Design of sparse FIR filters based on reweighted l1 -norm minimization

As the implementation cost of a digital filter mainly depends on the number of filter coefficients, the filters with sparse coefficients are of great interest. In this paper, a reweighted l1 minimization procedure is proposed for the design of a class of linear-phase FIR filters with sparse coefficients. The proposed design algorithm is accomplished in two phases. In the first phase, we utilize the reweighted l1 norm to identify the zero coefficient positions. In the second phase, the sparse non-zero coefficients of the filter are re-optimized either in the mimimax sense or least-square sense. Numerical examples are given to show the effectiveness of the proposed method.