(New page: == System Response == The response of <math>\cos(2t)\,</math> is equal to <math>\frac{e^{2jt}+e^{-2jt}}{2}\,</math>. We already had the response of <math>e^{2jt}\,</math> is <math>te^{-2j...) |
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Latest revision as of 18:27, 15 September 2008
System Response
The response of $ \cos(2t)\, $ is equal to $ \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}\, $.
Assuming the system is a LTI system, we can substitute the response of $ \frac{e^{2jt}+e^{-2jt}}{2}\, $ with the values above.
Thus the system will produce the following response as an output :
$ \frac{te^{2jt}+te^{-2jt}}{2}\, $
$ =t\frac{e^{2jt}+e^{-2jt}}{2}\, $
$ =t\cos(2t)\, $
