Improved RNS FIR Filter Architectures

Abstract

A new architecture for implementing finite-impulse response (FIR) filters using the residue number system (RNS) is detailed. The design is based on using a restricted modulus set, with moduli of the form 2™, 2n — 1, and 2n+ 1. This does not restrict the modulus set to the common 3 modulus set {2n — 1, 2n, 2n+1}, but any number of pairwise relatively prime moduli of this form, for example, {5, 7, 17, 31, 32, 33}. Based on a comparison with a 2’s complement design, the new RNS design can offer a significant speed improvement. The gain is obtained by using a set of small moduli, selected so as to minimize critical path delay and area. An algorithmic approach is used to obtain full adder based architectures that are optimized for area and delay. The modulus set is optimum based on cost parameters for each modulus. This new architecture presents a practical approach to implementing a fast RNS FIR filter. © 2004, The Institute of Electrical and Electronics Engineers, Inc. All rights reserved.