# Thread: Fourier series example non-periodic

1. ## Fourier series example non-periodic

Hello,

Does anyone have a link showing an example of a fourier series pertaining to 2 non-periodic functions?

I need help getting a single fourier series for the following function:

$\displaystyle f(x)=x$
$\displaystyle 0<x<=1$

$\displaystyle f(x)=1$
$\displaystyle 1<x<=2$

Thanks!

2. Originally Posted by Texasmath
Hello,

Does anyone have a link showing an example of a fourier series pertaining to 2 non-periodic functions?

I need help getting a single fourier series for the following function:

$\displaystyle f(x)=x$
$\displaystyle 0<x<=1$

$\displaystyle f(x)=1$
$\displaystyle 1<x<=2$

Thanks!
Only periodic functions have Fourier series. (For non-periodic functions, you use Fourier transforms).

You want a Fourier series for the single periodic function

f(x)= x for $\displaystyle 0< x\le 1$
f(x)= 1 for $\displaystyle 1< x\le 2$
and "extended by periodicity": f(x+ 2)= f(x).

Use the usual formulas for the Fourier coefficients. You will need to break the integral into two parts, from 0 to 1 and from 1 to 2.