### Introduction

in such topics as digital control and digital signal processing. In this introductory Section we lay the foundations of the subject by briefly discussing sequences, shifting of sequences and difference equations. Readers familiar with these topics can proceed directly to Section 21.2 where z-transforms are first introduced.

#### Prerequisites

- have competence with algebra

#### Learning Outcomes

- explain what is meant by a sequence and by a difference equation
- distinguish between first and second order difference equations
- shift sequences to the left or right

#### Contents

1 Preliminaries: Sequences and Difference Equations1.1 Sequences

1.2 Nomenclature

1.3 A second order difference equation

1.4 Shifting of sequences