Is initial value theorem sufficient to prove causality of a system?

1. How do you prove a system is causal?
2. How do you know if Z transform is causal?
3. What is the importance of causality in DSP?

How do you prove a system is causal?

A system is said to be causal if it does not respond before the input is applied. In other words, in a causal system, the output at any time depends only on the values of the input signal up to and including that time and does not depend on the future values of the input.

How do you know if Z transform is causal?

Z -Transform for Causal System

Causal system can be defined as h(n)=0,n<0. For causal system, ROC will be outside the circle in Z-plane.

What is the importance of causality in DSP?

The causality of systems also plays an important role in digital signal processing, where filters are constructed so that they are causal, sometimes by altering a non-causal formulation to remove the lack of causality so that it is realizable.