(New page: Category:ECE301Spring2011Boutin Category:Problem_solving ---- = Practice Question on Computing the Fourier Transform of a Discrete-time Signal = Compute the Fourier transform of ...) |
|||
| Line 15: | Line 15: | ||
---- | ---- | ||
=== Answer 1 === | === Answer 1 === | ||
| − | + | ||
| + | <math class="inline">{\mathcal X} (\omega) = \sum_{n=-\infty}^\infty x[n]e^{-j\omega n}=\sum_{n=-\infty}^\infty 3^n u[-n]e^{-j\omega n}=\sum_{n=-\infty}^0 3^n e^{-j\omega n}=\sum_{n=-\infty}^0 \Bigg(\frac{3}{e^{j\omega}}\Bigg)^n</math> Let k=-n | ||
| + | |||
| + | <math>= \sum_{n=0}^\infty \Bigg(\frac{e^{j\omega}}{3}\Bigg)^k</math> | ||
| + | |||
| + | <math>\mathcal X (\omega) = \frac{1}{1-\frac{e^{j\omega}}{3}}</math> | ||
| + | |||
| + | --[[User:Cmcmican|Cmcmican]] 19:42, 28 February 2011 (UTC) | ||
| + | |||
=== Answer 2 === | === Answer 2 === | ||
Write it here. | Write it here. | ||
Revision as of 15:42, 28 February 2011
Contents
Practice Question on Computing the Fourier Transform of a Discrete-time Signal
Compute the Fourier transform of the signal
$ x[n] = 3^n u[-n].\ $
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
$ {\mathcal X} (\omega) = \sum_{n=-\infty}^\infty x[n]e^{-j\omega n}=\sum_{n=-\infty}^\infty 3^n u[-n]e^{-j\omega n}=\sum_{n=-\infty}^0 3^n e^{-j\omega n}=\sum_{n=-\infty}^0 \Bigg(\frac{3}{e^{j\omega}}\Bigg)^n $ Let k=-n
$ = \sum_{n=0}^\infty \Bigg(\frac{e^{j\omega}}{3}\Bigg)^k $
$ \mathcal X (\omega) = \frac{1}{1-\frac{e^{j\omega}}{3}} $
--Cmcmican 19:42, 28 February 2011 (UTC)
Answer 2
Write it here.
Answer 3
Write it here.
