# Spectral function

From AMS Glossary

## spectral function

(

*Or*spectrum.) The Fourier representation of a given function, that is, the Fourier transform if the given function is aperiodic, or the set of coefficients of the Fourier series if the given function is periodic.The existence of the spectral function depends on the mathematical behavior of the given function. If it exists, the spectral function will in general be a complex function, having both amplitude and phase.

*See also*continuous spectrum, discrete spectrum.