MATLAB: Band of a fft signal

bandfourier

How can I calculate the frequency band of a Fourier Transformed signal?

In vector X I have the values of my aperiodic signal

Then I do fft(X), so I have my signal in function of frequency

Now how can I know its band?

Best Answer

Hi, you have to know the sampling frequency of your input. If you have the Signal Processing Toolbox, the easiest way is to use spectrum.periodogram because that does a lot of the work for you.

I'll assume that your sampling frequency is 1000 Hz for this example.

Fs = 1e3;
t = 0:1/Fs:1-(1/Fs);
x = cos(2*pi*100*t)+sin(2*pi*200*t)+randn(size(t));
plot(psd(spectrum.periodogram,x,'Fs',1e3,'NFFT',length(x)));

With fft(), note I have not scaled the output to exactly match spectrum.periodogam, but that is easy.

    xdft = fft(x);
    xdft = xdft(1:length(x)/2+1);
    freq = 0:Fs/length(x):Fs/2;
    figure;
    plot(freq,20*log10(abs(xdft)));

Related Solutions

MATLAB: Amplitude spectrum

There are a couple things you can do. Let x be your speech signal and fs your sampling frequency. The following two are power estimates.

    plot(psd(spectrum.periodogram,x,'Fs',fs));
If you do not want it in dB:
    psdest = psd(spectrum.periodogram,x,'Fs',fs);
    plot(psdest.Frequencies,psdest.Data);
    xlabel('Hz'); grid on;

Finally, just using fft()

      xdft = fft(x);
      % assume x is even length
      xdft = xdft(1:length(x)/2+1);
      freq = 0:fs/length(x):fs/2;
      plot(freq,abs(xdft));
      xlabel('Hz');

MATLAB: Calculate frequency band using Parseval

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.

Best Answer

Related Solutions

MATLAB: Amplitude spectrum

MATLAB: Calculate frequency band using Parseval

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