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| − | [[ | + | = [[:Category:Problem solving|Practice Problem]] on Z-transform computation = |
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| − | + | Compute the compute the z-transform (including the ROC) of the following DT signal: | |
| − | Compute the compute the z-transform (including the ROC) of the following DT signal: | + | |
| − | <math>x[n]= n^2 \left( u[n+3]- u[n-1] \right) </math> | + | <math>x[n]= n^2 \left( u[n+3]- u[n-1] \right) </math> |
(Write enough intermediate steps to fully justify your answer.) | (Write enough intermediate steps to fully justify your answer.) | ||
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---- | ---- | ||
| − | ==Share your answers below== | + | |
| − | 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! | + | == Share your answers below == |
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| + | 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! | ||
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| − | + | === Answer 1 === | |
| − | + | Andrei Henrique Patriota Campos | |
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| − | < | + | <span class="texhtml">''x''[''n''] = ''n''<sup>2</sup>(''u''[''n'' + 2] − ''u''[''n'' − 1])</span>. |
| − | <math> | + | <math>X(z) = \sum_{n=-\infty}^{+\infty} x[n] z^{-n}</math> |
| − | <math>= | + | <math>= \sum_{n=-3}^{0} n^2 z^{-n}</math> |
| − | == | + | <span class="texhtml"> = 9''z''<sup>3</sup> + 4''z''<sup>2</sup> + ''z''</span> |
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| − | < | + | <span class="texhtml"> = ''z''<sup>3</sup>(9 + 4''z''<sup> − 1</sup> + ''z''<sup> − 2</sup>)</span> |
| − | < | + | <span class="texhtml"> = ''X''(''z'') = (9 + 4''z''<sup> − 1</sup> + ''z''<sup> − 2</sup>) / (''z''<sup> − 3</sup>)</span>, for all z in complex plane. |
| − | + | === Answer 3 === | |
| − | + | Muhammad Syafeeq Safaruddin | |
| − | < | + | <span class="texhtml">''x''[''n''] = ''n''<sup>2</sup>(''u''[''n'' + 3] − ''u''[''n'' − 1])</span> |
| + | <span class="texhtml">''x''[''n''] = ''n''<sup>2</sup>(δ(''n'' + 3) + δ(''n'' + 2) + δ(''n'' + 1) + δ(''n''))</span> | ||
| + | <math>X(z) = \sum_{n=-\infty}^{+\infty} x[n] z^{-n}</math> | ||
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| + | <math>X(z) = \sum_{n=-\infty}^{+\infty} n^2(\delta(n+3)+\delta(n+2)+\delta(n+1)+\delta(n)) z^{-n}</math> | ||
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| + | <span class="texhtml">''X''(''z'') = 9''z''<sup>3</sup> + 4''z''<sup>2</sup> + ''z'' + 1</span> for all z in complex plane | ||
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| + | <br> | ||
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| + | === Answer 3 === | ||
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| + | Write it here. | ||
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| + | === Answer 4 === | ||
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Write it here. | Write it here. | ||
| − | ===Answer | + | |
| − | + | === Answer 5 === | |
| − | ---- | + | |
| − | [[ | + | Tony Mlinarich |
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| + | <math>X(z) = \sum_{n=\-infty}^{+\infty} x[n] z^{-n}</math> | ||
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| + | <math>X(z) = n^2(\delta(n+3)+\delta(n+2)+\delta(n+1)+\delta(n)+\delta(n-1)) z^{-n}<\math> | ||
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| + | <span class="texhtml">''X''(''z'') = 9''z''<sup>3</sup> + 4''z''<sup>2</sup> + ''z'' + ''1/z''<\span> | ||
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| + | [[2013 Fall ECE 438 Boutin|Back to ECE438 Fall 2013 Prof. Boutin]] | ||
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| + | [[Category:ECE301]] [[Category:ECE438]] [[Category:ECE438Fall2013Boutin]] [[Category:Problem_solving]] [[Category:Z-transform]] | ||
Revision as of 15:27, 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
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}<\math> <span class="texhtml">''X''(''z'') = 9''z''<sup>3</sup> + 4''z''<sup>2</sup> + ''z'' + ''1/z''<\span> [[2013 Fall ECE 438 Boutin|Back to ECE438 Fall 2013 Prof. Boutin]] [[Category:ECE301]] [[Category:ECE438]] [[Category:ECE438Fall2013Boutin]] [[Category:Problem_solving]] [[Category:Z-transform]] $
