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Diffstat (limited to 'buch/papers/fm')
-rw-r--r-- | buch/papers/fm/01_AM-FM.tex | 41 | ||||
-rw-r--r-- | buch/papers/fm/02_frequenzyspectrum.tex | 2 | ||||
-rw-r--r-- | buch/papers/fm/03_bessel.tex | 145 | ||||
-rw-r--r-- | buch/papers/fm/04_fazit.tex | 32 | ||||
-rw-r--r-- | buch/papers/fm/FM presentation/FM_presentation.pdf (renamed from buch/papers/fm/RS presentation/FM_presentation.pdf) | bin | 357597 -> 357597 bytes | |||
-rw-r--r-- | buch/papers/fm/FM presentation/FM_presentation.tex (renamed from buch/papers/fm/RS presentation/FM_presentation.tex) | 4 | ||||
-rw-r--r-- | buch/papers/fm/FM presentation/README.txt | 1 | ||||
-rw-r--r-- | buch/papers/fm/FM presentation/images/100HZ.png (renamed from buch/papers/fm/RS presentation/images/100HZ.png) | bin | 8601 -> 8601 bytes | |||
-rw-r--r-- | buch/papers/fm/FM presentation/images/200HZ.png (renamed from buch/papers/fm/RS presentation/images/200HZ.png) | bin | 8502 -> 8502 bytes | |||
-rw-r--r-- | buch/papers/fm/FM presentation/images/300HZ.png (renamed from buch/papers/fm/RS presentation/images/300HZ.png) | bin | 9059 -> 9059 bytes | |||
-rw-r--r-- | buch/papers/fm/FM presentation/images/400HZ.png (renamed from buch/papers/fm/RS presentation/images/400HZ.png) | bin | 9949 -> 9949 bytes | |||
-rw-r--r-- | buch/papers/fm/FM presentation/images/bessel.png (renamed from buch/papers/fm/RS presentation/images/bessel.png) | bin | 40393 -> 40393 bytes | |||
-rw-r--r-- | buch/papers/fm/FM presentation/images/bessel2.png (renamed from buch/papers/fm/RS presentation/images/bessel2.png) | bin | 102494 -> 102494 bytes | |||
-rw-r--r-- | buch/papers/fm/FM presentation/images/bessel_beta1.png (renamed from buch/papers/fm/RS presentation/images/bessel_beta1.png) | bin | 40696 -> 40696 bytes | |||
-rw-r--r-- | buch/papers/fm/FM presentation/images/bessel_frequenz.png (renamed from buch/papers/fm/RS presentation/images/bessel_frequenz.png) | bin | 11264 -> 11264 bytes | |||
-rw-r--r-- | buch/papers/fm/FM presentation/images/beta_0.001.png (renamed from buch/papers/fm/RS presentation/images/beta_0.001.png) | bin | 6233 -> 6233 bytes | |||
-rw-r--r-- | buch/papers/fm/FM presentation/images/beta_0.1.png (renamed from buch/papers/fm/RS presentation/images/beta_0.1.png) | bin | 6630 -> 6630 bytes | |||
-rw-r--r-- | buch/papers/fm/FM presentation/images/beta_0.5.png (renamed from buch/papers/fm/RS presentation/images/beta_0.5.png) | bin | 8167 -> 8167 bytes | |||
-rw-r--r-- | buch/papers/fm/FM presentation/images/beta_1.png (renamed from buch/papers/fm/RS presentation/images/beta_1.png) | bin | 11303 -> 11303 bytes | |||
-rw-r--r-- | buch/papers/fm/FM presentation/images/beta_2.png (renamed from buch/papers/fm/RS presentation/images/beta_2.png) | bin | 14703 -> 14703 bytes | |||
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-rw-r--r-- | buch/papers/fm/FM presentation/images/fm_10Hz.png (renamed from buch/papers/fm/RS presentation/images/fm_10Hz.png) | bin | 6781 -> 6781 bytes | |||
-rw-r--r-- | buch/papers/fm/FM presentation/images/fm_20hz.png (renamed from buch/papers/fm/RS presentation/images/fm_20hz.png) | bin | 7834 -> 7834 bytes | |||
