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

TL;DR

This paper introduces an optimization framework for designing multiplier-less multistage decimation filters using cyclotomic polynomials, offering efficient techniques and guidelines for various architectures in oversampled digital signal processing.

Contribution

It presents a novel optimization approach leveraging cyclotomic polynomials for designing efficient, multiplier-less multistage decimation filters with practical design guidelines.

Findings

Optimized decimation filters with simple coefficients {-1,0,+1}

Effective design techniques based on cyclotomic polynomial properties

Guidelines for simplifying multistage filter design

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 stemming 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. Design guidelines are provided with the aim to simplify the design of the constituent decimation filters in the multistage chain.