Instrumentation and Control Systems, 3rd Edition

Appendix D

The z-Transform

D.1 The z-Transform

Computer systems use data that has been sampled at regular intervals. The z-transform (see Section 13.7.1) is used for such sampled-data systems in much the same way the Laplace transform (see Appendix C) is used for continuous data systems. Thus if we have a continuous input function f(t) and samples are taken every t seconds, we have an output of a series of sampled functions

$f\left(t\right),f\left(2t\right),f\left(3t\right),f\left(4t\right)\dots f\left(kt\right)$

where k is an integer. Each impulse in the sequence is a unit impulse, represented by the function δ(t), multiplied by the value of f(t) at that time. We can write f*(t) to describe the sequence ...