Fourier’s Transform

Abstract

Consider the trigonometrical series of the following form

$$ \frac{a_0}{2}+\sum \limits _{n=1}^{\infty }\left( a_n\cos n\omega x+ b_n\sin n\omega x\right) . $$

Since the functions $\cos n\omega x$ and $\sin n\omega x$ are periodical functions having the period $T=2\pi /\omega$ we say that the series (4.1.1) is a periodical series.