A discrete optimization method for high-order FIR filters with finite wordlength coefficients

This paper suggests a discrete optimization method which can solve high order FIR filter problems within a practically reasonable computing time. The error spectrum caused by rounding off the coefficients is shaped through the discrete optimization so to be effectively cancelled, in the L2norm sense, by other factors connected in cascade. In order to save computing time, the error spectrum is evaluated in a time domain, and parameters are divided into small groups during searching for the optimum solution. LPF and BPF design examples, with 200 lengths, show the proposed approach can reduce coefficient wordlengths by 2 or 3 bits, compared with results obtained by only rounding off. The execution time on the general purpose computer, ACOS System 900, is 97 seconds.