(New page: Provided that: : <math> e^{j2t} </math>----------> System ----------> <math> te^{-2jt} </math><br> : <math> e^{-j2t} </math>----------> System ----------> <math> te^{2jt} </math><br>) |
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| Line 1: | Line 1: | ||
| − | Provided that: | + | Provided that: <br> |
| − | + | (1) <math> e^{j2t}\ </math> ----------> System ----------> <math> te^{-2jt}\ </math><br> | |
| − | : <math> e^{-j2t} </math>----------> System ----------> <math> te^{2jt} </math><br> | + | (2) <math> e^{-j2t}\ </math>----------> System ----------> <math> te^{2jt}\ </math><br> |
| + | (3) The System is Linear. <br> | ||
| + | |||
| + | The following should hold true: | ||
| + | <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> | ||
| + | |||
| + | : <math>\cos x = \mathrm{Re}\{e^{ix}\} ={e^{ix} + e^{-ix} \over 2}</math> | ||
Revision as of 07:02, 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} $
- $ \cos x = \mathrm{Re}\{e^{ix}\} ={e^{ix} + e^{-ix} \over 2} $
