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Math Help - Fourier series example non-periodic

  1. #1
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    Question 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:

    f(x)=x
    0<x<=1

    f(x)=1
    1<x<=2

    Thanks!
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  2. #2
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    Quote Originally Posted by Texasmath View Post
    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:

    f(x)=x
    0<x<=1

    f(x)=1
    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 0< x\le 1
    f(x)= 1 for 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.
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