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Assertion (A): The stability of the system is assured if the ROC includes the unit circle in z-plane. Reason (R): For a causal stable system all the poles should be outside the unit circle in the z-plane.

Assertion (A): The stability of the system is assured if the ROC includes the unit circle in z-plane. Reason (R): For a causal stable system all the poles should be outside the unit circle in the z-plane. Correct Answer A is true but R is false

A causal system LTI system is stable if and only if all of poles of H(z) lie inside the unit circle.

Related Questions

The transfer function of a discrete time LTI system is given by
$$H\left( z \right) = {{2 - {3 \over 4}{z^{ - 1}}} \over {1 - {3 \over 4}{z^{ - 1}} + {1 \over 8}{z^{ - 2}}}}$$
Consider the following statements:
S1 : The system is stable and causal for
$$ROC:\left| z \right| > {1 \over 2}$$
S2 : The system is stable but not causal for
$$ROC:\left| z \right| S3 : The system is neither stable nor causal for
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For the above system,
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