Signal Energy and Power Calculations
Background
The energy of a signal within specific time limits is defined as:
$ E=\int_{t_1}^{t_2} |x(t)|^2\, dt $
The average power of a signal between specific time limits is defined as:
$ P=\frac{1}{t_2-t_1}\int_{t_1}^{t_2} |x(t)|^2\, dt $
Example
Given that a signal $ \,\! x(t)=4t^2+2 $, find the Energy and Power from $ t_1=0 $ to $ t_2=3 $
$ \,\! E=\int_{0}^{3} |4t+2|^2\, dt =\int_{0}^{3} |16t^4+16t^2+4|\, dt =\frac{16}{5}t^5+\frac{16}{3}t^3+4t\bigg]_0^3 =933.6 $
$ \,\! P=\frac{1}{t_2-t_1}933.6=311.2 $
