Difference between revisions of "Energy in a signal"
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===Energy of a Signal=== 
===Energy of a Signal=== 

From circuit analysis we know that the power generated by a voltage source is, 
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/Braket_notation braket] notation as 

−  +  : <math> <v(t)  v(t)> \!</math> or <math> <vv> \!</math> 

−  +  By [[Rayleigh's Theorem]], 

−  +  : <math> <vv> = \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 braket notation as
 or
This implies that the energy of a signal can be found by the fourier transform of the signal,