-rw-r--r-- | buch/papers/fm/FM presentation/images/fm_30Hz.png (renamed from buch/papers/fm/RS presentation/images/fm_30Hz.png) | bin | 8601 -> 8601 bytes | |||
-rw-r--r-- | buch/papers/fm/FM presentation/images/fm_3Hz.png (renamed from buch/papers/fm/RS presentation/images/fm_3Hz.png) | bin | 6558 -> 6558 bytes | |||
-rw-r--r-- | buch/papers/fm/FM presentation/images/fm_40Hz.png (renamed from buch/papers/fm/RS presentation/images/fm_40Hz.png) | bin | 8795 -> 8795 bytes | |||
-rw-r--r-- | buch/papers/fm/FM presentation/images/fm_5Hz.png (renamed from buch/papers/fm/RS presentation/images/fm_5Hz.png) | bin | 5766 -> 5766 bytes | |||
-rw-r--r-- | buch/papers/fm/FM presentation/images/fm_7Hz.png (renamed from buch/papers/fm/RS presentation/images/fm_7Hz.png) | bin | 6337 -> 6337 bytes | |||
-rw-r--r-- | buch/papers/fm/FM presentation/images/fm_frequenz.png (renamed from buch/papers/fm/RS presentation/images/fm_frequenz.png) | bin | 11042 -> 11042 bytes | |||
-rw-r--r-- | buch/papers/fm/FM presentation/images/fm_in_time.png (renamed from buch/papers/fm/RS presentation/images/fm_in_time.png) | bin | 27400 -> 27400 bytes | |||
-rw-r--r-- | buch/papers/fm/Makefile | 8 | ||||
-rw-r--r-- | buch/papers/fm/Quellen/A2-14.pdf | bin | 0 -> 259673 bytes | |||
-rw-r--r-- | buch/papers/fm/Quellen/FM_presentation.pdf | bin | 0 -> 357597 bytes | |||
-rw-r--r-- | buch/papers/fm/Quellen/Frequency modulation (FM) and Bessel functions.pdf (renamed from buch/papers/fm/RS presentation/Frequency modulation (FM) and Bessel functions.pdf) | bin | 159598 -> 159598 bytes | |||
-rw-r--r-- | buch/papers/fm/Quellen/Seydel2022_Book_HöhereMathematikImAlltag.pdf | bin | 0 -> 4118379 bytes | |||
-rw-r--r-- | buch/papers/fm/RS presentation/README.txt | 1 | ||||
-rw-r--r-- | buch/papers/fm/RS presentation/RS.tex | 123 | ||||
-rw-r--r-- | buch/papers/fm/main.tex | 2 | ||||
-rw-r--r-- | buch/papers/fm/packages.tex | 2 | ||||
-rw-r--r-- | buch/papers/fm/references.bib | 11 |
40 files changed, 179 insertions, 193 deletions
diff --git a/buch/papers/fm/01_AM-FM.tex b/buch/papers/fm/01_AM-FM.tex index ef55d55..163c792 100644 --- a/buch/papers/fm/01_AM-FM.tex +++ b/buch/papers/fm/01_AM-FM.tex @@ -7,30 +7,41 @@ \rhead{AM- FM} Das sinusförmige Trägersignal hat die übliche Form: -\(x_c(t) = A_c \cdot cos(\omega_c(t)+\varphi)\). +\(x_c(t) = A_c \cdot \cos(\omega_c(t)+\varphi)\). 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 Vilfalt der Modulationsarten keine Einschrenkung. +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. +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 -TODO: -Hier beschrieib ich was AmplitudenModulation ist und mache dan den link zu Frequenzmodulation inkl Formel \[cos( cos x)\] - - - -%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. - +To do: Bilder jeder Modulationsart +\subsection{AM - Amplitudenmodulation} +Das Ziel ist FM zu verstehen doch dazu wird zuerst AM erklärt welches einwenig einfacher zu verstehen ist und erst dann übertragen wir die Ideeen 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. \[ \Rightarrow \cos( \cos x) \] diff --git a/buch/papers/fm/02_frequenzyspectrum.tex b/buch/papers/fm/02_frequenzyspectrum.tex