calculate frequency band using Parseval
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I have the fft of my signal, but I don't know its frequency band and there are no lobe to extimate it.
Can I use Parseval's Theorem to calculate the band?
Could anyone post the code?
Accepted Answer
Wayne King
on 28 Sep 2011
Hi, You can determine what percentage of power lies within a certain band. Here I determine the frequency with maximum power and then find the percentage of power lying in a band that is the maximum frequency plus or minus 2 DFT bins
Fs = 1e3;
t = 0:1/Fs:1-(1/Fs);
x = cos(2*pi*100*t)+randn(size(t));
psdest = psd(spectrum.periodogram,x,'Fs',1e3,'NFFT',length(x));
[mx,I] = max(psdest.Data);
relperc = ...
100*avgpower(psdest,[psdest.Frequencies(I-2) psdest.Frequencies(I+2)])/avgpower(psdest,[0 Fs/2])
Or you could use cumsum() to get the cumulative percent power and figure out the power in a band with the appropriate subtraction.
xdft = fft(x);
xdft = xdft(1:length(x)/2+1);
relpower = 100*cumsum(abs(xdft).^2)/norm(xdft,2)^2;
plot(relpower);
The following gives you the percentage power at 100 Hz plus or minus two DFT bins.
relpower(103)-relpower(99)
Note it's very close to the answer returned by the first method.
More Answers (1)
Wayne King
on 28 Sep 2011
Hi, If you have the DFT (discrete Fourier transform) as implemented by fft(), then you have the frequencies. The frequencies are of the form (Fs*k)/N where Fs is the sampling frequency, N is the length of the signal and k runs from 0,1,...N/2 (for N even)
Parseval's theorem just demonstrates that energy is conserved.
x = randn(1e3,1);
xdft = fft(x);
norm(x,2)
(1/sqrt(length(x)))*norm(xdft,2)
2 Comments
Wayne King
on 28 Sep 2011
I should note that the DFT is periodic with period N so the other half of the frequencies can be thought of as the negative version of the above, or you can just let k run from 0,..... N-1
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