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=Part B: The basics of linearity= | =Part B: The basics of linearity= | ||
==System’s response to cos(2t)== | ==System’s response to cos(2t)== | ||
| + | Using Euler's formula, we get | ||
| + | |||
| + | <math>e^{(2jt)} = cos{(2t)} + jsin{(2t)} --> system --> t*{(cos{(2t)} - jsin{(2t)})}\,</math><br> | ||
| + | <math>e^{(-2jt)} = cos{(2t)} - jsin{(2t)} --> system --> t*{(cos{(2t)} + jsin{(2t)})}\,</math><br><br> | ||
Revision as of 17:47, 19 September 2008
Part B: The basics of linearity
System’s response to cos(2t)
Using Euler's formula, we get
$ e^{(2jt)} = cos{(2t)} + jsin{(2t)} --> system --> t*{(cos{(2t)} - jsin{(2t)})}\, $
$ e^{(-2jt)} = cos{(2t)} - jsin{(2t)} --> system --> t*{(cos{(2t)} + jsin{(2t)})}\, $
