# Inverse Z transform - contour integration

1. Apr 30, 2015

### etf

Hi!
Here is my task:
Find inverse z transform of $$X(z)=\frac{1}{2-3z}$$, if $$|z|>\frac{2}{3}$$ using definition formula.
I found that $$x(n)$$ is $$\frac{1}{3}(\frac{2}{3})^{n-1}u(n-1)$$ (using other method). But how can I find it using definition formula, $$x(n)=\frac{1}{2\pi j}\oint_{C}^{ } X(z)z^{n-1}dz$$ ?
Thanks in advance

Last edited: Apr 30, 2015
2. May 3, 2015

3. May 3, 2015

### SteamKing

Staff Emeritus
There is a similar integral technique for finding inverse Laplace transforms:

http://en.wikipedia.org/wiki/Inverse_Laplace_transform

No one uses it.

It's more practical to get your transform (Laplace or Z) into a form which can be looked up in a table.

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