# Harmonic spectrum

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A harmonic spectrum is a spectrum containing only frequency components whose frequencies are whole number multiples of the fundamental frequency; such frequencies are known as harmonics.

In other words, if $\omega\,$ is the fundamental frequency, then a harmonic spectrum has the form

$\{\dots, -2\omega, -\omega, 0, \omega, 2\omega, \dots\}.$

A standard result of Fourier analysis is that a function has a harmonic spectrum if and only if it is periodic.