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Signals and Systems by Smarajit Ghosh

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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 image then

 

image

 

where a1 and a2 are constants.

Proof:

Let      x(n) = a1x1(n) + a2x2(n)

 

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

 

image

 

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 ...

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