(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>
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To look at this in more detail, we must first understand that <math>cos(2t)\!</math> can be expressed as follows: <math> \frac{1}{2}(e^{-2jt}+e^{2jt})\!</math>

Revision as of 15:04, 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 follows: $ \frac{1}{2}(e^{-2jt}+e^{2jt})\! $

Alumni Liaison

Ph.D. 2007, working on developing cool imaging technologies for digital cameras, camera phones, and video surveillance cameras.

Buyue Zhang