Error getting Fourier transform of a 1d signal

Hello,

I have an almost-sinusoidal signal (see attached file), which I believe is composed of a mixture of maybe 2 (or 3) Fourier modes:

I wanted to verify this by plotting its Fourier transform. I expected a flat signal with a bunch of peaks at the signal harmonics. However, using fft() on the signal gives me a 2d plot that makes absolutely no sense to me. Can someone please help me to understand what is going on?

[Turlough Hughes]

What code have you used so far?

[Anshuman Pal]

Just fft() on the signal.

[Star Strider]

Remember that you need to plot the absolute value (use the abs function) of the fresult fo the fft.

Also, since the signal has a D-C offset, subtract the mean of the signal before taking the fft in order to see the peaks more clearly:

FTsignal = fft(signal - mean(signal))/numel(signal);

assuming that ‘signal’ is a vector.

[Anshuman Pal]

Thank you, this is precisely what I needed!

One final question --- I expect the wavenumber of one peak to be an integer multiple of the other. How can I verify/disprove this?

Answer 1

[Star Strider]

The easiest way to determine the location of the peaks is to use the findpeaks function (with the appropriate name-value pairs to isolate your peaks of interest). I cannot guarantee that the frequencies will be integer multiples of each other, however findpeaks is the best way to identify them.

Improve the frequency resolution by increasing the length of the fft itself. Specify an appropriately large value for ‘n’ (the second argument) to increase the frequency resolution to whatever you want.

[Anshuman Pal]

Note: The actual answer to my question is given in the comments. I needed to plot the absolute part of the mean-centred version of my signal:

FTsignal = fft(signal - mean(signal))/numel(signal);
plot(abs(FTsignal));

And I did indeed get two peaks as expected:

[Star Strider]

Actually, findpeaks found the same peak in both ths positive and negative frequencies.

I do not remember seeing the ‘testData.txt’ file previously,, although I may have overlooked it.

Try this:

D = load('testData.txt');
signal = D;
L = numel(signal);
Fs = 1;                                                                     % Sampling Frequency (Need Correct Time Vector)
Fn = Fs/2;
t = linspace(0, 1, L)/Fs;

figure
plot(t, signal);                                                            % Time Domain Plot
grid

FTsignal = fft(signal - mean(signal), 2*2^(nextpow2(L)+1))/L;
Fv = linspace(0, 1, fix(numel(FTsignal)/2)+1)*Fn;
Iv = 1:numel(Fv);

[Pks,Locs] = findpeaks(abs(FTsignal(Iv))*2, 'MinPeakProminence',1.25E-4);
DLocs = diff([0 Locs]);

figure
histfit(DLocs, 20, 'kernel')                                                % Histogram Of ‘Locs’ Differences

figure
plot(Fv, abs(FTsignal(Iv))*2)                                               % Fourier Transform Plot
hold on
plot(Fv(Locs), Pks, '^r');
hold off
grid
xlim([0  0.25])

This calculates the Fourier transform, then uses findpeaks to locate ‘significant’ peaks, and then plots the distribution (histfit) of the differences in the peak locations to demonstrate that they do appear to have some sort of regularity.

[Anshuman Pal]

Thanks a lot! This is precisely what I needed. Can you please explain how you are using L, fs, fn, and Iv in the above code? What exactly was wrong with my over-simplified code?

[Star Strider]

As always, my pleasure!

The variables: ‘L’ is the length of the ‘signal’ vector, ‘Fs’ is the sampling frequency, ‘Fn’ is the Nyquuist frequency, ‘Fv’ is the frequency vector, and ‘Iv’ is the index vector.

Your code is correct as far as it goes, however it does not go far enough. Mine accounted for many of the details, allowing it to return the frequencies you are interested in.

[Anshuman Pal]

Thank you. And on what basis do you choose the values for the parameters MinPeakProminence in findpeaks and the number of bins in histfit?

[Star Strider]

As always, my pleasure!

I experimented with them until I got the result I wanted.

With respect to peak prominences, it is possible to get those directly from findpeaks by requesting extra outputs, then choosing the minimum that returns what you want. Here, I just experimented.

The same for histfit. I experimented with different bin numbers until I got what appeared to me to be an acceptable result.