Sparse FIR Filter Design via Partial 1-Norm Optimization

In this brief, we consider a sparse linear-phase FIR filter design problem. Recent methods assume that all the coefficients can be nullified and, thus, various 0 or 1-norm-based optimization techniques are applied on each of them. In contrast, the proposed algorithm is based on two important observations: 1) Given design specifications, some coefficients cannot be nullified, otherwise the specifications cannot be satisfied. 2) Impulse responses on neighboring positions of an FIR filter cannot vary dramatically so as to guarantee the smoothness of the corresponding magnitude responses over most of frequencies. In view of these facts, several rules are adopted in the proposed algorithm to select indices of potential zero coefficients to be used in 1-norm optimization. Simulation results have demonstrated the effectiveness of the proposed design algorithm.