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| + | a) <math>\omega_c > 0</math> | ||
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| + | b) to recover x(t) from <math>x(t) c(t)</math>, multiply <math>x(t) c(t)</math> by <math class="inline">e^{-j \omega_c t }.</math> | ||
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Revision as of 15:52, 7 April 2011
Contents
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) $?
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 > 0 $
b) to recover x(t) from $ x(t) c(t) $, multiply $ x(t) c(t) $ by $ e^{-j \omega_c t }. $
Answer 2
Write it here.
Answer 3
Write it here.
