Physics:Harmonic spectrum

Approximating a square wave by [math]\displaystyle{ \sin(t) + \sin(3t)/3 + \sin(5t)/5 }[/math]

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. "The individual partials are not heard separately but are blended together by the ear into a single tone."

In other words, if [math]\displaystyle{ \omega }[/math] is the fundamental frequency, then a harmonic spectrum has the form

[math]\displaystyle{ \{\dots, -2\omega, -\omega, 0, \omega, 2\omega, \dots\}. }[/math]

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

See also

• Fourier series
• Harmonic series (music)
• Periodic function
• Scale of harmonics
• Undertone series