index 1c6044d..80e1c65 100644 --- a/buch/papers/fm/02_frequenzyspectrum.tex +++ b/buch/papers/fm/02_frequenzyspectrum.tex @@ -7,7 +7,9 @@ \label{fm:section:teil1}} \rhead{Problemstellung} +TODO Hier Beschreiben ich das Frequenzspektrum und wie AM und FM aussehen und generiert werden. +Somit auch die Herleitung des 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 diff --git a/buch/papers/fm/03_bessel.tex b/buch/papers/fm/03_bessel.tex index fdaa0d1..edb932b 100644 --- a/buch/papers/fm/03_bessel.tex +++ b/buch/papers/fm/03_bessel.tex @@ -4,25 +4,136 @@ % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % \section{FM und Besselfunktion -\label{fm:section:teil2}} -\rhead{Teil 2} +\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} + \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} +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. +\newline +Mit dem \refname{fm:eq:addth1} wird aus dem modulierten Signal +\[ +\cos(\omega_c t + \beta\sin(\omega_mt)) +\] +das Signal +\[ + \cos(\omega_c t)\cos(\beta\sin(\omega_m t))-\sin(\omega_c)\sin(\beta\sin(\omega_m t)). + \label{fm:eq:start} +\] +Zu beginn wird der erste Teil +\[ + \cos(\omega_c)\cos(\beta\sin(\omega_mt)) +\] +mit hilfe der Bessel indentität \ref{fm:eq:besselid1} zum +\[ + J_0(\beta)\cos(\omega_c) + \sum_{k=1}^\infty J_{2k}(\beta) 2\cos(\omega_c t)\cos(2k\omega_m t) +\] +\newline +TODO 2 und \(\cos( )\) in lime. +wobei mit dem \colorbox{lime}{Additionstheorem} \ref{fm:eq:addth2} zum +\[ + J_0(\beta)\dot \cos(\omega_c t) + \sum_{k=1}^\infty J_{2k}(\beta) \{ \cos((\omega_c - 2k\omega_m) t)+\cos((\omega_c + 2k\omega_m) t) \} +\] +wird. +Wenn dabei \(2k\) durch alle geraden Zahlen von \(-\infty \to \infty\) mit \(n\) substituiert erhält man den vereinfachten Term +\[ + \sum_{n\, gerade} J_{n}(\beta) \cos((\omega_c + n\omega_m) t) + \label{fm:eq:gerade} +\] +\newline +nun zum zweiten Teil des Term \ref{fm:eq:start} +\[ + \sin(\omega_c)\sin(\beta\sin(\omega_m t)). +\] +Dieser wird mit der \ref{fm:eq:besselid2} Bessel indentität zu +\[ + J_0(\beta) \dot \sin(\omega_c t) + \sum_{k=1}^\infty J_{2k+1}(\beta) 2\sin(\omega_c t)\cos((2k+1)\omega_m t). +\] +Auch hier wird ein Additionstheorem \ref{fm:eq:addth3} gebraucht um aus dem Sumanden diesen Term +\[ + J_0(\beta) \dot \sin(\omega_c) + \sum_{k=1}^\infty J_{2k+1}(\beta) \{ \underbrace{\cos((\omega_c-(2k+1)\omega_m) t)}_{Teil1} - \cos((\omega_c+(2k+1)\omega_m) t) \} +\]zu gewinnen. +Wenn dabei \(2k +1\) durch alle ungeraden Zahlen von \(-\infty \to \infty\) mit \(n\) substituiert. +Zusätzlich dabei noch die letzte Bessel indentität \ref{fm:eq:besselid3} brauchen, ist bei allen ungeraden negativen \(n : J_{-n}(\beta) = -1 J_n(\beta)\). +Somit wird Teil1 zum negativen Term und die Summe vereinfacht sich zu +\[ + \sum_{n\, ungerade} -1 J_{n}(\beta) \cos((\omega_c + n\omega_m) t). + \label{fm:eq:ungerade} +\] +Substituiert man nun noch \(n \text{mit} -n \) so fällt das \(-1\) weg. +Beide Teile \ref{fm:eq:gerade} Gerade und \ref{fm:eq:ungerade} Ungerade 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 \ref{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 +% \includegraphics[width=0.5\textwidth]{/home/joshua/Documents/SeminarSpezielleFunktionen/buch/papers/fm/FM