Any continuous function defined on a finite interval of length can be represented as a weighted sum of cosine functions with periods :

where

is the frequency of the i-th Fourier component;

is the amplitude of the i-th component;

is the phase of the i-th component.

The function describing the dependence of the amplitude on the frequency in the above expression is called the amplitude spectrum of the function .

The function describing the dependence of the phase on the frequency is called the phase spectrum of the function .

Thus, the Fourier spectrum of a function is represented by two functions of the frequency - the amplitude spectrum and the phase spectrum . These two are often combined into a single complex-valued function :