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(ω_ct).

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 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) ω_c > ω_m = 1,000π must be met to insure that x(t) can be recovered.

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

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

Answer 2

a) w_c > w_m

    w_c > 1000pi

b) Multiply by cos(w_ct) then pass it through a Low Pass Filter with a gain of 2 and a cutoff f of w_c

    H(w) = 2 [u(w+w_c)-u(w-w_c)] --Ssanthak 12:49, 19 April 2011 (UTC)

Answer 3

Write it here.

Back to ECE301 Spring 2011 Prof. Boutin