(The basics of linearity)
(The basics of linearity)
Line 9: Line 9:
 
<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>
  
<math>\cos 2t = e^{2jt}\over 2 + e^{-2jt}\over 2 </math>
+
<math>\cos 2t = e^{2jt} \over 2 + e^{-2jt} \over 2 </math>

Revision as of 05:15, 19 September 2008

The basics of linearity

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

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

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

Alumni Liaison

Prof. Math. Ohio State and Associate Dean
Outstanding Alumnus Purdue Math 2008

Jeff McNeal