An improved search algorithm for the design of multiplierless FIR filters with powers-of-two coefficients

An improved algorithm is presented for the discrete optimization of finite-impulse-response (FIR) digital filter coefficients which are represented by a canonic signed-digit (CSD) code, i.e., numbers representable as sums or differences of powers-of-two. The proposed search algorithm allocates an extra nonzero digit in the CSD code to the larger coefficients to compensate for the very nonuniform nature of the CSD coefficient distribution. This results in a small increase in the filter complexity; however, the improvement in the frequency response is substantial. The coefficient optimization is performed in two stages. The first stage searches for an optimum scale factor and the second stage consists of a local bivariate search in the neighborhood of the scaled and rounded coefficients