Effect of sign change on ROC & z transform?

1. What is ROC in signals?
2. What are the properties of ROC in signal and system?
3. What is the significance of ROC in Z-transform?
4. What is the ROC of the Z-transform of the?

What is ROC in signals?

The Region of Convergence. The region of convergence, known as the ROC, is important to understand because it defines the region where the z-transform exists. The z-transform of a sequence is defined as. X(z)=∞∑n=−∞x[n]z−n. The ROC for a given x[n], is defined as the range of z for which the z-transform converges.

What are the properties of ROC in signal and system?

Properties of ROC of Laplace Transform

ROC contains strip lines parallel to jω axis in s-plane. If x(t) is absolutely integral and it is of finite duration, then ROC is entire s-plane. If x(t) is a right sided sequence then ROC : Res > σ_o. If x(t) is a left sided sequence then ROC : Res < σ_o.

What is the significance of ROC in Z-transform?

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 the Z-transform of the?

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.