Efficient implementation of FIR filters based on a novel common subexpression elimination algorithm

This paper presents a new cost-efficient algorithm to implement finite impulse response (FIR) filters based upon the common subexpression elimination (CSE) algorithm using canonical signed digit (CSD) representation of filter coefficients. The complexity of implementation of FIR filters is determined by the number of adders/subtractors needed to implement the multiplication operations. The new algorithm enables an efficient architecture, especially for high order FIR filters, that requires fewer adders/subtractors than similar algorithms previously reported. The algorithm relies on significant modifications to the iterated matched (ITM) algorithm presented in to find and eliminate more common subexpressions amongst filter coefficients which is translated into a significant power and area saving when implementing high-order FIR filters. Experimental results demonstrate that the proposed algorithm can contribute up to a 20 percent reduction in the complexity of FIR filters over some other CSE-based algorithms.