Energy in 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,

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


By Rayleigh's Theorem,

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