Fourier analysis

In music, if a note has frequency f, integer multiples of that frequency, 2f, 3f, 4f and so on, are known as harmonics. As a result, the mathematical study of overlapping waves is called harmonic analysis. Harmonic analysis is a diverse field including such branches as Fourier series, isospectral manifolds (hearing the shape of a drum), and topological groups. Signal processing, medical imaging, and quantum mechanics are three of the fields that use harmonic analysis extensively.

Fourier series | harmonic addition theorem