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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
Andrei Henrique Patriota Campos
x[n] = n2(u[n + 2] − u[n − 1]).
$ X(z) = \sum_{n=-\infty}^{+\infty} x[n] z^{-n} $
$ = \sum_{n=-3}^{0} n^2 z^{-n} $
= 9z3 + 4z2 + z
= z3(9 + 4z − 1 + z − 2)
= X(z) = (9 + 4z − 1 + z − 2) / (z − 3), for all z in complex plane.
Answer 3
Muhammad Syafeeq Safaruddin
x[n] = n2(u[n + 3] − u[n − 1])
x[n] = n2(δ(n + 3) + δ(n + 2) + δ(n + 1) + δ(n))
$ X(z) = \sum_{n=-\infty}^{+\infty} x[n] z^{-n} $
$ X(z) = \sum_{n=-\infty}^{+\infty} n^2(\delta(n+3)+\delta(n+2)+\delta(n+1)+\delta(n)) z^{-n} $
X(z) = 9z3 + 4z2 + z + 1 for all z in complex plane
Answer 3
Write it here.
Answer 4
Write it here.
Answer 5
Tony Mlinarich
$ X(z) = \sum_{n=-\infty}^{+\infty} x[n] z^{-n} $
$ X(z) = n^2(\delta (n+3)+\delta (n+2)+\delta (n+1)+\delta (n)+\delta (n-1)) z^{-n} $
X(z) = 9z3 + 4z2 + z + 1/z<\span>
