Redundant complex number arithmetic for high-speed signal processing

Abstract

This paper presents a new complex number representation called the Redundant Complex Number System (RCNS) as a useful basis for designing VLSI signal processors with complex arithmetic capability. RCNS described in this paper is defined as a positional number system that has a complex radix 2j and a digit set {-3,...,0,...,3} or {-2,...,0,...,2}. The use of complex radix 2j with the redundant digit set makes possible to construct high-speed complex number arithmetic circuits with highly regular structures. This paper discusses the elementary arithmetic algorithms of RCNS and their implementations.