Difference between revisions of "Energy in a signal"

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(Definition of Energy)
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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,
 
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===
 
===Energy of a signal===

Revision as of 20:40, 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 circiut analysis we know that the energy of a voltage source is,

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

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

W = \int_{-\infty}^\infty |\mathbf{V}|^2(t) \mathrm{d}\mathbf{t}

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