Fast and energy-efficient constant-coefficient FIR filters using residue number system

In this paper, we present constant-coefficient finite impulse response (FIR) filters design using residue number system (RNS) arithmetic. The novelty of our approach rests in an attempt to maximize the accumulated benefit of the application of RNS to the design of constant coefficient filters. To achieve this, we consider the impact of RNS on many layers: from coefficient representation and techniques of sharing of subexpressions in the multiplier block (MB), to its optimized usage in the MB and accumulation pipeline hardware design. As a result, we propose a common subexpression elimination (CSE) based synthesis technique for RNS-based MBs, along with a high-performance RNS-based FIR filter architecture that employs RNS arithmetic principles but implements them mainly using more efficient 2's complement hardware. Several filters with numbers of taps ranging from 25 to 326 and dynamic ranges from 24 to 50 bits have been synthesized using TSMC 90 nm LP kit and Cadence RTL Compiler. Comparison of power, delay, and area of the new filters implemented using the 4- and 5-moduli RNSs against various equivalent 2's complement counterparts show uniform improvement in performance and power efficiency, often accompanied by significant reduction in area/power consumption as compared to 2's complement implementations. We observed up to 22% improvement in peformance (19% reduction in area) within bounded power envelope, or up to 14% reduction in power consumption (12% reduction in area) at same frequency.