Difference between revisions of "Energy in a signal"
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+  *[[Signals and systemsSignals and Systems]] 

===Definition of Energy=== 
===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, 

: <math> W = \int \mathbf{F} \cdot \mathrm{d}\mathbf{s}</math> 
: <math> W = \int \mathbf{F} \cdot \mathrm{d}\mathbf{s}</math> 

+  
+  Power represents a change in energy. 

+  : <math> P(t) = \frac{dW}{dt} </math> 

+  
+  This means we can also write energy as 

+  : <math> W = \int_{\infty}^{\infty} P(t)\,dt</math> 

+  
+  ===Energy of a Signal=== 

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

+  : <math>P(t) = {v^2(t) \over R}</math> 

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

+  : <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,