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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=-3}^{0} n^2 z^{-n} $
$ = 9 z^3 + 4 z^2 + z $
$ = z^3 (9 + 4 z^{-1} + z^{-2}) $
$ =X(z) = (9 + 4 z^{-1} + z^{-2})/(z^{-3}) $ for all z in complex plane. Write it here.
Answer 3
Write it here.
Answer 4
Write it here.
