Limits of the sum in the z transformation [closed]

1. What is the limitation of Z-transform?
2. What is the condition for Z-transform to exist?
3. What is the final value theorem for z transforms?
4. Does Z-transform exist on the whole z-plane?

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 the condition for Z-transform to exist?

For stability the ROC must contain the unit circle. If we need a causal system then the ROC must contain infinity and the system function will be a right-sided sequence. If we need an anticausal system then the ROC must contain the origin and the system function will be a left-sided sequence.

What is the final value theorem for z transforms?

The final value theorem of Z-transform enables us to calculate the steady state value of a sequence x(n), i.e., x(∞) directly from its Z-transform, without the need for finding its inverse Z-transform. ⇒(z−1)X(z)−zx(0)=[x(1)−x(0)]z0+[x(2)−x(1)]z−1+[x(3)−x(2)]z−2+...

Does Z-transform exist on the whole z-plane?

Thus we can conclude that the z-transform of the signal can exist anywhere on the z-plane but the DTFT of the signal can only exist on the unit circle.