engleski

Sparse FIR Filter Design Based on Signomial Programming

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 exactly solve the approximate problem. In this paper, we propose an approach which is based on the approximation of the l0-norm by an lp-norm with 0 < p < 1. We minimize the lp-norm using recently developed method for signomial programming (SGP). Our design starts with forming an SGP problem that describes filter specifications. The optimum solution of the problem is than 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.

FIR filter design ; lp-norm ; signomial programming ; sparsity

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