Energy in a signal

From Class Wiki
Revision as of 21:10, 10 October 2006 by Nathan (talk | contribs) (Energy of a Signal)

Jump to: navigation, search

Definition of Energy

Energy is the ability or potential for something to create change. Scientifically energy is defined as total work done by a 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}

Power represents a change in energy.

 P(t) = \frac{dW}{dt}

This means we can also write energy as

 W = \int_{-\infty}^{\infty} P(t)\,dt

Energy of a Signal

From circuit analysis we know that the power generated by a voltage source is,

P(t) = {v^2(t) \over R}

Assuming that R is 1 then the total energy is just,

W = \int_{-\infty}^\infty |v|^2(t) \, dt

This can be written using bra-ket notation as  <v(t)|v(t)>

This page is far from complete please feel free to pick up where it has been left off.