Primitive operator digital filter synthesis using a shift biased algorithm

A graph-based synthesis technique has been developed which allows digital filters to be realized with significantly reduced numbers of primitive arithmetic operations. Previously presented work has relied on the use of unity-gain graph edges. These methods are extended by the authors to permit the inclusion of edges with gains which may assume any power of two. This facilitates a tradeoff between addition or subtraction and shift operations which can be beneficial in many implementations. For VLSI implementations especially, judicious placement of processing elements, routing, and allocation of pipeline registers, make for an efficient filter implementation.<>