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A novel algorithm is presented in this paper to design sparse FIR filters in the weighted least-squares (WLS) sense. The original design problem is cast as a constrained l0-norm optimization problem. To tackle the nonconvexity, an efficient iterative procedure is developed. In each iterative step, a subproblem in a simpler form is constructed. It can be demonstrated that in each iteration an optimal solution to each subproblem can be efficiently and reliably attained by the successive activation algorithm proposed in this paper, such that the overall design algorithm can converge to a local solution of the original design problem. Since its major part only involves scalar operations, compared with other sparse filter design approaches, the proposed design algorithm is computationally efficient. The effectiveness of the proposed design algorithm is demonstrated by numerical examples.