Distribute the values from fft() logarithmically - not plotting

Hi all,

When I use fft(signal) on a music signal, I get linearly spaced power spectrum of length(signal) representing frequencies up to 44100hz. I want to distribute them on a log scale. If I semilogx(fft(abs(signal))) I can see what I want, but I want to be able to work with the values!

I think the best way to explain exactly what I want to do is explain what I want to achieve on a slightly higher level:

I want to sum the differences on the power spectrum of a music signal from one window to another. However for later purposes I want the (say) 20 frequency bins to be spaced logarithmically up to only 20000Hz.

I hope that explains my problem, please let me know if I should provide more detail. I have looked on google and had a search of this forum. Closest was this question with no answer http://www.mathworks.com.au/matlabcentral/answers/27211-audio-processing

I have:

binEdges = logspace(log10(20), log10(20000), numBins+1);

which defines the bins, but then I don't know how to test for the frequencies in the returned fft array.

Thanks very much for any help!

Answer 1

[Conrad]

did the fourier transform 'myself':

N=441; % length of sample
numBins=20;
F_min = 20;       
F_max = 20000;
f_frac = logspace( log10(F_min/Fs), log10(F_max/Fs), numBins);
W = exp(-1j * (0:N*2-1)' * 2 * pi * f_frac );
logbinned = sample * W

And this seems to go fine! I end up with a numBins long vector with the magnitudes of the frequency bins. (I think?!) It looks a bit different when plotted to semilogx(abs(fft(sample))) but I guess that's just because they can end up being computed different. Speed is good enough for me at the moment.

Does anyone see any problems with this?

Answer 2

[Honglei Chen]

If your frequency bins falls on frequency bins of an FFT, you can try Goertzel algorithm

http://www.mathworks.com/help/signal/ref/goertzel.html

[Conrad]

I guess the problem here is that it will calculate the magnitudes at the frequencies, rather than across a bin? Unless I'm understanding this wrong?

Answer 3

[Walter Roberson]

Possibly histc() passing binEdges as the second argument

[Conrad]

my old solution involved this. But that doesn't help too much as the fft has still been calculated in a linear space, and trying to map it afterward results in a loss of data or a necessity for too many samples