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| − | == Share your answers below == | + | == 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! | 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! | ||
| − | '''No need to write your name: we can find out who wrote what by checking the history of the page.''' | + | '''No need to write your name: we can find out who wrote what by checking the history of the page.''' |
| − | + | ||
| − | + | ---- | |
| + | === Answer 1 === | ||
<span class="texhtml">''x''[''n''] = ''n''<sup>2</sup>(''u''[''n'' + 2] − ''u''[''n'' − 1])</span>. | <span class="texhtml">''x''[''n''] = ''n''<sup>2</sup>(''u''[''n'' + 2] − ''u''[''n'' − 1])</span>. | ||
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<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. | <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 2 === | + | === Answer 2 === |
Muhammad Syafeeq Safaruddin | Muhammad Syafeeq Safaruddin | ||
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<br> | <br> | ||
| − | === Answer 3 === | + | === Answer 3 === |
Write it here. | Write it here. | ||
| − | === Answer 4 === | + | === Answer 4 === |
| − | Write it here. | + | Write it here. |
| − | === Answer 5 === | + | === Answer 5 === |
| − | Tony Mlinarich | + | Tony Mlinarich |
| − | <math>X(z) = \sum_{n=-\infty}^{+\infty} x[n] z^{-n}</math> | + | <math>X(z) = \sum_{n=-\infty}^{+\infty} x[n] z^{-n}</math> |
| − | < | + | <span class="texhtml">''X''(''z'') = ''n''<sup>2</sup>(δ(''n'' + 3) + δ(''n'' + 2) + δ(''n'' + 1) + δ(''n'') + δ(''n'' − 1))''z''<sup> − ''n''</sup></span> |
| − | <span class="texhtml">''X''(''z'') = 9''z''<sup>3</sup> + 4''z''<sup>2</sup> + ''z'' + ''1/z'' | + | <span class="texhtml">''X''(''z'') = 9''z''<sup>3</sup> + 4''z''<sup>2</sup> + ''z'' + ''1/z''<\span> |
| + | </span> | ||
| + | <br> [[2013 Fall ECE 438 Boutin|Back to ECE438 Fall 2013 Prof. Boutin]] | ||
| − | + | === Answer 7 === | |
| − | + | Yixiang Liu | |
| − | + | <math>X(z) = \sum_{n=-\infty}^{+\infty} x[n] z^{-n}</math> | |
| − | + | ||
| − | + | ||
| − | + | ||
| − | <math>X(z) = \sum_{n=-\infty}^{+\infty} x[n] z^{-n}</math> | + | |
| − | <math>X(z) = \sum_{n=-\infty}^{+\infty} n^{2}[{u[n+3]-u[n-1]}]z^{-n}</math> | + | <math>X(z) = \sum_{n=-\infty}^{+\infty} n^{2}[{u[n+3]-u[n-1]}]z^{-n}</math> |
| − | This expression equals to zero except n = -3, -2, -1 | + | This expression equals to zero except n = -3, -2, -1 |
| − | so < | + | so <span class="texhtml">''X''(''z'') = ''x''[ − 3]''z''<sup>3</sup> + ''x''[ − 2]''z''<sup>2</sup> + ''x''[ − 1]''z''<sup>1</sup></span> |
= 9z^{3} + 4z^{2} + z | = 9z^{3} + 4z^{2} + z | ||
| − | === Answer 8 === | + | === Answer 8 === |
| − | Xi Wang | + | Xi Wang |
| − | <math>X(z) = \sum_{n=-\infty}^{+\infty} x[n] z^{-n}</math> | + | <math>X(z) = \sum_{n=-\infty}^{+\infty} x[n] z^{-n}</math> |
<span class="texhtml"> = ''X''(''z'') = (9''z''<sup> + 3</sup> + 4''z''<sup> + 2</sup> + ''z''. The range of the value of z is from negative infinity to positive infinity | <span class="texhtml"> = ''X''(''z'') = (9''z''<sup> + 3</sup> + 4''z''<sup> + 2</sup> + ''z''. The range of the value of z is from negative infinity to positive infinity | ||
