### Introduction

z-transform of a sequence. We then obtain the z-transform of some important sequences and discuss useful properties of the transform.

Most of the results obtained are tabulated at the end of the Section.

The z-transform is the major mathematical tool for analysis in such areas as digital control and digital signal processing.

#### Prerequisites

• understand sigma ( $\Sigma$ ) notation for summations
• be familiar with geometric series and the binomial theorem
• have studied basic complex number theory including complex exponentials

#### Learning Outcomes

• define the z-transform of a sequence
• obtain the z-transform of simple sequences from the definition or from basic properties of the z-transform