A study of pseudo-random sequences

Abstract

This thesis consists of two main sections: 1. Theoretical Chapter One provides an introduction which gives the historical background and motivation of the study of pseudo-random sequences, as well as their classifications and general properties. A Survey of existing classes of pseudo-random sequences, definitions, and their boundary conditions, is given in Chapter Two. Five important classes of pseudo-random sequences are studied in detail in Chapters Three to Six. Two classes of Barker Sequences which have been modified by the author are given in Chapter Three. The concept of the “cyclic circle” is introduced by the author to link all multi-level pseudo-random sequences, and is used to study the properties of such sequences in Chapter Four. An explanation of how M-sequences may be obtained from the difference set, and two original methods of designing M-sequence generators are described in Chapter Five. A simplified explanation by the author of the concept of projecting maximal length sequences from m-space into a binary plane to generate Planar sequences is given in Chapter Six. 2. Practical Chapter Seven discusses the design of sequential circuits. The concept of “structural matrix”, derived by the author, is defined and its application to the analysis, synthesis and simplification of synchronous sequential circuits is given. Chapter Eight discusses the design of high speed pseudo-random sequence generators. An original method of designing high-speed M-sequence generators, as well as a general algorithm for speeding up the generation of multi-level pseudo-random sequences are given. A selection of significant applications of pseudo-random sequences is discussed in Chapter Nine. The advantages of using pseudo-random sequences over conventional methods are described.