Analysis of the chinese remainder theorem and cyclotomic polynomials-based algorithms for cyclic convolution-part II: Complex rational number system

Abstract

This paper investigates the factorization properties of cyclotomic polynomials over the field of complex rational numbers. Based on this factorization and the Chinese remainder theorem, we analyze the mathematical structure of the associated algorithms for computing the cyclic convolution of data sequences. The relevant results pertaining to finite integer and complex integer rings are also summarized. Note: This work is being reported in two parts. In Part I, we analyze the structure of the cyclic convolution algorithms over the rational number system. In Part II, we describe complex cyclotomic polynomials and the structure of the resulting cyclic convolution algorithms over the complex rational number system.