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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) $?
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) $ \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.
