I am working on a signal processing application, which involves an IFT. My background is CS and not signal processing maths.
Consider an N-FFT configured with 256 "bins" (N = 256) for processing a 100Hz bandwidth. The application is in the a-priori position of knowing at a given time where the input data can be sparse, in terms of only a subset of the total bandwidth being active.
Ex: at time T, there is a signal in a band B of [26,40]Hz, while at [0,25) and (40,100] Hz the signal is zero.
My questions are whether :
in such cases the 256-FFT could be configured to operate only as a 16-FFT (as B = 40 - 26 = 15, 2^2 < 15 <= 2^4) , and potentially avoid doing reams of computation as a 256-FFT where the add/multiply would be on zero values (and thus redundant) .
if so, professional impls of the FFT already do this (a quick scan of the input vector etc to determine whether such sparsity exists etc before beginning the computation proper) .