MaplePrimes - answers and comments on Question, Deconstruct a waveform into its fundamental frequencies

DiscreteTransforms

Pseudomodo — Thu, 04 Aug 2011 22:44:45 Z

Isn't that what DiscreteTransforms is all about?

Demodulation as an Optimization Problem

herclau — Fri, 12 Aug 2011 23:08:55 Z

I hope this document will be useful .. Solving Demodulation as an Optimization Problem

Spectral Analysis of an airconditioner

herclau — Mon, 15 Aug 2011 16:26:08 Z

I ask for comments and critical eye to this implementation, since they are present the 10 Hz
How could validate these results?
What is the uncertainty in these results?

map(with, [plots, DiscreteTransforms, AudioTools]);
audiofile := cat(currentdir(), "\\airconditioner.wav");

x := Read(audiofile);

fs := attributes(x)[1];

Preview(x, method = nearest, color = [blue]);

mono := ToMono(x);

Preview(mono, method = nearest, color = [blue]);

bCall := Vector(mono);

n := Statistics:-Count(bCall);

tb := Vector(n, proc (i) options operator, arrow; (i-1)/fs end proc);

plot(tb, bCall, style = line, color = blue, title = "airconditioner", labels = ["Time (seconds)", "Amplitude"], axes = box);

m := Statistics:-Count(bCall);
n := 2^ceil(log[2](m));
y := FourierTransform(bCall, normalization = none, padding = n-m)[2];

f := Vector(n, proc (i) options operator, arrow; (i-1)*fs/n end proc);

p := y*~conjugate~(y)/n; #Power of the DFT

plot(f[1 .. floor((1/2)*n)], abs(p[1 .. floor((1/2)*n)]), view = [0 .. 400, DEFAULT], color = blue, style = line, title = "Component Frequencies of an airconditioner", labels = ["Frequency (Hz)", "power"], axes = box);

plot(f[1 .. floor((1/2)*n)], abs(p[1 .. floor((1/2)*n)]), view = [0 .. 40, DEFAULT], color = blue, style = line, title = "Component Frequencies of an airconditioner", labels = ["Frequency (Hz)", "power"], axes = box);

Spectral Analysis of a airconditioner

airconditioner.mw

Gracias

please demonstrate

Christopher2222 — Fri, 05 Aug 2011 06:38:14 Z

Maybe, please demonstrate.

nice work

Christopher2222 — Tue, 16 Aug 2011 01:30:37 Z

Nicely done! I can't answer the questions you pose but the work you have done is appreciated.

Also, for some reason, Maple 12 does not like the p := y*~conjugate~(y)/n; line

elementwise

Pseudomodo — Tue, 16 Aug 2011 07:28:12 Z

@Christopher2222 You can use map there, instead of the elementwise operator-modifier ~.

map(t->abs(t)^2,v);

map(t->t*conjugate(t),v);