(New page: = Practice Question on sampling and reconstruction (related to Nyquist rate) = The signal <math> x(t)= \frac{\sin (3 \pi t)}{\pi t} </math> is sampled with a sampling period <math cla...) |
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| − | = Practice Question on sampling and reconstruction (related to Nyquist rate) = | + | = [[:Category:Problem_solving|Practice Question]] on sampling and reconstruction (related to Nyquist rate) = |
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The signal | The signal | ||
<math> x(t)= \frac{\sin (3 \pi t)}{\pi t} </math> | <math> x(t)= \frac{\sin (3 \pi t)}{\pi t} </math> | ||
| − | is sampled with a sampling period < | + | is sampled with a sampling period <span class="texhtml">''T''</span>. For what values of T is it possible to reconstruct the signal from its sampling? |
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== Share your answers below == | == Share your answers below == | ||
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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! | ||
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=== Answer 1 === | === Answer 1 === | ||
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| + | from the Table | ||
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| + | x(w) = u(w+3pi)-u(w-3pi) | ||
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| + | <br> | ||
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| + | Thus the signal is bandlimited with a w<sub>m</sub> = 3pi | ||
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| + | We must sample above the Nyquist Rate which is equal to 2w<sub>m</sub> or 6pi | ||
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| + | w<sub>s</sub> > 6pi | ||
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| + | T = 2pi/w<sub>s</sub> < 2/6 = 1/3 | ||
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| + | <br> | ||
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| + | The signal can be reconstructed for all T < 1/3. | ||
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| + | --[[User:Ssanthak|Ssanthak]] 12:09, 20 April 2011 (UTC) | ||
| + | <br> | ||
| + | :Instructor's comment: Why do you say that we "must" sample above Nyquist? Is it possible that one could still be able to reconstruct when sampling below Nyquist? -pm | ||
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| + | I guess must was a bad choice of words, we should sample above Nyquist to guarantee that we can reconstruct the signal. In this case I do not believe we can sample below the Nyquist rate because the signal is present in all frequencies from -3pi to 3pi. If the signal was asymmetric then we could sample below Nyquist provided the copies never overlap. | ||
| + | <br> | ||
| + | --[[User:Ssanthak|Ssanthak]] 15:50, 20 April 2011 (UTC) | ||
| + | :TA's comment: I think you meant that the spectrum of the signal might not always be symmetric and not the signal itself (in time domain). The signal is complex if its spectrum is not even symmetric. | ||
=== Answer 2 === | === Answer 2 === | ||
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Write it here | Write it here | ||
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=== Answer 3 === | === Answer 3 === | ||
| − | Write it here. | + | |
| + | Write it here. | ||
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Latest revision as of 10:29, 11 November 2011
Contents
The signal
$ x(t)= \frac{\sin (3 \pi t)}{\pi t} $
is sampled with a sampling period T. For what values of T is it possible to reconstruct the signal from its sampling?
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
from the Table
x(w) = u(w+3pi)-u(w-3pi)
Thus the signal is bandlimited with a wm = 3pi
We must sample above the Nyquist Rate which is equal to 2wm or 6pi
ws > 6pi
T = 2pi/ws < 2/6 = 1/3
The signal can be reconstructed for all T < 1/3.
--Ssanthak 12:09, 20 April 2011 (UTC)
- Instructor's comment: Why do you say that we "must" sample above Nyquist? Is it possible that one could still be able to reconstruct when sampling below Nyquist? -pm
I guess must was a bad choice of words, we should sample above Nyquist to guarantee that we can reconstruct the signal. In this case I do not believe we can sample below the Nyquist rate because the signal is present in all frequencies from -3pi to 3pi. If the signal was asymmetric then we could sample below Nyquist provided the copies never overlap.
--Ssanthak 15:50, 20 April 2011 (UTC)
- TA's comment: I think you meant that the spectrum of the signal might not always be symmetric and not the signal itself (in time domain). The signal is complex if its spectrum is not even symmetric.
Answer 2
Write it here
Answer 3
Write it here.
