(New page: Through the system, the following transformations are made: <math>e^{2jt} \to t e^{-2jt}</math> <math>e^{2jt} \to t e^{-2jt}</math>) |
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<math>e^{2jt} \to t e^{-2jt}</math> | <math>e^{2jt} \to t e^{-2jt}</math> | ||
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<math>e^{2jt} \to t e^{-2jt}</math> | <math>e^{2jt} \to t e^{-2jt}</math> | ||
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| + | By observation, we know the system multiplies by t and is time reversing. | ||
| + | |||
| + | Given that: | ||
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| + | <math> \cos{t} = \frac{\exp^{jt} + \exp{-jt}}{2}</math> | ||
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| + | |||
| + | Then | ||
| + | |||
| + | \cos{2t} \to t \frac{\exp^{-2jt} + \exp{2jt}}{2} = t \cos{t} </math> | ||
Revision as of 03:17, 19 September 2008
Through the system, the following transformations are made:
$ e^{2jt} \to t e^{-2jt} $
$ e^{2jt} \to t e^{-2jt} $
By observation, we know the system multiplies by t and is time reversing.
Given that:
$ \cos{t} = \frac{\exp^{jt} + \exp{-jt}}{2} $
Then
\cos{2t} \to t \frac{\exp^{-2jt} + \exp{2jt}}{2} = t \cos{t} </math>
