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This paper presents a method for designing sparse FIR filters by means of a sequence of p-norm minimization problems with p gradually decreasing from 1 toward 0. The lack of convexity for p < 1 is partially overcome by appropriately initializing each subproblem. A necessary condition of optimality is derived for the subproblem of p-norm minimization, forming the basis for an efficient local search algorithm. Examples demonstrate that the method is capable of producing filters approaching the optimal level of sparsity for a given set of specifications.