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Signals and Systems by Smarajit Ghosh

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6.23 CAUSALITY AND STABILITY IN TERMS OF z-TRANSFORM

Let us derive the conditions for causality and stability of the LTI system in terms of z-transform. The condition for a causal LTI system is given by

 

h(n) = 0 for n < 0      (6.87)

 

where h(n) is the unit sample response of the LTI system. The ROC of the system will be exterior to the circle having radius < ∞ when the system is causal. The following is the necessary and sufficient condition for the system to be BIBO stable:

 

image

 

The system function is given by

 

image

 

Since the magnitude of ...

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