Equations
The energy expanded from a time t1 to a time t2 in a CT signal is calculated by
$ E = \int_{t_1}^{t_2} \! |x(t)|^2\ dt $
The power over a time period t1 to t2 is calculated by
$ P_{avg}=\frac{1}{t_2-t_1} \int_{t_1}^{t_2} |x(t)|^2\ dt \! $
The equation used to calculate both energy and power will be
$ y(t) = e^{t} $
Calculating Energy
The energy of $ y(t) = e^{t} $ over the time period 0 to 2 seconds is found as follows:
$ E = \int_{0}^{2} |e^{t}|^2\ dt \! $
$ =\int_{0}^{2} e^{2t}\ dt $
$ = \frac{1}{2}[e^{2t}]_{t=0}^{t=2} \! $
$ E = \frac{1}{2}(e^4 -1)\! $
Calculating Power
The power of $ y(t) = e^{t} $ over the time period 0 to 2 seconds is found as follows:
$ P =\frac{1}{2-0} \int_{0}^{2} |e^{t}|^2\ dt \! $
$ = \frac{1}{2}\int_{0}^{2} e^{2t}\ dt \! $
$ = \frac{1}{2}*\frac{1}{2}[e^{2t}]_{t=0}^{t=2} \! $
$ = \frac{1}{4}(e^2 -1)\! $
