Lecture 31 : Z Transform and Region of Convergence
Z-transform
The response of a linear time-invariant system with impulse response h[n] to a complex exponential input of the form can be represented in the following way :
where
In the complex z-plane , we take a circle with unit radius centered at the origin.
H(w) is periodic with period with respect to ' w ' .
When we replace z by ,we get periodicity of in the form of a circle.
can be represented in the following way :
with respect to ' w ' .
,we get periodicity of 
