "916dbcbb3f70747c44a77c7bcd40155683ae19c65e1c03b4aa3499c5328201f1" + }, + "kernelspec": { + "display_name": "Python 3.8.10 64-bit", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + }, + "orig_nbformat": 4 + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/buch/papers/fm/Python animation/Bessel-FM.py b/buch/papers/fm/Python animation/Bessel-FM.py new file mode 100644 index 0000000..cf30e16 --- /dev/null +++ b/buch/papers/fm/Python animation/Bessel-FM.py @@ -0,0 +1,42 @@ +import numpy as np +from scipy import signal +from scipy.fft import fft, ifft, fftfreq +import scipy.special as sc +import scipy.fftpack +import matplotlib.pyplot as plt +from matplotlib.widgets import Slider + +# Number of samplepoints +N = 600 +# sample spacing +T = 1.0 / 800.0 +x = np.linspace(0.01, N*T, N) +beta = 1.0 +y_old = np.sin(100.0 * 2.0*np.pi*x+beta*np.sin(50.0 * 2.0*np.pi*x)) +y = 0*x; +xf = fftfreq(N, 1 / 400) +for k in range (-5, 5): + y = sc.jv(k,beta)*np.sin((100.0+k*50) * 2.0*np.pi*x) + yf = fft(y) + plt.plot(xf, np.abs(yf)) + +axbeta =plt.axes([0.25, 0.1, 0.65, 0.03]) +beta_slider = Slider( +ax=axbeta, +label="Beta", +valmin=0.1, +valmax=3, +valinit=beta, +) + +def update(val): + line.set_ydata(fm(beta_slider.val)) + fig.canvas.draw_idle() + + +beta_slider.on_changed(update) +plt.show() + +yf_old = fft(y_old) +plt.plot(xf, np.abs(yf_old)) +plt.show()
\ No newline at end of file diff --git a/buch/papers/fm/Quellen/A2-14.pdf b/buch/papers/fm/Quellen/A2-14.pdf Binary files differnew file mode 100644 index 0000000..7348cca --- /dev/null +++ b/buch/papers/fm/Quellen/A2-14.pdf diff --git a/buch/papers/fm/Quellen/FM_presentation.pdf b/buch/papers/fm/Quellen/FM_presentation.pdf Binary files differnew file mode 100644 index 0000000..496e35e --- /dev/null +++ b/buch/papers/fm/Quellen/FM_presentation.pdf diff --git a/buch/papers/fm/Quellen/Frequency modulation (FM) and Bessel functions.pdf b/buch/papers/fm/Quellen/Frequency modulation (FM) and Bessel functions.pdf Binary files differnew file mode 100644 index 0000000..a6e701c --- /dev/null +++ b/buch/papers/fm/Quellen/Frequency modulation (FM) and Bessel functions.pdf diff --git a/buch/papers/fm/Quellen/Seydel2022_Book_HöhereMathematikImAlltag.pdf b/buch/papers/fm/Quellen/Seydel2022_Book_HöhereMathematikImAlltag.pdf Binary files differnew file mode 100644 index 0000000..2a0bddd --- /dev/null +++ b/buch/papers/fm/Quellen/Seydel2022_Book_HöhereMathematikImAlltag.pdf diff --git a/buch/papers/fm/main.tex b/buch/papers/fm/main.tex index 1e75235..731f56f 100644 --- a/buch/papers/fm/main.tex +++ b/buch/papers/fm/main.tex @@ -1,36 +1,42 @@ +% !TeX root = ../../buch.tex % % main.tex -- Paper zum Thema <fm> % % (c) 2020 Hochschule Rapperswil -% -\chapter{Thema\label{chapter:fm}} -\lhead{Thema} +% + +\chapter{FM Bessel\label{chapter:fm}} +\lhead{FM} \begin{refsection} -\chapterauthor{Hans Muster} - -Ein paar Hinweise für die korrekte Formatierung des Textes -\begin{itemize} -\item -Absätze werden gebildet, indem man eine Leerzeile einfügt. -Die Verwendung von \verb+\\+ ist nur in Tabellen und Arrays gestattet. -\item -Die explizite Platzierung von Bildern ist nicht erlaubt, entsprechende -Optionen werden gelöscht. -Verwenden Sie Labels und Verweise, um auf Bilder hinzuweisen. -\item -Beginnen Sie jeden Satz auf einer neuen Zeile. -Damit ermöglichen Sie dem Versionsverwaltungssysteme, Änderungen -in verschiedenen Sätzen von verschiedenen Autoren ohne Konflikt -anzuwenden. -\item -Bilden Sie auch für Formeln kurze Zeilen, einerseits der besseren -Übersicht wegen, aber auch um GIT die Arbeit zu erleichtern. -\end{itemize} - -\input{papers/fm/teil0.tex} -\input{papers/fm/teil1.tex} -\input{papers/fm/teil2.tex} -\input{papers/fm/teil3.tex} + +\chapterauthor{Joshua Bär} + +Die Frequenzmodulation ist eine Modulation die man auch schon im alten Radio findet. +Falls du dich an die Zeit erinnerst, konnte man zwischen \textit{FM-AM} Umschalten, +dies bedeutete so viel wie: \textit{F}requenz-\textit{M}odulation und \textit{A}mplituden-\textit{M}odulation. +Durch die Modulation wird ein Nachrichtensignal \(m(t)\) auf ein Trägersignal (z.B. ein Sinus- oder Rechtecksignal) abgebildet (kombiniert). +Durch dieses Auftragen vom Nachrichtensignal \(m(t)\) kann das modulierte Signal in einem gewünschten Frequenzbereich übertragen werden. +Der ursprünglich Frequenzbereich des Nachrichtensignal \(m(t)\) erstreckt sich typischerweise von 0 Hz bis zur Bandbreite \(B_m\). +\newline +Beim