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==Power Example== | ==Power Example== | ||
<math>P={1\over(4\pi-0)}\int_{0}^{4\pi}\!|sin(t)|^2dt</math> | <math>P={1\over(4\pi-0)}\int_{0}^{4\pi}\!|sin(t)|^2dt</math> | ||
| + | |||
| + | <math>P={1\over(4\pi-0)}\int_{0}^{4\pi}\!(\frac{1-cos(2t)}{2})dt</math> | ||
| + | |||
| + | <math>P=\frac{1}{2}-\frac{1}{16\pi}sin(8\pi)</math> | ||
| + | |||
| + | <math>P=\frac{1}{2}</math> | ||
Revision as of 18:35, 5 September 2008
Signal Energy
$ E = \int_{t_1}^{t_2}\!|x(t)|^2dt $
Signal Energy Example
$ E = \int_{0}^{4\pi}\!|sin(t)|^2dt $
$ E = \int_{0}^{4\pi}\!(\frac{1-cos(2t)}{2})dt $
$ E = 2 \pi - \frac{1}{4}\sin(8\pi) $
$ E = 2\pi $
Power
$ P={1\over(t_2-t_1)}\int_{t_1}^{t_2}\!|x(t)|^2dt $
Power Example
$ P={1\over(4\pi-0)}\int_{0}^{4\pi}\!|sin(t)|^2dt $
$ P={1\over(4\pi-0)}\int_{0}^{4\pi}\!(\frac{1-cos(2t)}{2})dt $
$ P=\frac{1}{2}-\frac{1}{16\pi}sin(8\pi) $
$ P=\frac{1}{2} $
