(→x(t)*cos(t) ⇒ \frac{\pi}{j}[\delta(\omega - \pi) - \delta(\omega + \pi)].) |
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| Line 4: | Line 4: | ||
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 | ||
| − | + | <math>x(t)*cos(t)</math> ⇒ <math>\frac{1}{2}[X(e^{j(\theta - \pi/4)}) | |
+ X(e^{j(\theta + \pi/4)}) ]</math>. | + X(e^{j(\theta + \pi/4)}) ]</math>. | ||
Revision as of 09:13, 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{1}{2}[X(e^{j(\theta - \pi/4)}) + X(e^{j(\theta + \pi/4)}) ] $.
