In this paper, an exchange algorithm is proposed to design sparse linear phase finite impulse response (FIR) filters with reduced effective length. The sparse FIR filter design problem is formally an l0-norm minimization problem. This original design problem is re-formulated by encoding the filter coefficients using a binary encoding vector, which represents the locations of the zero and non-zero filter coefficients. An iterative 0-1 exchange process with proper direction control is proposed to propel the minimax approximation error toward the specified upper bound of error for sparsity maximization. The effective length is optimized with a lower priority than sparsity in the proposed algorithm. Simulation results show that the proposed algorithm is superior to the existing algorithms in terms of both sparsity and/or effective length in most cases.
