Английская Википедия:Harmonic spectrum

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Файл:Fourier Series-Square wave 3 H (no scale).png
Approximating a square wave by <math>\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."[1]

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.

See also

References

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Шаблон:Acoustics Шаблон:Mathanalysis-stub Шаблон:Signal-processing-stub

  1. Benward, Bruce and Saker, Marilyn (1997/2003). Music: In Theory and Practice, Vol. I, p.xiii. Seventh edition. McGraw-Hill. Шаблон:ISBN.