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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>
 
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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--[[User:Cmcmican|Cmcmican]] 20:56, 7 April 2011 (UTC)
  
 
=== Answer 2  ===
 
=== Answer 2  ===

Revision as of 16:56, 7 April 2011


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) $?


Share your answers below

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 }. $

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

Answer 2

Write it here.

Answer 3

Write it here.


Back to ECE301 Spring 2011 Prof. Boutin

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Basic linear algebra uncovers and clarifies very important geometry and algebra.

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