Periodic sequence generators using ordinary arithmetic

Periodic sequences are usually generated by shift registers with feedback using mod 2 arithmetic. In this paper we analyze periodic sequence generators using ordinary arithmetic. It is shown that the simplest periodic sequence generators using ordinary arithmetic are linear. An exact expression is given for the smallest number of stages required to generate periodic sequences of a given period. A table of maximum period attainable using a given number of stages is also included. A canonical form for optimal periodic sequence generators is described. It is shown that an implementation using analog storage and arithmetic elements (like CCD shift registers and operational amplifier) it is possible to obtain multilevel periodic sequences with the optimal sequence generators.