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} $
