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Now suppose the input signal was multiplied by a cosine wave then the fourier transform of the wave would look as follows
 
Now suppose the input signal was multiplied by a cosine wave then the fourier transform of the wave would look as follows
  
 
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==<math>x(t)*cos(t)</math> &rArr; <math>\frac{\pi}{j}[\delta(\omega - \pi) - \delta(\omega + \pi)]</math>.==
==<math>x(t)*cos(t)</math> &rArr; <math>\frac{\pi}{j}[\delta(\omega - \pi) - \delta(\omega + \pi)]</math>. ==
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Revision as of 09:07, 24 October 2008

Now we know that
$ x(t) $$ X(\omega) $

Now suppose the input signal was multiplied by a cosine wave then the fourier transform of the wave would look as follows

$ x(t)*cos(t) $$ \frac{\pi}{j}[\delta(\omega - \pi) - \delta(\omega + \pi)] $.

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

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