Module 4 : Laplace and Z Transform
Lecture 36 : Analysis of LTI systems with rational system functions
 

Theorem 2

For a discrete rational system stability implies and is implied by the unit circle in the z plane belonging to the ROC of the system function.

PROOF :-

(a) For the stability of the system function

If the discrete rational system is stable then

The z transform of the impulse response (or the system function ) converges for | z | = 1.

(b) For a stability to be implied by | z | =1 (the unit circle ) belonging to the ROC of the system function

A pole cannot lie on the unit circle | z | = 1 in a stable system.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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