### Introduction

A sequence can be obtained by
**
sampling
**
a continuous function or signal and in this Section we show first of all how to extend our knowledge of
$z$
-transforms so as to be able to deal with sampled signals. We then show how the
$z$
-transform of a sampled signal is related to the Laplace transform of the unsampled version of the signal.

#### Prerequisites

- possess an outline knowledge of Laplace transforms and of $z$ -transforms

#### Learning Outcomes

- take the $z$ -transform of a sequence obtained by sampling
- state the relation between the $z$ -transform of a sequence obtained by sampling and the Laplace transform of the underlying continuous signal

#### Contents

1 Sampling theory1.1 Sampled sinusoids

1.2 Shift theorems

2 z-transforms and Laplace transforms

2.1 Table 2: z-transforms of some sampled signals

2.2 Table of z-transforms