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Signals and Systems by Smarajit Ghosh

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6.19 INVERSE z-TRANSFORM USING POWER SERIES EXPANSION

The z-transform of the sequence x(n) is given by

 

image

 

Eq. (6.76) gives the expansion in power series form. From power series we get the following sequence:

 

x(n) = {∙∙∙∙∙∙∙∙∙∙x(−2), x(−1), x(0), x(1), x(2), ∙∙∙∙∙∙∙∙∙∙∙}

 

It is possible to get the power series expansion directly or by long division. In power series expansion technique ROC has a vital role.

Example 6.9 Determine the inverse Z-transform of image by long division method when (a) ROC: | z | > 1 and (b) ROC: respectively.

Solution

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