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Fourier series

  1. Feb 19, 2009 #1
    1. The problem statement, all variables and given/known data

    find the fourier series for the function

    0 -pi<x<pi
    f(x)={
    sinx 0<x<pi


    2. Relevant equations



    3. The attempt at a solution
    I don't know how to do this and can't find a good explanation anywhere, any kind of help is appreciated...even just a push in the right direction
     
    Last edited: Feb 19, 2009
  2. jcsd
  3. Feb 19, 2009 #2
    Are you saying your function is
    f(x) = 0 x<-pi
    = sin(x) 0<x<pi
    = 0 x>pi
    If so, that is not periodic and does not have a Fourier series in the usual sense, although it probably has a Fourier transform. Is that what you want?
     
  4. Feb 19, 2009 #3
    we are supposed to assume that the function is continued outside of the interval with period 2pi periodically.
    i just realized there was a mistake with the bounds also, but i fixed it now. it is a piecewise function which equals 0 from -pi to pi and sinx from 0 to pi
     
  5. Feb 19, 2009 #4

    Dick

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    I'm going to guess that the problem is to find the fourier series on the interval [-pi,pi] of the function f(x)=sin(x) for x in [0,pi] and f(x)=0 for x in [-pi,0]. If so, then the coefficients of that series are defined in terms of integrals of sin(x) times sin(nx) and cos(nx). Since f(x)=0 for x<0, just integrate from 0 to pi. Can you do any of them?
     
  6. Feb 19, 2009 #5
    ok thanks so then i have integral from 0 to pi of sinxcosnx dx. would this just give 0 since sinx is odd and cosnx is even, giving an odd function?
     
  7. Feb 19, 2009 #6

    Dick

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  8. Feb 19, 2009 #7
    oh right. thanks so much!
     
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