(New page: Category:ECE301Spring2011Boutin Category:Problem_solving ---- = Practice Question on signal modulation= Let x(t) be a signal whose Fourier transform <math class="inline">{\mathcal...)
 
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=== Answer 1  ===
 
=== Answer 1  ===
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a) <math>\omega_c > \omega_m = 1,000 \pi</math>  must be met to insure that x(t) can be recovered.
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b) To demodulate, first multiply again by  <math>\cos ( \omega_c t ).</math>  Then feed the resulting signal through a low pass filter with a gain of 2 and a cutoff frequency of <math>\omega_c.</math>
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--[[User:Cmcmican|Cmcmican]] 20:56, 7 April 2011 (UTC)
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=== Answer 2  ===
 
=== Answer 2  ===
 
Write it here.
 
Write it here.

Revision as of 16:56, 7 April 2011


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 sinusoidal carrier

$ c(t)= \cos ( \omega_c t ). $

a) What conditions should be put on $ \omega_c $ to insure that x(t) can be recovered from the modulated signal $ x(t) c(t) $?

b) Assuming the conditions you stated in a) are met, how can one recover x(t) from the modulated signal $ x(t) c(t) $?


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Answer 1

a) $ \omega_c > \omega_m = 1,000 \pi $ must be met to insure that x(t) can be recovered.

b) To demodulate, first multiply again by $ \cos ( \omega_c t ). $ Then feed the resulting signal through a low pass filter with a gain of 2 and a cutoff frequency of $ \omega_c. $

--Cmcmican 20:56, 7 April 2011 (UTC)

Answer 2

Write it here.

Answer 3

Write it here.


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