The generation of equivalent digital filter structures by a modified multiplier extraction approach

The multiplier extraction approach provides a matrix representation of digital filters which determines both their structure and transfer function. The properties of this representation are investigated, and a modified version is proposed for representing the structure of a class of digital filters which do not introduce product of multiplier terms in the transfer function. This method is used as the basis of a transformation technique for generating alternative structures which realize a given transfer function. All known canonical nonproduct of multiplier second-order sections which use the minimum number of "2-input" adders may be generated by this method. Extension to higher order structures is considered by example.