Difference between revisions of "Energy in a signal"

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(Energy of a Signal)
(Energy of a Signal)
Line 12: Line 12:
 
===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) = {\mathbf{V}^2(t) \over R}</math>
+
: <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 |\mathbf{V}|^2(t) \, dt</math>
+
: <math>W = \int_{-\infty}^\infty |V|^2(t) \, dt</math>
   
   

Revision as of 21:05, 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,

 W = \int \mathbf{F} \cdot \mathrm{d}\mathbf{s}

Power represents a change in energy.

 P(t) = \frac{dW}{dt}

This means we can also write energy as

 W = \int_{-\infty}^{\infty} P(t)\,dt

Energy of a Signal

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

P(t) = {V^2(t) \over R}

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

W = \int_{-\infty}^\infty |V|^2(t) \, dt


This page is far from complete please feel free to pick up where it has been left off.