Efficient time domain synthesis of pipelined recursive filters

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 resulting 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