A Study on Periodic Sequences

Abstract

This paper contains two parts. In one part, the minimum length required to identifying two periodic sequences will be formulated. In the other, two methods for decomposing a periodic sequence into two or more periodic sequences which have periods shorter than that of the original sequence will be presented. The theorems and methods derived in this paper may be applied to many fields, such as coding and decoding implementations,data processing, numerical analysis, data compression,etc.