Editing Harmonic spectrum

[[File:Fourier Series-Square wave 3 H (no scale).png|thumb|Approximating a [[Square wave (waveform)|square wave]] by <math>\sin(t) + \sin(3t)/3 + \sin(5t)/5</math>]]
A '''harmonic spectrum''' is a [[spectrum of an operator|spectrum]] containing only frequency components whose [[frequency|frequencies]] are [[Integer|whole number]] multiples of the [[fundamental frequency]]; such frequencies are known as [[harmonic]]s. "The individual partials are not heard separately but are blended together by the ear into a single tone."<ref>{{Cite book |last=Benward |first=Bruce |url={{google books|plainurl=y|id=-iK8PwAACAAJ&dq=978-0-07-294262-0}} |title=Music in Theory and Practice |last2=White |first2=Gary |date=1999 |publisher=McGraw-Hill Higher Education |isbn=978-0-697-35375-7 |language=en|volume= 1 |p=xiii|edition=7}}</ref>

In other words, if <math>\omega</math> is the fundamental frequency, then a harmonic spectrum has the form 
:<math>\{\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 function|periodic]].

==See also==
* [[Fourier series]]
* [[Harmonic series (music)]]
* [[Periodic function]]
* [[Scale of harmonics]]
* [[Undertone series]]

==References==
{{reflist}}

{{Acoustics}}
{{Mathanalysis-stub}}
{{Signal-processing-stub}}
[[Category:Functional analysis]]
[[Category:Acoustics]]
[[Category:Sound]]