Comb decimator design based on symmetric polynomials with roots on the unit circle: Two-stage multiplierless design and improved magnitude characteristic

摘要

This paper presents a theoretical background for design of comb decimator based on theorem of symmetric polynomials with roots on the unit circle. A simple multiplierless filter, called zero-separation (ZS) filter, which separates doubled comb zeros, is derived. The separation of doubled comb zeros improves comb aliasing rejection. In order to get more benefits of the ZS filter, a two-stage structure is considered. The classic comb filters are in both stages of the proposed structure. Additionally, in the second stage, a ZS filter is inserted to improve comb aliasing rejection. The passband droop is compensated by the compensator which works at low rate and is designed using particle swarm optimization (PSO). The method is illustrated with various examples. The comparisons with methods from literature prove the benefits of the proposed work.