Fourier derived integral equations that extract harmonic coefficients from any signal.

Evidence

The Fourier coefficients discussed earlier are not found by trial and error. Fourier also developed equations for extracting them. For any periodic function, f(t) the harmonic coefficients a0, an and bn can be found from: Like many things in acoustics, dealing with the Fourier series in trigono­ metric form is messy and inconvenient. — David Howard, Jamie Angus, coustics and Psychoacoustics, 2728

Categorization

• XREF: This is the analysis half of the analysis-synthesis pair — the method underlying every spectrum analyzer the reader might use.