How can a composite signal be decomposed?

Spectral analysis of a repetitive waveform into a harmonic series can be done by Fourier analyis.

This idea is generalised in the Fourier transform which converts any function of time expressed as a into a transform function of frequency. The time function is generally real while the transform function, also known as a the spectrum, is generally complex.

A function and its Fourier transform are known as a Fourier transform pair, and the original function is the inverse transform of the spectrum.