(New page: Category:ECE301Spring2011Boutin Category:Problem_solving ---- = Practice Question on Computing the inverse z-transform = Compute the inverse z-transform of the following signal. ...) |
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== Share your answers below == | == Share your answers below == | ||
Prof. Mimi gave me this problem in class on Friday, so I'm posting it and my answer here. | Prof. Mimi gave me this problem in class on Friday, so I'm posting it and my answer here. | ||
| − | --[[User:Cmcmican|Cmcmican]] 22: | + | --[[User:Cmcmican|Cmcmican]] 22:22, 16 April 2011 (UTC) |
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=== Answer 1 === | === Answer 1 === | ||
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<math>=\sum_{n=-\infty}^\infty u[-n](-3)^{-n} z^{-n}</math> | <math>=\sum_{n=-\infty}^\infty u[-n](-3)^{-n} z^{-n}</math> | ||
| − | <math> | + | By comparison with <math class="inline">\sum_{n=-\infty}^\infty x[n] z^{-n}:</math> |
| − | --[[User:Cmcmican|Cmcmican]] 22: | + | <math>x[n]=(-3)^{-n}u[-n]\,</math> |
| + | |||
| + | --[[User:Cmcmican|Cmcmican]] 22:22, 16 April 2011 (UTC) | ||
=== Answer 2 === | === Answer 2 === | ||
Revision as of 18:22, 16 April 2011
Contents
Practice Question on Computing the inverse z-transform
Compute the inverse z-transform of the following signal.
$ X(z)=\frac{1}{1+3z} \mbox{, } \Big|z\Big|<\frac{1}{3} $
Prof. Mimi gave me this problem in class on Friday, so I'm posting it and my answer here. --Cmcmican 22:22, 16 April 2011 (UTC)
Answer 1
$ X(z)=\sum_{k=0}^\infty (-3z)^k=\sum_{k=-\infty}^\infty u[k](-3)^kz^k $
let n=-k
$ =\sum_{n=-\infty}^\infty u[-n](-3)^{-n} z^{-n} $
By comparison with $ \sum_{n=-\infty}^\infty x[n] z^{-n}: $
$ x[n]=(-3)^{-n}u[-n]\, $
--Cmcmican 22:22, 16 April 2011 (UTC)
Answer 2
Write it here.
Answer 3
Write it here.
