Energy in a signal

Definition of Energy

Enegry is the ability or pentential for something to create change. Scientifically enegry is defined as total work done force. Work can be mathematically calculated as the line integral of force per infinatesimal unit distance,

$W=\int \mathbf {F} \cdot \mathrm {d} \mathbf {s}$

Energy of a signal

From circiut analysis we know that the energy of a voltage source is,

$W={V^{2}(t) \over R}$

Assuming that R is 1 then the total energy is just, $W=\int _{-\infty }^{\infty }|\mathbf {V} |^{2}\mathrm {d} \mathbf {t}$