Fourier Spectrum:
Any continuous function defined on a finite interval
can be represented as a weighted sum of cosine functions with periods
where
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
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
where
The concept of the spectrum plays an important role in signal processing , time series analysis , spectral analysis .
See also: power spectrum .