Question

I am trying to do an FFT on some data I have captured. I am working in the 10MHz-100MHz range, so my 8192 sample captures will not be big enough to convey anything meaningful when doing an FFT on them. So I am taking many non-overlapping captures of a sine wave and want to average them together.

What I am currently doing (in Scilab) in a for-loop for every file is:

temp1 = read_csv(filename,"\t");
temp1_fft = fft(temp1);
temp1_fft = temp1_fft .* conj(temp1_fft);
temp1_fft = log10(temp1_fft);
fft_code = fft_code + temp1_fft;

And then when I am done with all the files I:
fft_code = fft_code./numFiles;

But I am not so sure that I am handling this correctly. Is there a better way for non-overlapping samples?

Answer 1

I think you are close, but you should average the magnitude of the spectrums (temp1_fft) before taking the log10. Otherwise you essentially end up multiplying them instead of averaging. So instead, just move the log10 to outside the for loop like so (I don’t know scilab syntax):

for filename in files:
    temp1 = read_csv(filename,"\t");
    temp1_fft = fft(temp1);
    temp1_fft = temp1_fft .* conj(temp1_fft);
    fft_code = fft_code + temp1_fft;

fft_code = fft_code./numFiles;
fft_code = log10(fft_code);

You definitely want to use the magnitude (you are already doing this when you multiply by the conj), as the phase information will depend on when your sampling began relative to the signal. If you need the phase information, you have to make sure your acquisitions are in sync with the signal somehow.

What this does is called “Power Spectrum Averaging”:

Power Spectrum Averaging is also called RMS Averaging. RMS averaging computes the weighted mean of the sum of the squared magnitudes (FFT times its complex conjugate). The weighting is either linear or exponential. RMS averaging reduces fluctuations in the data but does not reduce the actual noise floor. With a sufficient number of averages, a very good approximation of the actual random noise floor can be displayed. Since RMS averaging involves magnitudes only, displaying the real or imaginary part, or phase, of an RMS average has no meaning and the power spectrum average has no phase information.