Line 5: Line 5:
 
=<math>\frac{e^{2jt}+e^{-2jt}}{2}</math> --> system<br>  
 
=<math>\frac{e^{2jt}+e^{-2jt}}{2}</math> --> system<br>  
 
=<math>\frac{1}{2}(e^{2jt}+e^{-2jt})</math> -->system<br>
 
=<math>\frac{1}{2}(e^{2jt}+e^{-2jt})</math> -->system<br>
=<math>\frac{1}{2}e^{2jt}-->system +\frac{1}{2}e^{-2jt}-->system <br>
+
=<math>\frac{1}{2}e^{2jt}-->system +\frac{1}{2}e^{-2jt}</math>-->system <br>
=<math>\frac{1}{2}te^{-2jt} +\frac{1}{2}te^{2jt}<br>
+
=<math>\frac{1}{2}te^{-2jt} +\frac{1}{2}te^{2jt}</math><br>
=<math>\frac{1}{2}t(e^{-2jt} +e^{2jt})<br>
+
=<math>\frac{1}{2}t(e^{-2jt} +e^{2jt})</math><br>
=<math>\frac{1}{2}t\cos(2t)<br>
+
=<math>\frac{1}{2}t\cos(2t)</math><br>

Revision as of 15:52, 18 September 2008

$ e^{2jt} --> system --> te^{-2jt} $
$ e^{-2jt} --> system --> te^{2jt} $

=>$ \cos(2t) $ --> system =$ \frac{e^{2jt}+e^{-2jt}}{2} $ --> system
=$ \frac{1}{2}(e^{2jt}+e^{-2jt}) $ -->system
=$ \frac{1}{2}e^{2jt}-->system +\frac{1}{2}e^{-2jt} $-->system
=$ \frac{1}{2}te^{-2jt} +\frac{1}{2}te^{2jt} $
=$ \frac{1}{2}t(e^{-2jt} +e^{2jt}) $
=$ \frac{1}{2}t\cos(2t) $

Alumni Liaison

Abstract algebra continues the conceptual developments of linear algebra, on an even grander scale.

Dr. Paul Garrett