EFFICIENT TIME-DOMAIN SYNTHESIS OF PIPELINED RECURSIVE FILTERS

Abstract

An efficient technique is developed for the synthesis of pipelined recursive filters directly from the time domain specifications. Based on the modified least-squares approximation, the pipelinable denominator form that contains only the powers of z(-R) is designed inherently by expressing the design criterion in terms of only the nonzero denominator coefficients and a final design is derived. Due to the lack of the conventional transformation overheads, the multiplications needed are fewer in the resulted filters. Moreover, we introduce a new kind of companion matrix that characterizes the stable properties of pipelined recursive filters. Using this result, we prove that the proposed direct synthesis method can always guarantee the stability.