Energy of a signal
Consider the signal $ \ y = \sin(t) $ Lets find the energy over one cycle:
$ Energy = \int_{t_1}^{t_2}\!|x(t)|^2 dt $
$ Energy = \int_{0}^{2 \pi}\!|sin(t)|^2 dt $
$ Energy = \int_{0}^{2 \pi}\!|frac{1-cos(2t)| dt $
$ Energy = \int_{0}^{2 \pi}\!|sin(t)|^2 dt $
Average Power of a Signal
$ Avg. Power = {1\over(t_2-t_1)}\int_{t_1}^{t_2}\!|x(t)|^2 dt $
