(→Function) |
(→Signal Energy) |
||
| Line 3: | Line 3: | ||
== Signal Energy == | == Signal Energy == | ||
| + | <math>\,Energy = \int_0^{2\pi}{|cos(x)|^2dx}</math> | ||
| + | :::<math>\, = \int_0^{2\pi}{|\frac{1+cos(2x)}{2}|dx}</math> | ||
| + | :::<math>\, = \frac{1}{2}\int_0^{2\pi}{(1 + cos(2x))dx}</math> | ||
| + | |||
| + | :::<math>\, = \frac{1}{2}(x + \frac{1}{2}sin(2x))|_0^{2/pi}</math> | ||
| + | |||
| + | :::<math>\, = \frac{1}{2}(2\pi + 0 - 0 - 0)</math> | ||
| + | |||
| + | :::<math>\, = \pi</math> | ||
== Signal Power == | == Signal Power == | ||
Revision as of 06:45, 3 September 2008
Function
$ \,y = cos(x) $
Signal Energy
$ \,Energy = \int_0^{2\pi}{|cos(x)|^2dx} $
- $ \, = \int_0^{2\pi}{|\frac{1+cos(2x)}{2}|dx} $
- $ \, = \frac{1}{2}\int_0^{2\pi}{(1 + cos(2x))dx} $
- $ \, = \frac{1}{2}(x + \frac{1}{2}sin(2x))|_0^{2/pi} $
- $ \, = \frac{1}{2}(2\pi + 0 - 0 - 0) $
- $ \, = \pi $
