Design of high-speed multiplierless filters using a nonrecursive signed common subexpression algorithm

In this work, a new algorithm called nonrecursive signed common subexpression elimination (NR-SCSE) is discussed, and several applications in the area of multiplierless finite-impulse response (FIR) filters are developed. While the recursive utilization of a common subexpression generates a high logic depth into the digital structure, the NR-SCSE algorithm allows the designer to overcome this problem by using each subexpression once. The paper presents a complete description of the algorithm, and a comparison with two other well-known options: the graph synthesis, and the classical common subexpression elimination technique. Main results show that the NR-SCSE implementations of several benchmark circuits offer the best relation between occupied area and logic depth respect to the previous values published in the technical literature.