MINIMUM DENOMINATOR-MULTIPLIER PIPELINED RECURSIVE DIGITAL-FILTERS

Recursive digital filters implemented in direct form, transpose direct form, or cascade form can he pipelined with a new minimum denominator -multiplier (MDM) algorithmic transformation pipelining technique that permits hybrid pipelined solutions between the clustered look-ahead a nd scattered look-ahead techniques introduced by Parhi and Messerschmi tt. The new MDM technique makes use of asymmetrical scattering, in add ition to symmetrical scattering, to achieve stable pipelined recursive digital filters which in most cases have substantially fewer added mu ltipliers but in no case will have more added multipliers than the clu stered look-ahead or scattered look-ahead techniques. Furthermore, the MDM technique always results in a minimum number of denominator multi pliers resulting in a stable pipelined recursive digital filter which in nearly every ease has fewer multipliers than the minimum order augm entation technique recently introduced by Lim and Liu. Most importantl y, the MDM technique provides a unified approach to pipelining recursi ve digital filters that 1) guarantees the minimum number of denominato r 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 re sults in a minimum denominator-multiplier realization.