presentation/images/bessel.png} + \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. -%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? -% +\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 index 8c6c002..8d5eca4 100644 --- a/buch/papers/fm/04_fazit.tex +++ b/buch/papers/fm/04_fazit.tex @@ -6,35 +6,7 @@ \section{Fazit \label{fm:section:fazit}} \rhead{Zusamenfassend} -%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. + +TODO Anwendungen erklären und Sinn des Ganzen. diff --git a/buch/papers/fm/RS presentation/FM_presentation.pdf b/buch/papers/fm/FM presentation/FM_presentation.pdf Binary files differindex 496e35e..496e35e 100644 --- a/buch/papers/fm/RS presentation/FM_presentation.pdf +++ b/buch/papers/fm/FM presentation/FM_presentation.pdf diff --git a/buch/papers/fm/RS presentation/FM_presentation.tex b/buch/papers/fm/FM presentation/FM_presentation.tex index 92cb501..2801e69 100644 --- a/buch/papers/fm/RS presentation/FM_presentation.tex +++ b/buch/papers/fm/FM presentation/FM_presentation.tex @@ -1,4 +1,4 @@ -%% !TeX root = RS.tex +%% !TeX root = .tex \documentclass[11pt,aspectratio=169]{beamer} \usepackage[utf8]{inputenc} @@ -15,7 +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}{} 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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presentation/images/fm_frequenz.png Binary files differindex 26bfd86..26bfd86 100644 --- a/buch/papers/fm/RS presentation/images/fm_frequenz.png +++ b/buch/papers/fm/FM presentation/images/fm_frequenz.png diff --git a/buch/papers/fm/RS presentation/images/fm_in_time.png b/buch/papers/fm/FM presentation/images/fm_in_time.png Binary files differindex 068eafc..068eafc 100644 --- a/buch/papers/fm/RS presentation/images/fm_in_time.png +++ b/buch/papers/fm/FM presentation/images/fm_in_time.png diff --git a/buch/papers/fm/Makefile b/buch/papers/fm/Makefile index c84963f..aee954f 100644 --- a/buch/papers/fm/Makefile +++ b/buch/papers/fm/Makefile @@ -16,15 +16,17 @@ SOURCES := \ #FIGURES := $(patsubst tikz/%.tex, figures/%.pdf, $(TIKZFIGURES)) -#.PHONY: images -#images: $(FIGURES) +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) +standalone: standalone.tex $(SOURCES) $(FIGURES) mkdir -p standalone cd ../..; \ pdflatex \ 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/RS presentation/Frequency modulation (FM) and Bessel functions.pdf b/buch/papers/fm/Quellen/Frequency modulation (FM) and Bessel functions.pdf Binary files differindex a6e701c..a6e701c 100644 --- a/buch/papers/fm/RS presentation/Frequency modulation (FM) and Bessel functions.pdf +++ 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/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} diff --git a/buch/papers/fm/main.tex b/buch/papers/fm/main.tex index fcf4d1a..6af3386 100644 --- a/buch/papers/fm/main.tex +++ b/buch/papers/fm/main.tex @@ -27,7 +27,7 @@ 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. +Nun zur Modulation im nächsten Abschnitt.\cite{fm:NAT} \input{papers/fm/01_AM-FM.tex} \input{papers/fm/02_frequenzyspectrum.tex} 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 }, |