(New page: The response of the system to <math>e^{2jt}</math> is <math>te^{-2jt}</math> and <math>e^{-2jt}</math> is <math>t e^{2jt}</math> We are asked how the system will respond to cos(2t) By Eu...) |
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By Euler's formula we know cos(2t) = <math>\left ( \frac{1}{2} \right )(e^{2j} + e^{-2j})</math> | By Euler's formula we know cos(2t) = <math>\left ( \frac{1}{2} \right )(e^{2j} + e^{-2j})</math> | ||
| − | the response to the system should be | + | the response to the system should be <math>\left ( \frac{1}{2} \right )t(e^{-2j} + e^{2j})</math> |
| + | |||
| + | which is tcos(2t) | ||
Latest revision as of 16:12, 19 September 2008
The response of the system to $ e^{2jt} $ is $ te^{-2jt} $ and $ e^{-2jt} $ is $ t e^{2jt} $
We are asked how the system will respond to cos(2t)
By Euler's formula we know cos(2t) = $ \left ( \frac{1}{2} \right )(e^{2j} + e^{-2j}) $
the response to the system should be $ \left ( \frac{1}{2} \right )t(e^{-2j} + e^{2j}) $
which is tcos(2t)
