Region of convergence for discrete system

1. What is the ROC of the discrete-time signal?
2. How do you find the region of convergence?
3. What will be the ROC of z-transform of the discrete-time sequence?
4. How do you find the region of convergence in z-transform?

What is the ROC of the discrete-time signal?

The ROC (region of convergence) of the z-transform of a discrete-time signal is represented by the shaded region in the z-plane. If the signal x [ n ] = ( 2.0 ) | n | , − ∞ < n < ∞ , then the ROC of its z-transform is represented by.

How do you find the region of convergence?

Perhaps the best way to look at the region of convergence is to view it in the s-plane. What we observe is that for a single pole, the region of convergence lies to the right of it for causal signals and to the left for anti-causal signals.

What will be the ROC of z-transform of the discrete-time sequence?

Properties of ROC of Z-Transforms

ROC does not contain any poles. If x(n) is a finite duration causal sequence or right sided sequence, then the ROC is entire z-plane except at z = 0. If x(n) is a finite duration anti-causal sequence or left sided sequence, then the ROC is entire z-plane except at z = ∞.

How do you find the region of convergence in z-transform?

For x(n)=δ(n), i.e., impulse sequence is the only sequence whose ROC of Z-transform is the entire z-plane. If x(n) is an infinite duration causal sequence, then its ROC is |z|>a, i.e., it is the exterior of a circle of the radius equal to a.