Design of Multistage Decimation Filters Using Cyclotomic Polynomials: Optimization and Design Issues

Abstract

This paper focuses on the design of multiplier-less decimation filters suitable for oversampled digital signals. The aim is twofold. On one hand, it proposes an optimization framework for the design of constituent decimation filters in a general multistage decimation architecture. The basic building blocks embedded in the proposed filters belong, for a simple reason, to the class of cyclotomic polynomials (CPs): the first 104 CPs have a z-transfer function whose coefficients are simply -1, 0, +1. On the other hand, the paper provides a bunch of useful techniques, most of which stem from some key properties of CPs, for designing the proposed filters in a variety of architectures. Both recursive and non-recursive architectures are discussed by focusing on a specific decimation filter obtained as a result of the optimization algorithm. Comparisons are given with respect to classical comb filters and some recently proposed techniques. Design guidelines are provided with the aim to simplify the design of the constituent decimation filters in the multistage chain