Empfänger wird dann durch Demodulation das ursprüngliche Nachrichtensignal \(m(t)\) so originalgetreu wie möglich zurückgewonnen. +\newline +Beim Trägersignal \(x_c(t)\) handelt es sich um ein informationsloses Hilfssignal. +Durch die Modulation mit dem Nachrichtensignal \(m(t)\) wird es zum modulierten zu übertragenden Signal. +Für alle Erklärungen wird ein sinusförmiges Trägersignal benutzt, jedoch kann auch ein Rechtecksignal, +welches Digital einfach umzusetzten ist, +genauso als Trägersignal genutzt werden kann. +Zuerst wird erklärt was \textit{FM-AM} ist, danach wie sich diese im Frequenzspektrum verhalten. +Erst dann erklär ich dir wie die Besselfunktion mit der Frequenzmodulation( acro?) zusammenhängt. +Nun zur Modulation im nächsten Abschnitt.\cite{fm:NAT} + + +\input{papers/fm/00_modulation.tex} +\input{papers/fm/01_AM.tex} +\input{papers/fm/02_FM.tex} +\input{papers/fm/03_bessel.tex} +\input{papers/fm/04_fazit.tex} \printbibliography[heading=subbibliography] \end{refsection} + + diff --git a/buch/papers/fm/packages.tex b/buch/papers/fm/packages.tex index 4cba2b6..f0ca8cc 100644 --- a/buch/papers/fm/packages.tex +++ b/buch/papers/fm/packages.tex @@ -7,4 +7,4 @@ % if your paper needs special packages, add package commands as in the % following example %\usepackage{packagename} - +\usepackage{xcolor} diff --git a/buch/papers/fm/references.bib b/buch/papers/fm/references.bib index 76eb265..21b910b 100644 --- a/buch/papers/fm/references.bib +++ b/buch/papers/fm/references.bib @@ -23,6 +23,17 @@ volume = {2} } +@book{fm:NAT, + title = {Nachrichtentechnik 1 + 2}, + author = {Thomas Kneubühler}, + publisher = {None}, + year = {2021}, + isbn = {}, + inseries = {Script for students}, + volume = {} +} + + @article{fm:mendezmueller, author = { Tabea Méndez and Andreas Müller }, title = { Noncommutative harmonic analysis and image registration }, diff --git a/buch/papers/fm/standalone.tex b/buch/papers/fm/standalone.tex new file mode 100644 index 0000000..c161ed5 --- /dev/null +++ b/buch/papers/fm/standalone.tex @@ -0,0 +1,31 @@ +\documentclass{book} + +\def\IncludeBookCover{0} +\input{common/packages.tex} + +% additional packages used by the individual papers, add a line for +% each paper +\input{papers/common/addpackages.tex} + +% workaround for biblatex bug +\makeatletter +\def\blx@maxline{77} +\makeatother +\addbibresource{chapters/references.bib} + +% Bibresources for each article +\input{papers/common/addbibresources.tex} + +% make sure the last index starts on an odd page +\AtEndDocument{\clearpage\ifodd\value{page}\else\null\clearpage\fi} +\makeindex + +%\pgfplotsset{compat=1.12} +\setlength{\headheight}{15pt} % fix headheight warning +\DeclareGraphicsRule{*}{mps}{*}{} + +\begin{document} + \input{common/macros.tex} + \def\chapterauthor#1{{\large #1}\bigskip\bigskip} + \input{papers/fm/main.tex} +\end{document} diff --git a/buch/papers/fm/teil0.tex b/buch/papers/fm/teil0.tex deleted file mode 100644 index 55697df..0000000 --- a/buch/papers/fm/teil0.tex +++ /dev/null @@ -1,22 +0,0 @@ -% -% einleitung.tex -- Beispiel-File für die Einleitung -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{Teil 0\label{fm:section:teil0}} -\rhead{Teil 0} -Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam -nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam -erat, sed diam voluptua \cite{fm:bibtex}. -At vero eos et accusam et justo duo dolores et ea rebum. -Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum -dolor sit amet. - -Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam -nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam -erat, sed diam voluptua. -At vero eos et accusam et justo duo dolores et ea rebum. Stet clita -kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit -amet. - - diff --git a/buch/papers/fm/teil1.tex b/buch/papers/fm/teil1.tex deleted file mode 100644 index 6f9edf1..0000000 --- a/buch/papers/fm/teil1.tex +++ /dev/null @@ -1,55 +0,0 @@ -% -% teil1.tex -- Beispiel-File für das Paper -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{Teil 1 -\label{fm:section:teil1}} -\rhead{Problemstellung} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. -Nemo enim ipsam voluptatem quia voluptas sit aspernatur aut odit -aut fugit, sed quia consequuntur magni dolores eos qui ratione -voluptatem sequi nesciunt -\begin{equation} -\int_a^b x^2\, dx -= -\left[ \frac13 x^3 \right]_a^b -= -\frac{b^3-a^3}3. -\label{fm:equation1} -\end{equation} -Neque porro