(New page: Given the definition of Linear systems <math>\alpha x1(t) + \beta x2(t) <\math> is <math> \alpha y1(t)+ \beta y2(t).</math> Consider the following system: <math...) |
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Given the definition of [[3.A David Hartmann _ECE301Fall2008mboutin| Linear systems]] | Given the definition of [[3.A David Hartmann _ECE301Fall2008mboutin| Linear systems]] | ||
| − | <math>\alpha x1(t) + \beta x2(t) < | + | <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: | ||
Revision as of 14:11, 19 September 2008
Given the definition of Linear systems
$ \alpha x1(t) + \beta x2(t) $ is $ \alpha y1(t)+ \beta y2(t). $
Consider the following system: $ e^{2jt}\to system\to te^{-2jt} $
$ e^{-2jt}\to system\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} $
