Signal Power

The average power over an interval of time $ [t_1,t_2]\! $ is $ P_{avg}=\frac{1}{t_2-t_1}\int_{t_1}^{t_2} |x(t)|^2\ dt \! $.

Given that $ y(t) = t \! $ and time interval $ [0,2]\! $,

$ P_{avg} = \frac{1}{2-0} \int_{0}^{2} |t|^2\ dt \! $ $ =\frac{1}{2} [\frac{1}{3} t^3]_{0}^{2} \! $ $ =\frac{1}{6}[8-0] = \frac{4}{3} \! $

Signal Energy

The equation to calculate signal energy is as follows: $ E=\int_{t_1}^{t_2}x(t)dt $

using the same equation $ y(t) = t \! $ over a time interval $ [0,2]\! $ as the previous section,

$ E = \int_{0}^{2} t\ dt = \frac{1}{2}[t^2]_{0}^{2} = \frac{1}{2}[4 - 0] = 2 \! $