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| − | Given the definition of [[3.A David Hartmann - Linear | + | Given the definition of [[3.A David Hartmann - Linear System_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> |
| − | Consider the | + | Consider the system: |
| − | <math>e^{-2jt}\to F | + | <math>e^{-2jt}\to F ( e^{-2jt} ) \to te^{2jt}</math> |
From the given system: | From the given system: | ||
| − | <math>x(t)\to | + | <math>x(t)\to F( x(t) )\to tx(-t)</math> |
From Euler's formula | From Euler's formula | ||
<math>e^{iy}=cos{y}+i sin{y}</math> | <math>e^{iy}=cos{y}+i sin{y}</math> | ||
Revision as of 14:21, 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 system:
$ e^{-2jt}\to F ( e^{-2jt} ) \to te^{2jt} $
From the given system:
$ x(t)\to F( x(t) )\to tx(-t) $
From Euler's formula $ e^{iy}=cos{y}+i sin{y} $
