Power and Performance Analysis of Residue Number System Based FIR Filter Integrated with Wallace Tree Multiplier

Traditional FIR filters, essential in DSP for stability and linear phase, often lack efficiency in constrained environments [6]. This study implements a 6-tap RNS-based FIR filter with the moduli set <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\{15,16,17\}\left(2^{n}-1,2^{n}, 2^{n}+1, n=4\right)$</tex>, chosen for coprimality and efficiency. The simulations were conducted using Cadence Genus with the 45 nm technology library. After testing various multipliers, the Wallace Tree multiplier was selected for its superior parallelism and low latency. Power analysis reveals that the RNS FIR filter with the Wallace Tree multiplier exhibits a very minute increase in power consumption, with total power rising by just <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{1. 1 3}$</tex> times and leakage power by a mere 1.07 times compared to the traditional FIR filter, yet achieves <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{8 7. 1 4 \%}$</tex> logic utilization over traditional filter's <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{5 6. 8 4 \%}$</tex>, offering superior performance with nearly identical power [12]. This positions the RNS FIR with Wallace Tree as an excellent substitute for traditional FIRs in low-power DSP applications like wireless communication and image processing.