(The basics of linearity)
(The basics of linearity)
Line 4: Line 4:
  
 
<math>e^{(-2jt)}</math> --->[system]---><math>te^{(2jt)}</math>
 
<math>e^{(-2jt)}</math> --->[system]---><math>te^{(2jt)}</math>
 +
 +
<math>ae^{(2jt)}</math> --->[system]---><math>ate^{(-2jt)}</math>
 +
 +
<math>be^{(-2jt)}</math> --->[system]---><math>bte^{(-2jt)}</math>
  
 
<math>\cos x = \mathrm{Re}\{e^{ix}\} ={e^{ix} + e^{-ix} \over 2}</math>
 
<math>\cos x = \mathrm{Re}\{e^{ix}\} ={e^{ix} + e^{-ix} \over 2}</math>
  
 
<math>\cos 2t = \mathrm{Re}\{e^{jt}\} ={e^{2jt} + e^{-2jt} \over 2}</math>
 
<math>\cos 2t = \mathrm{Re}\{e^{jt}\} ={e^{2jt} + e^{-2jt} \over 2}</math>

Revision as of 05:11, 19 September 2008

The basics of linearity

$ e^{(2jt)} $ --->[system]--->$ te^{(-2jt)} $

$ e^{(-2jt)} $ --->[system]--->$ te^{(2jt)} $

$ ae^{(2jt)} $ --->[system]--->$ ate^{(-2jt)} $

$ be^{(-2jt)} $ --->[system]--->$ bte^{(-2jt)} $

$ \cos x = \mathrm{Re}\{e^{ix}\} ={e^{ix} + e^{-ix} \over 2} $

$ \cos 2t = \mathrm{Re}\{e^{jt}\} ={e^{2jt} + e^{-2jt} \over 2} $

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Basic linear algebra uncovers and clarifies very important geometry and algebra.

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