# Example of computation of Signal energy and Signal Power

$x(t) = \sqrt(t)$

$x_1(t) = \cos(t) + \jmath\sin(t)$

$E_\infty = \int_{-\infty}^\infty |x(t)|^2\,dt$

    $=\int_{-\infty}^\infty |\sqrt(t)|^2\,dt$
$=\int_0^\infty t\,dt$
$=.5*t^2|_0^\infty$
$=.5(\infty^2 - 0^2)$


$E_\infty = \infty$

$P_\infty = lim_{T \to \infty} \ 1/(2T) \int_{-T}^T |x(t)|^2\,dt$

    $= lim_{T \to \infty} \ 1/(2T) \int_{-T}^T |\sqrt(t)|^2\,dt$
$= lim_{T \to \infty} \ 1/(2T) .5*t^2|_0^T$
$= lim_{T \to \infty} \ 1/(2T) * .5(T^2 - 0^2)$
$= lim_{T \to \infty} \ 1/(2T) * .5T^2$
$= lim_{T \to \infty} \ 1/(4T)*T^2$
$= lim_{T \to \infty} T/4$


$P_\infty = \infty$

$|x_1(t)| = \sqrt{\cos^2(t)+\sin^2(t)}=1$

$E_\infty = \int_{-\infty}^\infty |x_1(t)|^2\,dt$

    $= \int_{-\infty}^\infty |1|^2 \,dt$
$= t|_{-\infty}^\infty$


$E_\infty = \infty$

$P_\infty = lim_{T \to \infty} \ 1/(2T) \int_{-T}^T |x_1(t)|^2\,dt$

    $= lim_{T \to \infty} \ 1/(2T) \int_{-T}^T |1|^2 \,dt$
$= lim_{T \to \infty} \ 1/(2T) * t|_{-T}^T$
$= lim_{T \to \infty} \ 1/(2T) * (T- (-T))$
$= lim_{T \to \infty} \ 1/(2T) * (2T)$
$= lim_{T \to \infty} \ 1$


$P_\infty = 1$

## Alumni Liaison

To all math majors: "Mathematics is a wonderfully rich subject."

Dr. Paul Garrett