How to find H(z) and H(k) from a given causal function

1. How do you find the causality of Z transform?
2. What is the Z transform of H N?
3. How do you determine the causality of a system?

How do you find the causality of Z transform?

Z -Transform for Causal System

For causal system, ROC will be outside the circle in Z-plane. Expanding the above equation, H(Z)=h(0)+h(1)Z−1+h(2)Z−2+......... For stability of causal system, poles of Transfer function should be inside the unit circle in Z-plane.

What is the Z transform of H N?

A LTI system is completely characterized by its impulse response h[n] or equivalently the Z-transform of the impulse response H(z) which is called the transfer function. Remember: x[n]∗h[n]Z⟶X(z)H(z).

How do you determine the causality of a system?

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.