ROC of inverse system function

1. How does the ROC help to find out inverse Z-transform?
2. What is the ROC of the Z-transform?
3. What is ROC in signals and systems?
4. What is inverse Z-transform?

How does the ROC help to find out inverse Z-transform?

Inverse Z Transform

Region of Convergence (ROC) The ROC determines the region on the Z Plane where the Z Transform converges. The ROC depends solely on the 'r' value that is contained in 'z'.

What is the ROC of the Z-transform?

The ROC of the Z-transform is a ring or disc in the z-plane centred at the origin. The ROC of the Z-transform cannot contain any poles. The ROC of Z-transform of an LTI stable system contains the unit circle. The ROC of Z-transform must be connected region.

What is ROC in signals and systems?

Region of Convergence (ROC) is defined as the set of points in s-plane for which the Laplace transform of a function x(t) converges. In other words, the range of Re(s) (i.e.,σ) for which the function X(s) converges is called the region of convergence.

What is inverse Z-transform?

The inverse Z-transform is defined as the process of finding the time domain signal x(n) from its Z-transform X(z). The inverse Z-transform is denoted as − x(n)=Z−1[X(z)] Since the Z-transform is defined as, X(z)=∞∑n=−∞x(n)z−n⋅⋅⋅(1)