Design of Sparse FIR Filters With Joint Optimization of Sparsity and Filter Order

Abstract

In this paper, two novel algorithms are developed to design sparse linear-phase (LP) FIR filters. Compared to traditional design methods, they can jointly optimize coefficient sparsity and order of an LP FIR filter, so as to achieve a balance between filtering performance and implementation efficiency. The design problem under consideration is formally cast as a regularized l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> -norm minimization problem, which is then tackled by two different design algorithms. In the first proposed algorithm, the objective function of the original design problem is replaced by its upper bound, which leads to a weighted l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> -norm minimization problem, while in the second one a group of auxiliary variables are introduced such that the original design problem can be equivalently transformed to another weighted l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> -norm minimization problem. The iterative-reweighted-least-squares (IRLS) algorithm is employed with appropriate modifications to solve both weighted l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> -norm minimization problems. Simulation results show that, compared to traditional approaches, the proposed algorithms can achieve comparable or better design results in terms of both sparsity and effective filter order.