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=== Answer 1 === | === Answer 1 === | ||
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| + | Yes, this signal is band limited. It is a sinc function, and its Fourier transform can be found using the table of formulas in the textbook on page 329. | ||
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| + | <math>\mathcal X (\omega) = \begin{cases} | ||
| + | 1 & \Big|\omega\Big| < 3\pi \\ | ||
| + | 0 & \mbox{otherwise} | ||
| + | \end{cases}</math> | ||
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| + | This is band limited. | ||
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| + | In addition, the <math class="inline">\omega_m</math> is <math class="inline">3\pi</math>. | ||
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| + | Therefore the Nyquist rate for this signal is <math class="inline">6\pi</math>. | ||
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| + | --[[User:Cmcmican|Cmcmican]] 23:11, 30 March 2011 (UTC) | ||
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=== Answer 2 === | === Answer 2 === | ||
Write it here. | Write it here. | ||
Revision as of 19:11, 30 March 2011
Contents
Practice Question on the Nyquist rate of a signal
Is the following signal band-limited? (Answer yes/no and justify your answer.)
$ x(t)= 7 \frac{\sin (3 \pi t)}{\pi t} \ $>
If you answered "yes", what is the Nyquist rate for this signal?
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
Yes, this signal is band limited. It is a sinc function, and its Fourier transform can be found using the table of formulas in the textbook on page 329.
$ \mathcal X (\omega) = \begin{cases} 1 & \Big|\omega\Big| < 3\pi \\ 0 & \mbox{otherwise} \end{cases} $
This is band limited.
In addition, the $ \omega_m $ is $ 3\pi $.
Therefore the Nyquist rate for this signal is $ 6\pi $.
--Cmcmican 23:11, 30 March 2011 (UTC)
Answer 2
Write it here.
Answer 3
Write it here.
