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#
# 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)
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