Efficient Recursive Digital Filters using Combined Look-Ahead Denominator Distribution and Numerator Decomposition

Abstract

This paper presents a new efficient method for designing stable look-ahead pipelined recursive digital filters with reduced multipliers. The multiplier savings are obtained by generating pipelined transfer functions which combine numerator decomposition with look-ahead denominator distribution. This is achieved by not restricting the denominator to either the clustered or scattered forms while also preserving term count from the unpipelined filter transfer function. The coefficients of the pipelined transfer function are obtained by running product solved using matrices and an algorithm with two stages: pre and post distribution, each having a multiplier cost which are minimised independently. The proposed method can produce pipelined filter designs requiring fewer multipliers when compared with previously reported methods. For example, for a range of second order transfer functions and pipelining levels, an average 40% reduction in multipliers can be achieved while an 18% reduction in multipliers necessary for pipelining is obtained for a sixth order filter. Furthermore, the proposed two-stage algorithm can accommodate pipelined adders as well as pipelined multipliers in the recursive filter structure, avoiding delay penalties otherwise suffered by previously reported methods. A detailed analysis has been carried out confirming that filters designed using the proposed method do not suffer increased noise.