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| − | Given the definition of [[3.A David Hartmann | + | Given the definition of [[3.A David Hartmann - Linear Systems_ECE301Fall2008mboutin| Linear systems]] we know the response to <math>\alpha x1(t) + \beta x2(t) </math> is <math> \alpha y1(t)+ \beta y2(t).</math> |
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| − | <math>\alpha x1(t) + \beta x2(t) </math> is <math> \alpha y1(t)+ \beta y2(t).</math> | + | |
Consider the following system: | Consider the following system: | ||
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| − | |||
| − | <math>e^{-2jt}\to | + | <math>e^{-2jt}\to F\left e^{-2jt} \right \to te^{2jt}</math> |
From the given system: | From the given system: | ||
Revision as of 14:18, 19 September 2008
Given the definition of Linear systems we know the response to $ \alpha x1(t) + \beta x2(t) $ is $ \alpha y1(t)+ \beta y2(t). $
Consider the following system:
$ e^{-2jt}\to F\left e^{-2jt} \right \to te^{2jt} $
From the given system:
$ x(t)\to system\to tx(-t) $
From Euler's formula $ e^{iy}=cos{y}+i sin{y} $
