The ROC of a Z-transform for shifted signal

1. What is the ROC of the z-transform of the signal?
2. What is the ROC of the z-transform of the discrete-time signal?
3. What is the time shifting property of z-transform?
4. What is the z-transform of delta function and its corresponding ROC?

What is the ROC of the z-transform of the signal?

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.

What is the ROC of the z-transform of the discrete-time signal?

That is, for a stable discrete time LTI system, ROC of H(z) must contain the unit circle |z|=1. 13. The ROC of z-transform of any signal cannot contain poles. Explanation: Since the value of z-transform tends to infinity, the ROC of the z-transform does not contain poles.

What is the time shifting property of z-transform?

Time Shifting: If we have a time-shifted sequence such as x[n-k], then its z-transform is given by Z x[n-k] = z^-kX(z). Let's take n – k = m, i.e., n = k + m and y[n] = x[n-k].

What is the z-transform of delta function and its corresponding ROC?

The ROC of z-transform X(z) never contains any poles.

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.