FIR filters involving shifts and only two additions, efficient for short word-length signal processing

This paper investigates a class of FIR filters having a recursive multiplierless realization; the filter coefficients are conditioned in a way that, the filter architecture comprises shifts and only two additions. Besides the frequency-domain specifications, the design algorithm should also consider the input word-length to satisfy these conditions. In this paper, stochastic beam search is used as a population-based design algorithm, which internally utilizes a Branch and Bound (B&B) search to optimize its individuals. Filters Involving Shifts and Only Two Additions (ISOTA) are directly applicable on unipolar data; for bipolar data, an addition as the pre-processing and probably another as the post-processing is required. These filters have two limitations; they are efficient only for the Short Word‐Length (SWL) inputs, and the achievable frequency responses are restricted to smooth transitions. The latter problem is resolved by cascading them with other multiplierless filters such as differentiators and comb filters. The first problem seems to constrain the applications to the ΣΔ converters with coarse quantizers; but a wider application area is expected, thanks to the ΣΔ signal processing, which is based on the converting high resolution signals into higher rate SWL data. Comparative examples and a practical application are presented.