Double check z-transform ROC of $a^nu[n]$

1. How do you find the ROC of z-transform?
2. What is the z-transform of the signal x n )= A NU N?
3. What is ROC with respect to z-transform?
4. What is the ROC of Δ N )?

How do you find the ROC of 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.

What is the z-transform of the signal x n )= A NU N?

Given signal, x(n) = an u(n) The z-transform of the above-given signal is given by. X ( z ) = ∑ n = − ∞ ∞ ⁡

What is ROC with respect to z-transform?

Region of convergence. The region of convergence (ROC) is the set of points in the complex plane for which the Z-transform summation converges.

What is the ROC of Δ N )?

For a two-sided signal, the ROC is between the two circles (poles) but does not contain any pole. For finite duration absolutely summable signal, the ROC is the entire Z-plane except possibly for Z = 0 or Z = ∞. For discrete-time Dicea delta function δ(n), the ROC in the entire z plane.