Minimax design of sparse FIR digital filters

In this paper, we present a novel algorithm to design sparse FIR digital filters in the minimax sense. To tackle the nonconvexity of the design problem, an efficient iterative procedure is developed to find a potential sparsity pattern. In each iteration, a subproblem in a simpler form is constructed. Instead of directly resolving these nonconvex subproblems, we resort to their respective dual problems. It can be proved that under a weak condition, globally optimal solutions of these subproblems can be attained by solving their dual problems. In this case, the overall iterative procedure can converge to a locally optimal solution of the original design problem. The real minimax design can then be achieved by refining the FIR filter obtained by the iterative procedure. The design procedure described above can be repeated for several times to further improve the sparsity of design results. The output of the previous stage can be used as the initial point of the subsequent design. Simulation results demonstrate the effectiveness of our proposed algorithm.