Causality and ROC of a stable LTI system

1. What is the causality condition for an LTI system?
2. What is the condition on ROC for a system to be causal and stable?
3. What is the ROC if the system is stable?
4. What is the condition on the ROC of the system function for stability of an LTI system?

What is the causality condition for an LTI system?

An LTI system is called causal if the output signal value at any time t depends only on input signal values for times less than t. It is easy to see from the convolution integral that if h(t) = 0 for t < 0, then the system is causal.

What is the condition on ROC for a system to be causal and stable?

For a system to be causal, all poles of its transfer function must be right half of s-plane. A system is said to be stable when all poles of its transfer function lay on the left half of s-plane.

What is the ROC if the system is stable?

A system is stable if the Region Of Convergence (ROC) of the transfer function includes the unit circle. Unfortunately the transfer function is ambigous. Multiple impulse responses can be mapped to the same transfer function.

What is the condition on the ROC of the system function for stability of an LTI system?

Explanation: For an LTI system, if the ROC of the system function includes the unit circle, then the systm is said to be BIBO stable.