(New page: ==The Basics of Linearity== If <math> e^{2jt} ==> te^{-2jt} </math> and <math> e^{-2jt} ==> te^{2jt} </math> :What is the response to to cos(2t)? ===Solution=== For any Linear system:...) |
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Latest revision as of 08:18, 18 September 2008
The Basics of Linearity
If $ e^{2jt} ==> te^{-2jt} $ and $ e^{-2jt} ==> te^{2jt} $
- What is the response to to cos(2t)?
Solution
For any Linear system:
Ax(t) + Bx(t) = Ay(t) + By(t)
Therefore
- $ e^{2jt} + e^{-2jt} = cos(2t) + jsin(2t) + cos(-2t) + jsin(-2t) $
- $ e^{2jt} + e^{-2jt} = 2cos(2t) $
- $ cos(2f) =System=> .5(te^{2jt} + te^{-2jt}) $
- $ cos(2f) =System=> .5(2tcos(2t)) $
- $ cos(2f) =System=> tcos(2t) $
