Recursive discrete Fourier transform with unified IIR filter structures

Abstract

In this paper, we propose two unified IIR filters to recursively compute the discrete Fourier transform (DFT). With the advantage of local connection, regularity and modularity, the proposed methods can compute all DFT coefficients with the same filter structure. Based on stability behavior, the proposed IIR filter structures with optimal coefficients can achieve more accurate results than the traditional ones whose filter coefficients should be changed for computing the different DFT coefficients. Simulation results verify the aforementioned theoretical observations.