How does number of points change a FFT in MATLAB

Question

When taking fft(signal, nfft) of a signal, how does nfft change the outcome and why? Can I have a fixed value for nfft, say 2^18, or do I need to g

Answer 1

Most modern FFT implementations (including MATLAB's which is based on FFTW) now rarely require padding a signal's time series to a length equal to a power of two. However, nearly all implementations will offer better, and sometimes much much better, performance for FFT's of data vectors w/ a power of 2 length. For MATLAB specifically, padding to a power of 2 or to a length with many low prime factors will give you the best performance (N = 1000 = 2^3 * 5^3 would be excellent, N = 997 would be a terrible choice).

Zero-padding will not increase frequency resolution in your PSD, however it does reduce the bin-size in the frequency domain. So if you add NZeros to a signal vector of length N the FFT will now output a vector of length ( N + NZeros )/2 + 1. This means that each bin of frequencies will now have a width of:

Bin width (Hz) = F_s / ( N + NZeros )

Where F_s is the signal sample frequency.

If you find that you need to separate or identify two closely space peaks in the frequency domain, you need to increase your sample time. You'll quickly discover that zero-padding buys you nothing to that end - and intuitively that's what we'd expect. How can we expect more information in our power spectrum w/o adding more information (longer time series) in our input?

Best,

Paul

Answer 2

There is no inherent reason to use a power-of-two (it just might make the processing more efficient in some circumstances).

However, to make the FFTs of two different signals "commensurate", you will indeed need to zero-pad one or other (or both) signals to the same lengths before taking their FFTs.

---

However, I feel obliged to say: If you need to ask this, then you're probably not at a point on the DSP learning curve where you're going to be able to do anything useful with the results. You should get yourself a decent book on DSP theory, e.g. this.