Peak-error-constrained sparse FIR filter design using iterative L1 optimization

In this paper, a novel algorithm is presented for the design of sparse linear-phase FIR filters. Compared to traditional l1-optimization-based methods, the proposed algorithm minimizes l1 norm of a portion (instead of all) of nonzero coefficients. In this way, some nonzero coefficients at crucial positions are not affected by l1 norm utilized in the objective function. The proposed algorithm employs an iterative procedure and the index set of these crucial coefficients is updated in each iteration. Simulation results demonstrate that the proposed algorithm can achieve better design results than both greedy methods and traditional l1-optimization-based methods.