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Output = Response(<math>\frac{e^{2jt}+e^{-2jt}}{2}\,</math>) | Output = Response(<math>\frac{e^{2jt}+e^{-2jt}}{2}\,</math>) | ||
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| + | = Response(<math>\frac{e^{2jt}</math>)+ | ||
<math>=\frac{te^{2jt}+te^{-2jt}}{2}\,</math> | <math>=\frac{te^{2jt}+te^{-2jt}}{2}\,</math> | ||
Revision as of 08:16, 18 September 2008
System Response
Based on the Euler Formula, $ \cos(2t)\,= \frac{e^{2jt}+e^{-2jt}}{2}\, $.
We already had the response of $ e^{2jt}\, $ is $ te^{-2jt}\, $ and the response of $ e^{-2jt}\, $ is $ te^{2jt}\, $.
Since the system is a LTI system, we have
Output = Response($ \frac{e^{2jt}+e^{-2jt}}{2}\, $)
= Response($ \frac{e^{2jt} $)+
$ =\frac{te^{2jt}+te^{-2jt}}{2}\, $
$ =t\frac{e^{2jt}+e^{-2jt}}{2}\, $
$ =t\cos(2t)\, $
