MATLAB: Calculate frequency band using Parseval

bandfftfrequencyparseval

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?

Best Answer

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.
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