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Signals and Systems by Smarajit Ghosh

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6.7 z-TRANSFORM OF UNIT SAMPLE SEQUENCE

The unit sample sequence is given below:

 

image

 

The z-transform of x(n) by definition can be written as

 

image

 

Therefore, the z-transform of unit sample sequence is 1 which is constant and does not depend on values of z. Hence ROC is entire z-plane.

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