Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Short Fourier series question

  1. Dec 7, 2011 #1
    1. The problem statement, all variables and given/known data


    2. Relevant equations

    Usual equations for calculating fourier series coefficients

    3. The attempt at a solution

    Well essentially I don't know what to let f(x) equal to for calculating the coefficients a0, an and bn. Should I use 1 + x/pi or 1 - x/pi? And what about the limits? I was thinking maybe between -pi and pi.

    Anyway here's my progress thus far, I think the graph is ok anyways.


    Thanks dudes. I would use latex but I suck at it :yuck:
  2. jcsd
  3. Dec 7, 2011 #2

    I like Serena

    User Avatar
    Homework Helper

    Looks fine.
    Just start with the generic formula for a0.
    The integral can be calculated by splitting it into the sum of 2 integrals.
  4. Dec 7, 2011 #3
    Take for example:

    [tex]a_1=\frac{1}{\pi}\int_{-\pi}^{\pi} f(x)\cos(x)dx[/tex]

    now, I want to integrate that function between -pi and pi but it's defined differently in two intervals. Why not just split up the intervals and write:

    [tex]a_1=\frac{1}{\pi}\left(\int_{-\pi}^{0} (1+x\pi)\cos(x)dx+\int_{0}^{\pi} (1-x\pi)\cos(x)dx\right)[/tex]

    However it is an even function so there are short-cuts for computing them. But for now, you may want to just do it this way.
  5. Dec 7, 2011 #4
    Great I understand completely now, thanks everyone. :smile:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook