(New page: The formula of <math>\cos(2t)\,</math> = <math>\frac{e^{2jt}+e^{-2jt}}{2}\,</math>. We know the response of <math>e^{2jt}\,</math> is <math>te^{-2jt}\,</math> and the response of <math>e^...) |
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Latest revision as of 16:02, 19 September 2008
The formula of $ \cos(2t)\, $ = $ \frac{e^{2jt}+e^{-2jt}}{2}\, $.
We know the response of $ e^{2jt}\, $ is $ te^{-2jt}\, $ and the response of $ e^{-2jt}\, $ is $ te^{2jt}\, $.
So with an input of cos(2t),we will get the output as :
$ \frac{te^{2jt}+te^{-2jt}}{2}\, $
$ =t\frac{e^{2jt}+e^{-2jt}}{2}\, $
$ =t\cos(2t)\, $ ,which is the output.
