Harmonic analysis
（重定向自Fourier theory）
![The harmonics of color. The harmonic-analysis chart shows how the different wavelengths interact with red light. At a difference of λ/2 (wavelength/2), red is perfectly in sync with its second-generation harmonic in the ultraviolet. All other wavelengths in the visual spectrum have less than a λ/2 difference between them, forming harmonic oscillations in the combined waves. At λ/14, the oscillations will cycle every fourteenth wave, while at λ/8 they will cycle every eighth. The oscillations are most rapid at λ/4, cycling every fourth wave, while at λ/3 they cycle every seventh wave, and at λ/2.5 they cycle every thirteenth. The lower section shows how the λ/4 harmonic interacts in visible light (green and red), as photographed in an optical flat.](/Images/godic/202501/14/Light_wave_harmonic_diagram.svg0212.png")
0212.png")
![Fourier transform of bass guitar time signal of open string A note (55 Hz), computed with https://sourceforge.net/projects/amoreaccuratefouriertransform/ .](/Images/godic/202501/14/Fourier_Transform_of_bass_guitar_time_signal0212.png")
![Analyseur harmonique mécanique de Lord Kelvin datant de 1878.](/Images/godic/202501/14/Harmonic_analyser0212.jpg")
Harmonic analysis is a branch of mathematics concerned with the representation of functions or signals as the superposition of basic waves, and the study of and generalization of the notions of Fourier series and Fourier transforms (i.e. an extended form of Fourier analysis). In the past two centuries, it has become a vast subject with applications in areas as diverse as signal processing, quantum mechanics, tidal analysis and neuroscience.