Energy in a signal

• Signals and Systems

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 power of a voltage source is,

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

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.