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 $

Alumni Liaison

Ph.D. 2007, working on developing cool imaging technologies for digital cameras, camera phones, and video surveillance cameras.

Buyue Zhang