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How to obtain Fourier power spectrum of velocity data?

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Lukos on 1 Feb 2019
Commented: Star Strider on 17 Feb 2019
I would like to know which frequencies are hidden in my velocity signal (=velocity vector).
I started straight forward: I took the "fft" of the vector and plotted its amplitude against the frequencies, but this does not give me the desired result, i.e. no clear frequency peaks were observed.
Since the velocity vector is non-periodic, i tried to smoothen the beginning and end of the signal by means of a hanning window. Unfortunately, it did not work.
I attached all the data in the zip-file it contains:
  • UpV_irreg.mat (velocity vector)
  • t_irreg.mat (corresponding time vector)
  • fft_test.m (my code)
Any help would be greatly appreciated.


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Accepted Answer

Star Strider
Star Strider on 1 Feb 2019
See if the pwelch (link) function will do what you want. It may also not show any specific frequency peaks (it tends to combine closely-spaced peaks), however it will do essentially everything you describe as what you want to do.


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Lukos on 17 Feb 2019
How do I interpret the amplitude in the frequency domain?
I would like to convert the amplitude in the frequency domain to the time domain, i.e. what is the amplitude of the velocity data (in the time domain).
The amplitudes in the frequency domain where obtained by normalizing the fft of the veloicty signal with the number of samples L and by multiplying its magnitude by a factor 2 (since it is one-sided?). What scaling do I need to perform to obtain the time domain amplitudes of the velocity signal? Thanks in advance!
Star Strider
Star Strider on 17 Feb 2019
The amplitude in the frequency domain and time domain are the same in the code I posted. Note that MATLAB computes a two-sided Fourier transform, so the energy is equally divided between the positive and negative frequencies. It is therefore necessary to multiply the amplitude by 2 in the plotted one-sided Fourier transform to display the amplitude accurately:
plot(Fv, abs(FT_D(Iv))*2)
The discrete nature of the fft usually results in some ‘leakage’ of signal energy to near-by frequencies, so the peak amplitude in the fft may not always match (may be less than) the amplitude of the time-domain signal.
If you want to calculate the time-domain signal from the frequency-domain signal, you need to use the original two-sided Fourier transform results, without the amplitude scaling necessary for the one-sided Fourier transform.
I do not understand your reason for doing this, however. If you want to do frequency-selective filtering of your signal, do that in the time domain with some of the filter designs that the Signal Processing Toolbox (among others) allows you to create.

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