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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?
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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.
