Coefficient transformations for area-efficient implementation of multiplier-less FIR filters

Abstract

Techniques based on common sub-computation extraction can be used to minimize number of additions in the multiplier-less implementations of Finite Impulse Response (FIR) filters. We present two types of coefficient transforms which used in conjunction with these techniques enable area-efficient realization of multiplier-less FIR filters. (i) Number theoretic transforms-that use redundant binary representations such as Canonical Sign Digit (CSD) (ii) Signal Flow Graph transformations that modify the coefficient values while retaining the output functionality. We demonstrate this with results of 6 different coefficient transforms for 14 low pass FIR filters with number of taps ranging from 16 to 128.