| Line 9: | Line 9: | ||
Given that: | Given that: | ||
| − | <math> \cos{t} = \frac{ | + | <math> \cos{t} = \frac{e^{jt} + e^{-jt}}{2}</math> |
Then | Then | ||
| − | <math> \cos{2t} \to t \frac{ | + | <math> \cos{2t} \to t \frac{e^{-2jt} + e^{2jt}}{2} = t \cos{t} </math> |
Revision as of 03:18, 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{e^{jt} + e^{-jt}}{2} $
Then
$ \cos{2t} \to t \frac{e^{-2jt} + e^{2jt}}{2} = t \cos{t} $
