1 files changed, 98 insertions, 0 deletions
diff --git a/buch/papers/fm/anim/fm.m b/buch/papers/fm/anim/fm.m
new file mode 100644
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+++ b/buch/papers/fm/anim/fm.m
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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)