# Difference between revisions of "Energy in a signal"

### 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 circiut analysis we know that the power generated by voltage source is,

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

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

$W = \int_{-\infty}^\infty |\mathbf{V}|^2(t) \mathrm{d}\mathbf{t}$

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