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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

a) $ \omega_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

Write it here.

Answer 3

Write it here.


Back to ECE301 Spring 2011 Prof. Boutin

Alumni Liaison

Ph.D. on Applied Mathematics in Aug 2007. Involved on applications of image super-resolution to electron microscopy

Francisco Blanco-Silva