Energy in a signal: Difference between revisions

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This implies that the energy of a signal can be found by the fourier transform of the signal,
This implies that the energy of a signal can be found by the fourier transform of the signal,
: <math> W = \int_{-\infty}^{\infty} |V(f)|^2\,df </math>
: <math> W = \int_{-\infty}^{\infty} |V(f)|^2\,df </math>
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Revision as of 21:22, 10 October 2006

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,

Power represents a change in energy.

This means we can also write energy as

Energy of a Signal

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

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

This can be written using bra-ket notation as

or

By Rayliegh's Theroem,

This implies that the energy of a signal can be found by the fourier transform of the signal,