(New page: Category:ECE301 Category:ECE438 Category:ECE438Fall2011Boutin Category:problem solving = Z-transform computation = Compute the compute the z-transform (including the ROC) o...) |
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===Answer 1=== | ===Answer 1=== | ||
| − | + | Begin with the definition of a Z-Transform. | |
| + | |||
| + | <math> X(z) = \sum_{n=-\infty}^{\infty}(n u[n]-n u[n-3])z^{-n}</math> | ||
| + | |||
| + | Simplify a little. (pull out the n and realize <math>u[n]-u[n-3]</math> is only non-zero for 0, 1, and 2.) | ||
| + | |||
| + | <math> X(z) = \sum_{n=0}^{2}n z^{-n}</math> | ||
| + | |||
| + | Then we have a simple case of evaluating for 3 points. | ||
| + | |||
| + | <math> \begin{align} | ||
| + | X(z) &= 0 z^{-0} + 1 z^{-1} + 2 z^{-2} \\ | ||
| + | &= \frac{z+2}{z^2} | ||
| + | \end{align}</math> | ||
| + | |||
=== Answer 2=== | === Answer 2=== | ||
Write it here. | Write it here. | ||
Revision as of 13:53, 9 September 2011
Z-transform computation
Compute the compute the z-transform (including the ROC) of the following DT signal:
$ x[n]= n u[n]-n u[n-3] $
(Write enough intermediate steps to fully justify your answer.)
You will receive feedback from your instructor and TA directly on this page. Other students are welcome to comment/discuss/point out mistakes/ask questions too!
Answer 1
Begin with the definition of a Z-Transform.
$ X(z) = \sum_{n=-\infty}^{\infty}(n u[n]-n u[n-3])z^{-n} $
Simplify a little. (pull out the n and realize $ u[n]-u[n-3] $ is only non-zero for 0, 1, and 2.)
$ X(z) = \sum_{n=0}^{2}n z^{-n} $
Then we have a simple case of evaluating for 3 points.
$ \begin{align} X(z) &= 0 z^{-0} + 1 z^{-1} + 2 z^{-2} \\ &= \frac{z+2}{z^2} \end{align} $
Answer 2
Write it here.
