Lesson 12
The z-Transform
The z-transform is the Discrete-Time counterpart of the Laplace Transform.
It is
We will see that
Aside: You can relate the z- transform and Laplace transform directly when you are dealing with sampled signals:
Take a CT signal and sample it:
The Laplace transform of the sampled signal is
Let and
, then
Thus, the z- transform with is
the same as the Laplace transform of a sampled
signal! Of course, if the signal is already discrete, the notion of
sampling is unnecessary for understanding and using the z- transform.