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<math>\frac{te^{-2jt}+te^{2jt}}{2}=t\frac{e^{-2jt}+e^{2jt}}{2}=tcos(2t)</math> | <math>\frac{te^{-2jt}+te^{2jt}}{2}=t\frac{e^{-2jt}+e^{2jt}}{2}=tcos(2t)</math> | ||
| − | <math>frac{e^{2jt}+e^{-2jt}}{2}=2cos2t\!</math> | + | <math>\frac{e^{2jt}+e^{-2jt}}{2}=2cos2t\!</math> |
Revision as of 14:59, 19 September 2008
$ e^{2jt} $ yields $ te^{-2jt} $ and $ e^{-2jt} $ yields $ te^{2jt} $
and the system is linear
since Euler's formulat states that : $ e^{jx} = \cos x + j\sin x \! $
$ e^{2jt} = \cos 2t + j\sin 2t \! $
and
$ e^{-2jt} = \cos -2t + j\sin -2t \! $ $ = \cos 2t - j\sin 2t \! $
$ \frac{te^{-2jt}+te^{2jt}}{2}=t\frac{e^{-2jt}+e^{2jt}}{2}=tcos(2t) $ $ \frac{e^{2jt}+e^{-2jt}}{2}=2cos2t\! $
