FFT of signal with random time period

[mcodesmart]

If I take the FFT of signal with a random time period, i.e. if I am measuring at time intervals which I pick at random, what will the results mean??

 

[mrflibble]

It means you like doing random things?

If I take the FFT of signal with a random time period, i.e. if I am measuring at time intervals which I pick at random, what will the results mean??

That sentence is rather ambiguous, but lets pick the least undefined part of it and go with that.

You have a deterministic non-random signal, and you are sampling it at random times, i.e non-evenly spaced samples in the time domain. And then what will the results mean?

Well, first of, you have an extra challenge, since Fast Fourier Transform works on evenly spaced samples. As in fixed sampling frequency. You can work with unevenly space datapoints by first extirpolating the uneven data onto a regular mesh in the time domain, and then apply your regular FFT. That way you can get stuff done in O(N log N), instead of the usual O(N^2). Do a search for Lomb-Scargle FFT for the unefficient method, and also search for "Fast Lomb-Scargle" by Press & Rybicki.

A related question meant to give you some hints: What is the fourier transform of an infinite sum of randomly spaced dirac impulses in the time domain? What is the energy content? Why is that relevant? Well, because this looks suspiciously much like the sampling function you are applying to your signal.

Hope that helps!

 

[mcodesmart]

Thanks for the directing me to the right place. It really helped. The Unevenly Spaced Lomb-Fourier Transform was the one thing I was thinking of implementing without knowing about it.