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x(t) = cos2t | x(t) = cos2t | ||
| − | after using Euler's Formula | + | after using Euler's Formula |
| + | |||
| + | <math>x(t) = \frac{1}{2} * e^{2jt} + \frac{1}{2} * e^{-2jt}</math> | ||
| + | |||
| + | <math>y(t) = t * x(-t)</math> | ||
| + | |||
| + | <math>y(t) = \frac{t}{2} * (e^{-2jt} + e^{2jt})</math> | ||
| + | |||
| + | <math>y(t) = \frac{t}{2} * (cos(2t) - jsin(2t) + cos(2t) + jsin(2t))</math> | ||
| + | |||
| + | <math>y(t) = \frac{t}{2} * (2cos(2t))</math> | ||
| + | |||
| + | |||
| + | |||
| + | <math>y(t) = t * cos(2t)</math> | ||
Latest revision as of 07:36, 18 September 2008
So the input will be x(t) and output will be y(t).
x(t) = cos2t
after using Euler's Formula
$ x(t) = \frac{1}{2} * e^{2jt} + \frac{1}{2} * e^{-2jt} $
$ y(t) = t * x(-t) $
$ y(t) = \frac{t}{2} * (e^{-2jt} + e^{2jt}) $
$ y(t) = \frac{t}{2} * (cos(2t) - jsin(2t) + cos(2t) + jsin(2t)) $
$ y(t) = \frac{t}{2} * (2cos(2t)) $
$ y(t) = t * cos(2t) $
