Fourier Spectrum:
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 ith Fourier component;

is the amplitude of the ith component;

is the phase of the ith 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 complexvalued function :
where

is the real part of a complex number;

is the imaginable part of a complex number;
The concept of the spectrum plays an important role in signal processing , time series analysis , spectral analysis .
See also: power spectrum .