Sparse Nonlinear-Phase FIR Filter Design Using Simulated Annealing Algorithm

Recently, sparse design is one of the hottest topics in the low complexity filter design field. However, a drawback of the sparse finite impulse response (FIR) filters is the larger group delay relative to their non-sparse counterparts. For some applications that are not sensitive to the phase information but the large group delay, nonlinear-phase FIR filters may be reasonable choices. So this paper considers the sparse design of nonlinear-phase FIR filters. In order to tackle the non-convex sparse design, we transfer it to the combinatorial optimization problem and then using simulated annealing (SA) to solve it. At each stage of the SA, the sparsity of the non-linear FIR filter coefficients is fixed to find the possible sparse pattern of the nonlinear-phase filter. Once a sparse pattern that satisfies the design constraints have been found, the sparsity is added by one and the SA moves to the next stage for sparser pattern. The SA based algorithm successively increases the sparsity until no sparser solution could be found. The proposed algorithm is evaluated through a set of design examples, and gives better results than other existing algorithms.