Short Cut for Z-Transform - Rhea

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Short Cut: Completely equivalent to complex integration formula

1.) Write X(z) as a power series

$ X(z) = \sum_{n=-\infty}^{\infty}x[n]z^{-n} $

2.) Observe that

$ X(z) = \sum_{n=-\infty}^{\infty}x[n]z^{-n} $

i.e.

$ X(z) = \sum_{n=-\infty}^{\infty}x[-n]z^{n} $

3.) By comparison,

$ x[-n] = c_{n} $

or

$ x[n] = c_{-n} $

Example:

$ X(z) = $