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=== Answer 2=== | === Answer 2=== | ||
| − | x[n] = 3^ | + | <math>= x[n] = 3^n u[n+3] |
===Answer 3=== | ===Answer 3=== | ||
Write it here. | Write it here. | ||
Revision as of 14:59, 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]=3^n u[n+3] \ $
(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
alec green
$ X(z) = \sum_{n=-\infty}^{+\infty} x[n]z^{-n} $
$ = \sum_{n=-3}^{+\infty} 3^{n}z^{-n} $
$ = \sum_{n=-3}^{+\infty} (\frac{3}{z})^{n} $
Let k = n+3:
$ = \sum_{k=0}^{+\infty} (\frac{3}{z})^{k-3} $
Using the geometric series property:
$ X(z) = \left\{ \begin{array}{l l} (\frac{z}{3})^3 \frac{1}{1-\frac{3}{z}} & \quad |z| > 3\\ \text{diverges} & \quad \text{else} \end{array} \right. $
Answer 2
$ = x[n] = 3^n u[n+3] ===Answer 3=== Write it here. ===Answer 4=== Write it here. ---- [[2013_Fall_ECE_438_Boutin|Back to ECE438 Fall 2013 Prof. Boutin]] $
