How to determine poles and zeros of the z-transform?

1. Which are poles and which are zeros?
2. How many poles can Roc of Z-Transform contain?
3. Is it possible to plot the pole zero using Z-Transform?

Which are poles and which are zeros?

A value of s s that causes the a transfer function to be 0 is called a zero, and a value of s s that causes the transfer function to be infinite is called a pole.

How many poles can Roc of Z-Transform contain?

The ROC cannot contain any poles.

By definition a pole is a where X(z) is infinite. Since X(z) must be finite for all z for convergence, there cannot be a pole in the ROC. If x[n] is a finite-duration sequence, then the ROC is the entire z-plane, except possibly z=0 or |z|=∞.

Is it possible to plot the pole zero using Z-Transform?

Once the poles and zeros have been found for a given Z-Transform, they can be plotted onto the Z-Plane.