Energy (of a function)

The informal name signal processing gives to $\|f\|_2^2$ .

$\|f\|_2^2 = \int_a^b f(x)^2\,dx$ is exactly the quantity physics and engineering call a signal's energy (up to a constant depending on units -- a voltage across a resistor dissipates power proportional to voltage squared, and integrating power over time gives total energy). "Energy" is used throughout signal processing as a synonym for the squared $L^2$ norm, even for a purely mathematical signal with no physical units at all.

Examples

Doubling a signal's amplitude quadruples its energy, since energy depends on the square of the values.