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Inverse Z transform - contour integration

  1. Apr 30, 2015 #1


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    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. jcsd
  3. May 3, 2015 #2

    rude man

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  4. May 3, 2015 #3


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


    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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