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| − | = Practice Question on signal modulation = | + | = Practice Question on signal modulation = |
Let x(t) be a signal whose Fourier transform <math>{\mathcal X} (\omega) </math> satisfies | Let x(t) be a signal whose Fourier transform <math>{\mathcal X} (\omega) </math> satisfies | ||
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=== Answer 2 === | === Answer 2 === | ||
| − | a) w<sub>c</sub> > w<sub>m</sub> | + | a) w<sub>c</sub> > w<sub>m</sub> |
| − | w<sub>c</sub> > 1000pi | + | w<sub>c</sub> > 1000pi |
| − | b)Since y(t) = x(t) e^jw<sub>c</sub>t | + | b)Since y(t) = x(t) e^jw<sub>c</sub>t |
| − | So x(t) = y(t) e^-jw<sub>c</sub>t | + | So x(t) = y(t) e^-jw<sub>c</sub>t |
| − | so to demodulate multiply by e^-jw<sub>c</sub>t | + | so to demodulate multiply by e^-jw<sub>c</sub>t |
| + | |||
| + | --[[User:Ssanthak|Ssanthak]] 12:39, 19 April 2011 (UTC) | ||
=== Answer 3 === | === Answer 3 === | ||
Revision as of 08:39, 19 April 2011
Contents
Practice Question on signal modulation
Let x(t) be a signal whose Fourier transform $ {\mathcal X} (\omega) $ satisfies
$ {\mathcal X} (\omega)=0 \text{ when }|\omega| > 1,000 \pi . $
The signal x(t) is modulated with the complex exponential carrier
$ c(t)= e^{j \omega_c t }. $
a) What conditions should be put on ωc to insure that x(t) can be recovered from the modulated signal x(t)c(t)?
b) Assuming the condition you stated in a) are met, how can one recover x(t) from the modulated signal x(t)c(t)?
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
a) ωc > 0
b) to recover x(t) from x(t)c(t), multiply x(t)c(t) by $ e^{-j \omega_c t }. $
--Cmcmican 20:56, 7 April 2011 (UTC)
Answer 2
a) wc > wm
wc > 1000pi
b)Since y(t) = x(t) e^jwct
So x(t) = y(t) e^-jwct
so to demodulate multiply by e^-jwct
--Ssanthak 12:39, 19 April 2011 (UTC)
Answer 3
Write it here.
