How to find the number of poles for an FFT?

I am trying to find the number of poles used by the FFT function in MATLAB. It looks like the number of poles change based on the input data, but I can't figure out what controls it beyond this. I have been made aware that an FFT should not use a prime number of poles. Does the MATLAB FFT function aviod using a prime number of poles?

[Mathieu NOE]

hello

sorry but a fft has no "poles" ; I don't think this is the right word (zeros and poles are for filters)

but you can specify the length of the fft , either the whole signal length (so one fft computation), or you cut your long signal in smaller buffers and do fft averaging

[Cameron Sellers]

Thank you for your response. I had the same thought when I was asked to provide the number of poles for my FFT calculations. I have done some more reasearch and it seems like an FFT does have poles, see how to determine the number of poles and zeros in Fourier transform, but there is no way to calulate them with certainity. Do you agree with that?

Doing more reaserch, Matlab uses FFTW which doesn't seem to care what size the input is, and has ways to deal with primes. The person who asked me this may not be aware of more modern approaches to taking FFTs, and that is why there is a disconnect with the question.

[Bruno Luong]

Non sense question to me.

FFT is a specific algorithm to carry out DFT

DFT (discrete integer, k) is not FT (real parameter, omega) and is not Laplace Transform (complex s).

Only Laplace transform has poles and zeros in complex plane.

[Cameron Sellers]

Yes I agree, thank you

Answer 1

[Star Strider]

Actually, if you have the Fourier transform of a transfer function, you can determine the number of poles and zeros by plotting only the imaginary part of the Fourier transform as a function of frequency. The poles are the infinite (or near-infinte) values (use only +Inf, however they ‘wrap’ from +Inf to -Inf), and the zeros are the zero-crossings of the imaginary component of the Fourier transform. The definition of ‘Inf’ is somewhat limited by the frequency resolution, however the trend should be obvious. It is possible to estimate the projections of the poles and zeros onto the frequency axis, as well.

[Cameron Sellers]

So a Fourier transform doesn't have poles and zeros by itself, but it can be used to show the poles and zeros of a transfer function?

[Star Strider]

Yes!

I’d forgotten about this in the Answer you cited, however I remember from my circuit synthesis course in grad school that it’s the way to get the frequencies of the poles and zeros of a transfer function in order to eventually realise it in hardware. (The rest of that involves using the various realisations, such as Cauer, to calculate the capacitor and inductor values and positions in the circuit. That gets too complicated to go into here.)