Harmonic Analysis

In music, if a note has frequency , integer multiples of that frequency,  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.

REFERENCES:

Stein, E. M. Harmonic Analysis. Princeton, NJ: Princeton University Press, 1993.