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 ω_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

a) ω_c > 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) w_c > w_m

    w_c > 1000pi

b)Since y(t) = x(t) e^jw_ct

        So x(t) = y(t) e^-jw_ct

   so to demodulate multiply by e^-jw_ct

Answer 3

Write it here.

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