Mathematics for Electrical Engineering and Computing

15

Laplace and z transforms

15.1 Introduction

In this chapter, we will present a quick review of Laplace transform methods for continuous and piecewise continuous systems and z transform methods for discrete systems. The widespread application of these methods means that engineers need increasingly to be able to apply these techniques in multitudes of situations.

Laplace transforms are used to reduce a differential equation to a simple equation in s -space and a system of differential equations to a system of linear equations. We discover that in the case of zero initial conditions, we can solve the system by multiplying the Laplace transform of the input function by the transfer function of the system. Furthermore, if we are only interested in the ...