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 l
₁
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 l
₁
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.