What is the restriction of using FFT ?

I read a paper saying Fourier analysis restriction : System must be linear; data must be strictly periodic or stationary otherwise the data will make little physical sense.

Can someone explain it to me? so does that mean FFT has it own limitation?

Answer 1

[David Young]

The points made apply to Fourier analysis in general, not specifically to the FFT, and amount to asking whether the model you are applying is appropriate for your data. That question can only be addressed at the level of theory and by empirical testing; either way, it needs to be addressed in the context of your problem.

The statement you quote is quite vague, and seems rather sweeping. Fourier analysis is applied all the time to systems which are only approximately linear and stationary - it's a question of whether the approximation is good enough to allow the results to be useful. Again, this is a matter for investigation in each case.

None of this says anything about the FFT. The FFT is an algorithm for computing the Discrete Fourier Transform (DFT), which is the appropriate version of the Fourier Transform for data that are of finite length and are regularly sampled. It always returns a very good estimate of the coefficients of the sine waves which, when summed, make up the original signal - in this sense it does not have limitations. It's an excellent tool, but it's just a tool and whether it's the right tool depends on understanding the problem at a higher level.

[632541]

Hi David Young,

What are the limitations in calculating FFT if there is large signal length?

Signal frequency is 1KHz to 100KHz . This is multisine signal.

Sampling freq. is 50MHz.

Thank you

Answer 2

[Matt J]

You can always take the FFT of a given signal. However, how the FFT of a signal changes when it passes through a system depends on whether the system is linear, time-invariant (LTI). If a system is LTI, its input/output behavior can be written as a convolution

   y=conv(h,x)

where h is the system impulse response. If the Fourier transforms Y,H,X of y,h, and x exist then they are related by

    Y=H*X

More general, nonlinear systems will not obey this relationship.