(New page: == The Basics of Linearity ==) |
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== The Basics of Linearity == | == The Basics of Linearity == | ||
| + | <math>e^{(2jt)}</math>--->[linear system]---><math>te^{(-2jt)}</math> | ||
| + | |||
| + | and that | ||
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| + | <math>e^{(-2jt)}</math>--->[linear system]---><math>te^{(2jt)}</math> | ||
| + | |||
| + | we can rewrite <math>cos(2t)</math> as <math> 0.5 * (e^{(2jt)}+e^{(-2jt)})</math> | ||
| + | |||
| + | knowing that for any x1(t) and x2(t) yielding y1(t) and y2(t) respectively when passed through a linear system that A*x1(t) + B*x2(t) yields A*y1(t) + B*y2(t) we can change A and B to 0.5 thus | ||
| + | |||
| + | <math>cos(2t)</math>--->linear system ---> <math> 0.5t * (e^{(2jt)}+e^{(-2jt)})</math> or <math> tcos(2t)</math> | ||
Latest revision as of 12:33, 19 September 2008
The Basics of Linearity
$ e^{(2jt)} $--->[linear system]--->$ te^{(-2jt)} $
and that
$ e^{(-2jt)} $--->[linear system]--->$ te^{(2jt)} $
we can rewrite $ cos(2t) $ as $ 0.5 * (e^{(2jt)}+e^{(-2jt)}) $
knowing that for any x1(t) and x2(t) yielding y1(t) and y2(t) respectively when passed through a linear system that A*x1(t) + B*x2(t) yields A*y1(t) + B*y2(t) we can change A and B to 0.5 thus
$ cos(2t) $--->linear system ---> $ 0.5t * (e^{(2jt)}+e^{(-2jt)}) $ or $ tcos(2t) $
