A new approach for high performance RNS-FIR filter using the moduli set {2<sup>k</sup> − 1, 2<sup>k</sup>, 2<sup>k−1</sup> − 1}

Abstract

This work proposes two finite impulse response (FIR) filters using Residue Number Systems (RNS) technique. The moduli set adopted is {2k − 1, 2k, 2k−1 − 1}. The proposed method uses Stored Coefficient Product (SCP) to compute the multiplication of input with the filter coefficient. Further, the circular shift property of the moduli set is exploited to improve the performance of the filter. The two proposed filters, RNS_P1 and RNS_P2, are compared with the conventional RNS-FIR filter (RNS_C) which uses the moduli set {2k − 1, 2k, 2k + 1}. The filters are implemented with VerilogHDL and are synthesized using Cadence RTL compiler in UMC 90nm technology. The performance of the filters are compared in terms of Area (A), Power (P), Delay (D) and Power-Delay Product (PDP). In comparison to RNS_C, the filter RNS_P1 improves gain in area by 75% and power by 72%, whereas RNS_P2 provides gain of 67% in area and 67.5% in power. However, the gain in delay and PDP for RNS_P2 are 31% and 71% respectively, as compared to 17% and 76% of the filter RNS_P1.