Energy in a signal: Difference between revisions
Jump to navigation
Jump to search
No edit summary |
|||
(20 intermediate revisions by 2 users not shown) | |||
Line 10: | Line 10: | ||
: <math> W = \int_{-\infty}^{\infty} P(t)\,dt</math> |
: <math> W = \int_{-\infty}^{\infty} P(t)\,dt</math> |
||
===Energy of a |
===Energy of a Signal=== |
||
From |
From circuit analysis we know that the power generated by a voltage source is, |
||
: <math>P(t) = { |
: <math>P(t) = {v^2(t) \over R}</math> |
||
Assuming that R is 1 then the total energy is just, |
Assuming that R is 1 then the total energy is just, |
||
: <math>W = \int_{-\infty}^\infty | |
: <math>W = \int_{-\infty}^\infty |v|^2(t) \, dt</math> |
||
This can be written using [http://en.wikipedia.org/wiki/Bra-ket_notation bra-ket] notation as |
|||
: <math> <v(t) | v(t)> \!</math> or <math> <v|v> \!</math> |
|||
This page is far from complete please feel free to pick up where it has been left off. |
|||
By [[Rayleigh's Theorem]], |
|||
: <math> <v|v> = \int_{-\infty}^{\infty} |V(f)|^2\,df </math> |
|||
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> |
Latest revision as of 02:38, 11 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
This implies that the energy of a signal can be found by the fourier transform of the signal,