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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 complex exponential carrier
$ c(t)= e^{j \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 condition 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
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Answer 2
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Answer 3
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