| + | </span> | ||
| − | === Answer 9 === | + | === Answer 9 === |
| − | <math>X(z) = \sum_{n=-\infty}^{+\infty} x[n] z^{-n}</math> | + | <math>X(z) = \sum_{n=-\infty}^{+\infty} x[n] z^{-n}</math> |
| − | <math>X(z) = \sum_{n=-3}^{+1} x[n] z^{-n}</math> | + | <math>X(z) = \sum_{n=-3}^{+1} x[n] z^{-n}</math> |
| − | <span class="texhtml"> = ''X''(''z'') = 9''z''<sup> + 3</sup> + 4''z''<sup> +2</sup> + ''z'' + 1</span> for all z in complex plane | + | <span class="texhtml"> = ''X''(''z'') = 9''z''<sup> + 3</sup> + 4''z''<sup> +2</sup> + ''z'' + 1</span> for all z in complex plane |
| + | <br> | ||
| + | === Answer 10 === | ||
| − | |||
Cary Wood | Cary Wood | ||
| − | <math>X(z) = \sum_{n=-\infty}^{+\infty} x[n] z^{-n}</math> | + | <math>X(z) = \sum_{n=-\infty}^{+\infty} x[n] z^{-n}</math> |
| − | <math>X(z) = \sum_{n=-3}^{0} x[n] z^{-n}</math> | + | <math>X(z) = \sum_{n=-3}^{0} x[n] z^{-n}</math> |
| − | <span class="texhtml"> = ''X''(''z'') = 9''z''<sup> + 3</sup> + 4''z''<sup> + 2</sup> + z, for all z in complex plane | + | <span class="texhtml"> = ''X''(''z'') = 9''z''<sup> + 3</sup> + 4''z''<sup> + 2</sup> + z, for all z in complex plane</span> |
| + | |||
| + | <br> | ||
| + | |||
| + | === Answer 11 === | ||
| + | |||
| + | Shiyu Wang | ||
| + | |||
| + | x[n] = n<sup>2</sup>(u[n + 3] − u[n − 1]) | ||
| + | |||
| + | x[n] = n<sup>2 (-3=< n < 1)</sup> | ||
| + | |||
| + | <math>X(z) = \sum_{n=-3}^{0} n^2 z^{-n}</math> <br> | ||
| + | |||
| + | === x(z)=9z<sup>3</sup>+4z<sup>2</sup>+z, for all z in complex plane except z=infinity === | ||
| + | |||
| + | [[Category:ECE301]] [[Category:ECE438]] [[Category:ECE438Fall2013Boutin]] [[Category:Problem_solving]] [[Category:Z-transform]] | ||
Revision as of 23:02, 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!
No need to write your name: we can find out who wrote what by checking the history of the page.
Answer 1
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 2
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) = n2(δ(n + 3) + δ(n + 2) + δ(n + 1) + δ(n) + δ(n − 1))z − n
X(z) = 9z3 + 4z2 + z + 1/z<\span>
Back to ECE438 Fall 2013 Prof. Boutin
Answer 7
Yixiang Liu
$ X(z) = \sum_{n=-\infty}^{+\infty} x[n] z^{-n} $
$ X(z) = \sum_{n=-\infty}^{+\infty} n^{2}[{u[n+3]-u[n-1]}]z^{-n} $
This expression equals to zero except n = -3, -2, -1
so X(z) = x[ − 3]z3 + x[ − 2]z2 + x[ − 1]z1
= 9z^{3} + 4z^{2} + z
Answer 8
Xi Wang
$ X(z) = \sum_{n=-\infty}^{+\infty} x[n] z^{-n} $
= X(z) = (9z + 3 + 4z + 2 + z. The range of the value of z is from negative infinity to positive infinity
Answer 9
$ X(z) = \sum_{n=-\infty}^{+\infty} x[n] z^{-n} $
$ X(z) = \sum_{n=-3}^{+1} x[n] z^{-n} $
= X(z) = 9z + 3 + 4z +2 + z + 1 for all z in complex plane
Answer 10
Cary Wood
$ X(z) = \sum_{n=-\infty}^{+\infty} x[n] z^{-n} $
$ X(z) = \sum_{n=-3}^{0} x[n] z^{-n} $
= X(z) = 9z + 3 + 4z + 2 + z, for all z in complex plane
Answer 11
Shiyu Wang
x[n] = n2(u[n + 3] − u[n − 1])
x[n] = n2 (-3=< n < 1)
$ X(z) = \sum_{n=-3}^{0} n^2 z^{-n} $
