can u help me for calculating its z transform

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- Jun 20th 2010, 03:32 AMmoonnightingaleZ transform help
can u help me for calculating its z transform

- Jun 20th 2010, 10:57 PMCaptainBlack
You want the one sided z-transform of $\displaystyle x_n=d^n,\ n=0, 1, ...\ $

The z-transform of this is:

$\displaystyle \displaystyle \left(\mathcal{Z}(x_n) \right)(z)=\sum_{n=0}^{\infty} x_n z^{-n}$ $\displaystyle \displaystyle

=\sum_{n=0}^{\infty} \left(\frac{d}{z}\right)^n$

You should recognise the right hand side as a geometic series which converges when $\displaystyle d<z$ and you should know how to sum that.

CB