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
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:
The system function is given by
Since the magnitude of ...