| Line 16: | Line 16: | ||
---- | ---- | ||
===Answer 1=== | ===Answer 1=== | ||
| − | <math> x[n] = n^2 (u[n+ | + | <math> x[n] = n^2 (u[n+2]-u[n-1])</math>. |
| − | <math> | + | <math>X(z) = \sum_{n=-\infty}^{+\infty} x[n] z^{-n}</math> |
<math>= \sum_{n=-2}^{0} x[n] e^{-j\omega n}</math> | <math>= \sum_{n=-2}^{0} x[n] e^{-j\omega n}</math> | ||
| Line 24: | Line 24: | ||
<math>= 1+ e^{j\omega} + e^{2j\omega} </math> | <math>= 1+ e^{j\omega} + e^{2j\omega} </math> | ||
| − | |||
Write it here. | Write it here. | ||
===Answer 3=== | ===Answer 3=== | ||
Revision as of 14:16, 12 September 2013
Contents
Practice Problem on Z-transform computation
Compute the compute the z-transform (including the ROC) of the following DT signal:
$ x[n]= n^2 \left( u[n+3]- u[n-1] \right) $
(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
$ x[n] = n^2 (u[n+2]-u[n-1]) $.
$ X(z) = \sum_{n=-\infty}^{+\infty} x[n] z^{-n} $
$ = \sum_{n=-2}^{0} x[n] e^{-j\omega n} $
$ = 1+ e^{j\omega} + e^{2j\omega} $
Write it here.
Answer 3
Write it here.
Answer 4
Write it here.
