On the stability and causality of a discrete system

1. What is causality and stability?
2. What is the condition of stability of a discrete-time system?
3. What are the conditions for stability and causality of an LTI system?
4. How do you know if a system is causal or stable?

What is causality and stability?

The condition for both causality and stability can now be derived as follows. A causal system should have a region of convergence outside the outermost pole. A stable system should have the unit circle in its region of convergence. Therefore, a causal and stable system should have all poles inside the unit circle.

What is the condition of stability of a discrete-time system?

In terms of time domain features, a discrete time system is BIBO stable if and only if its impulse response is absolutely summable. Equivalently, in terms of z-domain features, a continuous time system is BIBO stable if and only if the region of convergence of the transfer function includes the unit circle.

What are the conditions for stability and causality of an LTI system?

LTI System Properties

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.

How do you know if a system is causal or stable?

Hence, the system is causal. A system is said to invertible if the input of the system appears at the output. The system is said to be stable only when the output is bounded for bounded input. For a bounded input, if the output is unbounded in the system then it is said to be unstable.