11.13.2 Fourier Series
In data processing, we must first know the frequency components contained in a signal. The fundamental knowledge necessary for it is the Fourier series. We will briefly summaries it from the point of view of signal processing. One type of Fourier series is expressed by real numbers, while the other is by complex number.
(i) Real Fourier Series : A periodic function 
with period T can be expanded by trigonometric functions which belong to the orthogonal function systems as follows
(11.12)
where 
. This series is called the Fourier series or real Fourier series. Its coefficients are given by
(11.13)