A Greedy Common Subexpression Elimination Algorithm for Implementing FIR Filters

The complexity of finite impulse response (FIR) filters is dominated by the number of adders (subtractors) used to implement the coefficient multipliers. A greedy common subexpression elimination (CSE) algorithm with a look-ahead method based on the canonic signed digit (CSD) representation of filter coefficients for implementing low complexity FIR filters is proposed in this paper. Our look-ahead algorithm chooses the maximum number of frequently occurring common subexpressions and hence reduces the number of adders required to implement the filter. This adder reduction is achieved without any increase in critical path length. Design examples of FIR filters show that the proposed method offers an average adder reduction of about 20% over the best known CSE method.