Sparse FIR Filter Design Using Iterative Reweighted 1-Norm Minimization and Binary Search

Finite impulse response (FIR) filters with sparse coefficients have found many applications because of their low implementation complexity. This paper focuses on the design of sparse FIR filters satisfying prescribed frequency response specifications, which can be described as minimizing the 0-norm of its coefficient vector subject to magnitude constraints on its frequency response. This is an NP-hard problem whose optimal solution is very difficult to find. This paper presents a practical approach to this problem. It uses the iterative reweighted 1-norm minimization method to design a filter with many zero and/or small coefficients and then applies a binary search to finally determine how many and which of those smallest ones can be set to zero while not violating the magnitude constraints on the frequency response. Simulation examples demonstrate the effectiveness of the presented method.