diff options
| -rw-r--r-- | buch/papers/fm/anim/Makefile | 12 | ||||
| -rw-r--r-- | buch/papers/fm/anim/animation.tex | 85 | ||||
| -rw-r--r-- | buch/papers/fm/anim/fm.m | 98 |
3 files changed, 195 insertions, 0 deletions
diff --git a/buch/papers/fm/anim/Makefile b/buch/papers/fm/anim/Makefile new file mode 100644 index 0000000..f4c7850 --- /dev/null +++ b/buch/papers/fm/anim/Makefile @@ -0,0 +1,12 @@ +# +# Makefile +# +# (c) 2022 Prof Dr Andreas Müller +# +all: animation.pdf + +parts.tex: fm.m + octave fm.m + +animation.pdf: animation.tex parts.tex + pdflatex animation.tex diff --git a/buch/papers/fm/anim/animation.tex b/buch/papers/fm/anim/animation.tex new file mode 100644 index 0000000..4a6f428 --- /dev/null +++ b/buch/papers/fm/anim/animation.tex @@ -0,0 +1,85 @@ +% +% animation.tex +% +% (c) 2022 Prof Dr Andreas Müller, +% +\documentclass[aspectratio=169]{beamer} +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{epic} +\usepackage{color} +\usepackage{array} +\usepackage{ifthen} +\usepackage{lmodern} +\usepackage{amsmath} +\usepackage{amssymb} +\usepackage{nccmath} +\usepackage{mathtools} +\usepackage{adjustbox} +\usepackage{multimedia} +\usepackage{verbatim} +\usepackage{wasysym} +\usepackage{stmaryrd} +\usepackage{tikz} +\usetikzlibrary{shapes.geometric} +\usetikzlibrary{decorations.pathreplacing} +\usetikzlibrary{calc} +\usetikzlibrary{arrows} +\usetikzlibrary{3d} +\usetikzlibrary{arrows,shapes,math,decorations.text,automata} +\usepackage{pifont} +\usepackage[all]{xy} +\usepackage[many]{tcolorbox} +\mode<beamer>{% +\usetheme[hideothersubsections,hidetitle]{Hannover} +} +\beamertemplatenavigationsymbolsempty +\begin{document} + +\def\spektrum#1#2{ +\only<#1>{ + \begin{scope} + \color{red} + \input{#2} + \end{scope} +} +} + +\begin{frame} +\begin{center} +\begin{tikzpicture}[>=latex,thick] +\def\df{0.37} +\def\da{1} + +\draw[->,color=gray] (0,-0.1) -- (0,6.3) [right] coordinate[label={right:$a$}]; + +\foreach \a in {1,...,5}{ + \draw[color=gray!50] (-6,{(6-\a)*\da}) -- (6,{(6-\a)*\da}); +} +\draw[color=gray!50] (-6,{6*\da}) -- (6,{6*\da}); +\foreach \f in {-15,-10,-5,5,10,15}{ + \draw[color=gray!50] ({\f*\df},0) -- ({\f*\df},{6*\da}); +} + +\input{parts.tex} + +\draw[->] (-6.1,0) -- (6.9,0) coordinate[label={$f$}]; +\foreach \f in {-16,...,16}{ + \draw ({\f*\df},-0.05) -- ({\f*\df},0.05); +} +\foreach \f in {-15,-10,-5,5,10,15}{ + \node at ({\f*\df},-0.1) [below] {$\f f_m$}; + \draw ({\f*\df},-0.1) -- ({\f*\df},0.1); +} +\node at (0,-0.1) [below] {$0$}; + +\foreach \a in {1,...,5}{ + \node at (6,{(6-\a)*\da}) [right] {$-\a$}; +} +\node at (6,{6*\da}) [right] {$\phantom{-}0$}; + +\end{tikzpicture} +\end{center} +\end{frame} + +\end{document} diff --git a/buch/papers/fm/anim/fm.m b/buch/papers/fm/anim/fm.m new file mode 100644 index 0000000..9062818 --- /dev/null +++ b/buch/papers/fm/anim/fm.m @@ -0,0 +1,98 @@ +# +# fm.m -- animation frequenzspektrum +# +# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +global fc; +fc = 1e6; +global width; +width = 16; +global fm; +fm = 1000; +global gamma; +gamma = 2; +global resolution; +resolution = 300; + +function retval = spektrum(beta, fm) + global width; + global fc; + retval = zeros(2 * width + 1, 2); + center = width + 1; + for k = (0:width) + retval(center - k, 1) = fc - k * fm; + retval(center + k, 1) = fc + k * fm; + a = besselj(k, beta); + retval(center - k, 2) = a; + retval(center + k, 2) = a; + endfor +endfunction + +function drawspectrum(fn, spectrum, foffset, fscale, beta) + n = size(spectrum)(1,1); + for i = (1:n) + f = (spectrum(i, 1) - foffset)/fscale; + a = log10(spectrum(i, 2)) + 6; + if (a < 0) + a = 0; + end + fprintf(fn, "\\draw[line width=3.5pt] "); + fprintf(fn, "({%.2f*\\df},0) -- ({%.2f*\\df},{%.5f*\\da});\n", + f, f, abs(a)); + fprintf(fn, "\\node at ({-15*\\df},5.5) [right] {$\\beta = %.3f$};", beta); + endfor +endfunction + +function drawhull(fn, beta) + global resolution; + fprintf(fn, "\\begin{scope}\n"); + fprintf(fn, "\\clip ({-16.5*\\df},0) rectangle ({16.5*\\df},{6*\\da});\n"); + p = zeros(resolution, 2); + for k = (1:resolution) + nu = 16.5 * (k - 1) / resolution; + p(k,1) = nu; + y = log10(abs(besselj(nu, beta))) + 6; + p(k,2) = y; + end + fprintf(fn, "\\draw[color=blue] ({%.4f*\\df},{%.5f*\\da})", + p(1,1), p(1,2)); + for k = (2:resolution) + fprintf(fn, "\n -- ({%.4f*\\df},{%.5f*\\da})", + p(k,1), p(k,2)); + endfor + fprintf(fn, ";\n\n"); + fprintf(fn, "\\draw[color=blue] ({%.4f*\\df},{%.5f*\\da})", + p(1,1), p(1,2)); + for k = (2:resolution) + fprintf(fn, "\n -- ({%.4f*\\df},{%.5f*\\da})", + -p(k,1), p(k,2)); + endfor + fprintf(fn, ";\n\n"); + fprintf(fn, "\\end{scope}\n"); +endfunction + +function animation(betamin, betamax, steps) + global fm; + global fc; + global gamma; + fa = fopen("parts.tex", "w"); + for k = (1:steps) + % add entry to parts.tex + fprintf(fa, "\\spektrum{%d}{texfiles/a%04d.tex}\n", k, k); + % compute beta + x = (k - 1) / (steps - 1); + beta = betamin + (betamax - betamin) * (x ^ gamma); + % create a new file + name = sprintf("texfiles/a%04d.tex", k); + fn = fopen(name, "w"); + % write the hull + drawhull(fn, beta); + % compute and write the spectrum + spectrum = spektrum(beta, fm); + drawspectrum(fn, spectrum, fc, fm, beta); + fclose(fn); + endfor + fclose(fa); +endfunction + +animation(0.001,10.1,200) |