Efficient design of sparse FIR filters with optimized filter length

A large number of experiments have demonstrated that for an FIR filter the sparsity of filter coefficients is highly related to its filter order. However, traditional sparse FIR filter design methods focus on how to increase the number of zero-valued coefficients, but overlook the impact of filter orders on design performance. As an attempt to jointly optimize filter length and sparsity of an FIR filter, a novel method is proposed in this paper to design sparse linear-phase FIR filters. With peak error constraints, the objective function of the design problem is formulated as a combination of the sparsity of filter coefficients and a measure of the effective filter order. Then, the design problem is then recast as a weighted l₀-norm optimization problem, which is solved by an efficient numerical method based on the iterative-reweighted-least-squares (IRLS) algorithms. Experimental results illustrate that the proposed method can efficiently reduce the effective filter order while enhancing the sparsity of an FIR filter.