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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
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Answer 4
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