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<math> e^{j2t} + e^{-j2t}\ </math> ----------> System -----------> <math> te^{-2jt} + te^{2jt}\ </math><br><br>
 
<math> e^{j2t} + e^{-j2t}\ </math> ----------> System -----------> <math> te^{-2jt} + te^{2jt}\ </math><br><br>
  
The Key to approach this problem is: What is <math> {e^{j2t} + e^{-j2t}\ over 2} </math>
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The Key to approach this problem is: What is <math> {e^{j2t} + e^{-j2t} \over 2} </math>?
 
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<br>
: <math>\cos x = \mathrm{Re}\{e^{ix}\} ={e^{ix} + e^{-ix} \over 2}</math>
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Revision as of 06:03, 19 September 2008

Provided that:
(1) $ e^{j2t}\ $ ----------> System ----------> $ te^{-2jt}\ $
(2) $ e^{-j2t}\ $----------> System ----------> $ te^{2jt}\ $
(3) The System is Linear.

The following should hold true: $ e^{j2t} + e^{-j2t}\ $ ----------> System -----------> $ te^{-2jt} + te^{2jt}\ $

The Key to approach this problem is: What is $ {e^{j2t} + e^{-j2t} \over 2} $?

Alumni Liaison

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

Dr. Paul Garrett