quisquam est, qui dolorem ipsum quia dolor sit amet, -consectetur, adipisci velit, sed quia non numquam eius modi tempora -incidunt ut labore et dolore magnam aliquam quaerat voluptatem. - -Ut enim ad minima veniam, quis nostrum exercitationem ullam corporis -suscipit laboriosam, nisi ut aliquid ex ea commodi consequatur? -Quis autem vel eum iure reprehenderit qui in ea voluptate velit -esse quam nihil molestiae consequatur, vel illum qui dolorem eum -fugiat quo voluptas nulla pariatur? - -\subsection{De finibus bonorum et malorum -\label{fm:subsection:finibus}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga \eqref{000tempmlate:equation1}. - -Et harum quidem rerum facilis est et expedita distinctio -\ref{fm:section:loesung}. -Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil -impedit quo minus id quod maxime placeat facere possimus, omnis -voluptas assumenda est, omnis dolor repellendus -\ref{fm:section:folgerung}. -Temporibus autem quibusdam et aut officiis debitis aut rerum -necessitatibus saepe eveniet ut et voluptates repudiandae sint et -molestiae non recusandae. -Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis -voluptatibus maiores alias consequatur aut perferendis doloribus -asperiores repellat. - - diff --git a/buch/papers/fm/teil2.tex b/buch/papers/fm/teil2.tex deleted file mode 100644 index 6ab6fa0..0000000 --- a/buch/papers/fm/teil2.tex +++ /dev/null @@ -1,40 +0,0 @@ -% -% teil2.tex -- Beispiel-File für teil2 -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{Teil 2 -\label{fm:section:teil2}} -\rhead{Teil 2} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit -aspernatur aut odit aut fugit, sed quia consequuntur magni dolores -eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam -est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci -velit, sed quia non numquam eius modi tempora incidunt ut labore -et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima -veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, -nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure -reprehenderit qui in ea voluptate velit esse quam nihil molestiae -consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla -pariatur? - -\subsection{De finibus bonorum et malorum -\label{fm:subsection:bonorum}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis -est et expedita distinctio. Nam libero tempore, cum soluta nobis -est eligendi optio cumque nihil impedit quo minus id quod maxime -placeat facere possimus, omnis voluptas assumenda est, omnis dolor -repellendus. Temporibus autem quibusdam et aut officiis debitis aut -rerum necessitatibus saepe eveniet ut et voluptates repudiandae -sint et molestiae non recusandae. Itaque earum rerum hic tenetur a -sapiente delectus, ut aut reiciendis voluptatibus maiores alias -consequatur aut perferendis doloribus asperiores repellat. - - diff --git a/buch/papers/fm/teil3.tex b/buch/papers/fm/teil3.tex deleted file mode 100644 index 3bcfc4d..0000000 --- a/buch/papers/fm/teil3.tex +++ /dev/null @@ -1,40 +0,0 @@ -% -% teil3.tex -- Beispiel-File für Teil 3 -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{Teil 3 -\label{fm:section:teil3}} -\rhead{Teil 3} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit -aspernatur aut odit aut fugit, sed quia consequuntur magni dolores -eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam -est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci -velit, sed quia non numquam eius modi tempora incidunt ut labore -et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima -veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, -nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure -reprehenderit qui in ea voluptate velit esse quam nihil molestiae -consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla -pariatur? - -\subsection{De finibus bonorum et malorum -\label{fm:subsection:malorum}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis -est et expedita distinctio. Nam libero tempore, cum soluta nobis -est eligendi optio cumque nihil impedit quo minus id quod maxime -placeat facere possimus, omnis voluptas assumenda est, omnis dolor -repellendus. Temporibus autem quibusdam et aut officiis debitis aut -rerum necessitatibus saepe eveniet ut et voluptates repudiandae -sint et molestiae non recusandae. Itaque earum rerum hic tenetur a -sapiente delectus, ut aut reiciendis voluptatibus maiores alias -consequatur aut perferendis doloribus asperiores repellat. - - |
