# Z-Transform vs Inverse Z-Transform-Difference between Z-Transform and Inverse Z-Transform

This page on Z-Transform vs Inverse Z-Transform describes basic difference between Z-Transform and Inverse Z-Transform.

## Z-Transform

Z-Transform is basically a discrete time counterpart of Laplace Transform. Z-transform of a general discrete time signal is expressed in the equation-1 above. The range of values of 'Z' for which above equation is defined gives ROC (Reason of Convergence) of Z-transform.

ROC is the region of range of values for which the summation
converges.

Properties of ROC:
• ROC of X(z) consists of a ring in the Z-plane centered around the origin.
• ROC does not contain any pole.

## Properties of Z-Transform

Following are the properties of Z-transform.

## Inverse Z-Transform

The equation for inverse Z-transform is expressed above. Here integration symbol denotes integration around a counter clockwise circular contour at the origin with radius 'a'.

Following table mentions common Z-transform pairs for useful functions.