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 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.