Minimum denominator-multiplier pipelined recursive digital filters

Recursive digital filters implemented in direct form, transpose direct form, or cascade form can be pipelined with a new minimum denominator-multiplier (MDM) algorithmic transformation pipelining technique that permits hybrid pipelined solutions between the clustered look-ahead and scattered look-ahead techniques introduced by Parhi and Messerschmitt (1989). The new MDM technique makes use of asymmetrical scattering, in addition to symmetrical scattering, to achieve stable pipelined recursive digital filters which in most cases have substantially fewer added multipliers but in no case will have more added multipliers than the clustered look-ahead or scattered look-ahead techniques. Furthermore, the MDM technique always results in a minimum number of denominator multipliers resulting in a stable pipelined recursive digital filter which in nearly every case has fewer multipliers than the minimum order augmentation technique recently introduced by Lim and Liu (1992). Most importantly, the MDM technique provides a unified approach to pipelining recursive digital filters that 1) guarantees the minimum number of denominator multipliers for stability, 2) usually provides substantial reduction in the number of required multipliers compared to any other approach, and 3) reduces to any one of the other approaches if that approach results in a minimum denominator-multiplier realization