Spectrum

Short definition of Spectrum
Shows how the variance of a signal is distributed with respect to frequency or wavenumber

This is the common definition for Spectrum, but other definitions maybe discussed within the wiki.

The spectrum of a signal, say [math]\displaystyle{ u(t) }[/math], shows how the variance of this signal is distributed with respect to frequency. If the spectrum of [math]\displaystyle{ u }[/math] is [math]\displaystyle{ \Psi(f) }[/math], then the spectrum has the property that the variance of [math]\displaystyle{ u }[/math] is

[math]\displaystyle{ \overline{u} = \int_0^{\infty}\, \mathrm{d}f }[/math]