(→Linearity) |
(→Linearity) |
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If a linear system has a response to exp(2jt) of t*exp(-2jt) and a response to exp(-2jt) of t*exp(2jt), then it's response to cos(2t) must be t*cos(2t). | If a linear system has a response to exp(2jt) of t*exp(-2jt) and a response to exp(-2jt) of t*exp(2jt), then it's response to cos(2t) must be t*cos(2t). | ||
| − | To look at this in more detail, we must first understand that <math>cos(2t)\!</math> can be expressed as <math> \frac{1}{2}(e^{-2jt}+e^{2jt})\!</math> | + | To look at this in more detail, we must first understand that <math>cos(2t)\!</math> can be expressed as <math> \frac{1}{2}(e^{-2jt}+e^{2jt})\!</math> |
Revision as of 16:04, 18 September 2008
Linearity
If a linear system has a response to exp(2jt) of t*exp(-2jt) and a response to exp(-2jt) of t*exp(2jt), then it's response to cos(2t) must be t*cos(2t).
To look at this in more detail, we must first understand that $ cos(2t)\! $ can be expressed as $ \frac{1}{2}(e^{-2jt}+e^{2jt})\! $
