Practice Question on "Digital Signal Processing"

Topic: Computing a z-transform


Question

Compute the z-transform of the following signal.

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


Share your answers below

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)


Answer 1

$ 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.

Answer 2

$ 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} $

Answer 3

Write it here.


Back to ECE301 Spring 2011 Prof. Boutin

Alumni Liaison

Ph.D. 2007, working on developing cool imaging technologies for digital cameras, camera phones, and video surveillance cameras.

Buyue Zhang