Sparse FIR Filter Design Based on Signomial Programming

Abstract

The goal of sparse FIR filter design is to minimize the number of nonzero filter coefficients, while keeping its frequency response within specified boundaries. Such a design can be formally expressed via minimization of l₀-norm of filter’s impulse response. Unfortunately, the corresponding minimization problem has combinatorial complexity. Therefore, many design methods are developed, which solve the problem approximately, or which solve the approximate problem exactly. In this paper, we propose an approach, which is based on the approximation of the l₀-norm by an l_p-norm with 0 < p < 1. We minimize the l_p-norm using recently developed method for signomial programming (SGP). Our design starts with forming a SGP problem that describes filter specifications. The optimum solution of the problem is then found by using iterative procedure, which solves a geometric program in each iteration. The filters whose magnitude responses are constrained in minimax sense are considered. The design examples are provided illustrating that the proposed method, in most cases, results in filters with higher sparsity than those of the filters obtained by recently published methods.