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Signals and Systems by Smarajit Ghosh

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6.11 z-TRANSFORM OF THE SIGNAL x(n) = nan u(n)

Let us take x1(n) = anu(n)

The z-transform of x1(n) = anu(n) is given by

 

image

 

The given function is

 

x(n) = nanu(n) = nx1(n) because x1(n) = anu(n).

 

∴    X[z] = Z[nx1(n)]

 

By differentiation property of z-transform, we can write

 

image

 

Therefore, the z-transform of x(n) = n anu(n) is image having ROC: | z | > | a |.

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