Computing the Discrete Fourier Transform of signals with spectral frequency support

Abstract

We consider the problem of finding the Discrete Fourier Transform (DFT) of N − length signals with known frequency support of size k. When N is a power of 2 and the frequency support is a spectral set, we provide an O(k log k) algorithm to compute the DFT. Our algorithm uses some recent characterizations of spectral sets and is a generalization of the standard radix-2 algorithm.