Sparse Minimum-Phase FIR Filter Design by SDP

In this paper, a novel algorithm is developed for the design of minimum-phase FIR filters with sparse impulse responses. Traditional minimum-phase FIR filter design approaches are based on autocorrelation sequences of impulse responses and design problems are formulated as a semidefinite program. To achieve sparse designs, l(1) norm of filter coefficients is incorporated in the objective function as a regularization term. To improve the performance, a limited number of coefficients are minimized in l(1) norm, while others are left to enhance the accuracy of magnitude approximation. A heuristic procedure is further developed to iteratively identify zero coefficients. Simulation results demonstrate that, given specifications, the proposed algorithm can effectively improve the sparsity of impulse responses of an FIR filter, such that its implementation complexity can be reduced.