Constant-Coefficient FIR Filters Based on Residue Number System Arithmetic

Abstract

In this paper, the design of a Finite Impulse Response (FIR) filter based on the residue number system (RNS) is presented. We chose to implement it in the (RNS), because the RNS offers high speed and low power dissipation. This architecture is based on the single RNS multiplier-accumulator (MAC) unit. The three moduli set {2ⁿ⁺¹ , 2ⁿ , 2ⁿ -1}  , which avoids 2ⁿ +1 modulus, is used to design FIR filter. A numerical example illustrates the principles of residue encoding, residue arithmetic, and residue decoding for FIR filters.