Constrained Design of FIR Filters with Sparse Coefficients

We present an algorithm for the constrained design of FIR filters with sparse coefficients. In general, the filter design approach aims to minimize a filter order and maximize the filter performance. Although the FIR filter coefficients designed by the least squares method is optimal in the least squares sense, it is not necessarily optimal among the set of filters with the same number of multipliers, that is, less mean squared error can be achieved by a filter that has the same number of multipliers, but has longer impulse response with some zero-valued entries. Our method minimizes the number of nonzero entries in the impulse response together with the least squares error of its frequency response. In addition, we incorporate some constraints to the design and realize better performance than conventional constrained least squares design.