Iterative Sparse FFT for M‐sparse Vectors: Deterministic versus Random Sampling

Abstract

In a recent paper [3] we have proposed a deterministic stable sparse FFT algorithm for M-sparse vectors of length N = 2 J with runtime O(M 2 log 2 N) which generalizes the approach in [2]. Our method is based on a divide-and-conquer technique and requires to solve an equation system of Vandermonde type at each iteration step. To ensure numerical stability of the algorithm, the number of rows of the employed Vandermonde matrices at each step has been chosen adaptively in [3]. In this paper, we compare the results of [3] with a random sampling approach for determining the rows of the coefficient matrix.