(New page: ==Basics of Linearity == Given :<math>e^{2 x i}=t e^{-2 x i}\, </math> :<math>e^{-2 x i}=t e^{2 x i}\, </math> :<math>\cos x = \dfrac{e^{i x}+e^{-i x}}{2}</math> :<math>\cos 2x = \dfrac{e...) |
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Revision as of 06:58, 18 September 2008
Basics of Linearity
Given
- $ e^{2 x i}=t e^{-2 x i}\, $
- $ e^{-2 x i}=t e^{2 x i}\, $
- $ \cos x = \dfrac{e^{i x}+e^{-i x}}{2} $
- $ \cos 2x = \dfrac{e^{2 i x}+e^{-2 i x}}{2} $
The Systems response to $ \cos 2x $ is $ \ \dfrac{t e^{-2 i x} + t e^{2 i x}}{2} $
