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== Signal Power == | == Signal Power == | ||
| − | <math>\, Power = | + | <math>\, Power = \frac{1}{2\pi - 0}\int_0^{2\pi}{|cos(x)|^2dx}</math> |
| + | |||
| + | ''computation of the integral is the same as shown in the section above'' | ||
| + | |||
| + | :::<math>\, = \frac{1}{2\pi}\frac{1}{2}(2\pi + 0 - 0 - 0)</math> | ||
| + | |||
| + | :::<math>\, = \frac{1}{2} </math> | ||
Latest revision as of 06:49, 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 $
Signal Power
$ \, Power = \frac{1}{2\pi - 0}\int_0^{2\pi}{|cos(x)|^2dx} $
computation of the integral is the same as shown in the section above
- $ \, = \frac{1}{2\pi}\frac{1}{2}(2\pi + 0 - 0 - 0) $
- $ \, = \frac{1}{2} $
