Signals and Systems

6.3 PROPERTIES OF z-TRANSFORM

We have already introduced the z-transform. Let us now introduce the properties of z-transform.

6.3.1 Linearity

This property states that if then

 

 

where a₁ and a₂ are constants.

Proof:

Let      x(n) = a₁x₁(n) + a₂x₂(n)

 

The z-transform of x(n) is given by

 

 

Since the superposition principle is applicable to z-transform, it is linear and the ROC of X(z) is the overlap or intersection of the individual regions ...