Efficient recursive digital filters using combined look-ahead denominator distribution and numerator decomposition

This paper presents a new efficient method for designing stable look-ahead pipelined recursive digital filters with reduced multipliers. The multiplie r savings are obtained by generating pipelined transfer functions which com bine 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 filte r transfer function. The coefficients of the pipelined transfer function ar e obtained by running product solved using matrices and an algorithm with t wo stages: pre and post distribution, each having a multiplier cost which a re minimised independently. The proposed method can produce pipelined filte r designs requiring fewer multipliers when compared with previously reporte d 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 recur sive filter structure, avoiding delay penalties otherwise suffered by previ ously reported methods. A detailed analysis has been carried out confirming that filters designed using the proposed method do not suffer increased no ise.