Fourier Transform

Fourier Series

todo

From MATH213

Definition 1: L^{2} functions

A complex valued function $f$ is in the class $L^2([a,b])$ if

${\int }_a^b|f(x){|}^{2}dx$

exists and is finite.

$f$ is in the class $L^2$ if

${\int }_{-\infty }^{\infty }|f(x){|}^{2}dx$

exists and is finite.

We want to write $f(t)=\sum _{n=-\infty }^{\infty }{c}_n{e}^{\frac{2\pi n}{\tau }jt}$ for $t\in [\frac{-\tau }{2},\frac{\tau }{2}]$.

Our goal is to find $c_n$.

Definition 3: Fourier Series - Complex Form