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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

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
Z-transform ROC 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.


Z transform properties

Inverse 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.


Z transform pairs

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