Design of FIR filters with decimated impulse responses

In this paper, we present a numerical algorithm for the design of FIR filters with sparse impulse responses. Our method minimizes the number of nonzero entries in the impulse response together with the least squares error of its frequency response. We show that the FIR filters with sparse coefficients can outperform a conventional least squares approach and the Parks-McCllelan method under the condition of the same number of multipliers.