A New Cost-Aware Sensitivity-Driven Algorithm for the Design of FIR Filters

Abstract

Design for low complexity FIR filters has been an area of intensive research over the last two decades. Recent approaches to integrating common subexpression elimination with filter coefficient synthesis are based on single-minded reliance on bit width truncation or common subexpression sharing to fulfill the frequency response specifications. Such biases have a strong tendency to overfit or underfit the response prematurely, and increase the implementation cost. In this paper, a new algorithm is proposed to synthesize finite-precision coefficients with low implementation cost from the frequency response specifications of linear phase FIR filter. Overfitting is overcome by admitting the most sensitive subexpressions followed by isolated nonzero digits according to their sensitivities to the change in frequency response error if they are independently removed. To leverage on adder reuse of common subexpressions, common subexpressions of each length are admitted into the coefficients immediately after their most sensitive member. Trivial nonzero digits piggybacked on the admission of common subexpression are pruned to remove the excess slack from the finally selected least cost finite-precision coefficient set. To avoid underfitting, the filter length and word length of coefficients are not fixed but determined by how much incremental slack in the frequency response can be harvested from each additional tap and expanded bit. The effectiveness of the proposed algorithm in designing low power and area-efficient FIR filters is demonstrated by comparing its logic synthesis and power simulation results with other FIR filter coefficient synthesis algorithms. On average, the proposed algorithm saves about 20.9% to 72.7% of area and power consumptions on various sizes of benchmark FIR filters, and improves the area and power efficiency of a filter bank designed for feature extraction of EEG signals by 33.9% to 54.8% over the competing algorithms.