Energy in a signal

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Revision as of 21:05, 10 October 2006 by Nathan (talk | contribs) (Energy of a Signal)

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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


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