(New page: = Practice Question on sampling and reconstruction (related to Nyquist rate) = The signal <math> x(t)= e^{-j \pi t }\frac{\sin (3 \pi t)}{\pi t} </math> is sampled with a sampling per...) |
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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)= e^{-j \pi t }\frac{\sin (3 \pi t)}{\pi t} </math> | <math> x(t)= e^{-j \pi 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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| + | <br> --[[User:Ssanthak|Ssanthak]] 12:51, 20 April 2011 (UTC) | ||
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| + | :TA's comment: There are a couple of mistakes here. First, the factor <span class="texhtml">1 / 2π</span> is missing when applying the multiplication property of the FT. There is also a mistake when applying the frequency-shift property of the FT, since the result should be a spectrum which is shifted to the left and not to the right. The condition on the sampling frequency is incorrect too which was the result of considering the given signal as a real signal ,i.e. a signal that has an even symmetric spectrum (or considering it as pure imaginary signal that has odd symmetric spectrum). | ||
| + | Ooops that was the answer to the next question I moved it there. | ||
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| + | --[[User:Ssanthak|Ssanthak]] 12:42, 21 April 2011 (UTC) | ||
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=== 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 10:30, 11 November 2011
Contents
The signal
$ x(t)= e^{-j \pi 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
--Ssanthak 12:51, 20 April 2011 (UTC)
- TA's comment: There are a couple of mistakes here. First, the factor 1 / 2π is missing when applying the multiplication property of the FT. There is also a mistake when applying the frequency-shift property of the FT, since the result should be a spectrum which is shifted to the left and not to the right. The condition on the sampling frequency is incorrect too which was the result of considering the given signal as a real signal ,i.e. a signal that has an even symmetric spectrum (or considering it as pure imaginary signal that has odd symmetric spectrum).
Ooops that was the answer to the next question I moved it there.
--Ssanthak 12:42, 21 April 2011 (UTC)
Answer 2
Write it here
Answer 3
Write it here.
