Topic: Computing a z-transform

## Question

Compute the z-transform of the following signal.

$x[n]=u[-n]$

Prof. Mimi gave me this problem in class on Friday, so I'm posting it and my answer here. --Cmcmican 22:09, 16 April 2011 (UTC)

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

let k=-n

$=\sum_{k=0}^\infty z^{k}$

$X(z)=\frac{1}{1-z} \mbox{, ROC: }\Big|z\Big|<1$

--Cmcmican 22:09, 16 April 2011 (UTC)

TA's comment: Correct!
Instructor's comment: Exactly where do you get that the norm of z must be less than one for convergence? It is important to clearly state it.

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

$X(z) = \sum_{n = -\infty}^{0} z^{-n}$

let l = -n

$X(z) = \sum_{l=0}^{\infty}z^{l} = \begin{cases}\frac{1}{1-z}, &|z|<1 \\ diverdges, &else \end{cases}$