Can I Apply Multiple Properties of the Z Transform Simultaneously?

1. What is the limitation of Z-transform?
2. What is bilateral Z-transform?
3. How many Poles can Roc of Z-transform contain?

What is the limitation of Z-transform?

Limitations – The primary limitation of the Z-transform is that using Z-transform, the frequency domain response cannot be obtained and cannot be plotted.

What is bilateral Z-transform?

A two-sided (doubly infinite) Z-Transform, (Zwillinger 1996; Krantz 1999, p. 214). The bilateral transform is generally less commonly used than the unilateral Z-transform, since the latter finds widespread application as a technique essentially equivalent to generating functions.

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|=∞.