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Homework Help: Prove Convolution is Commutative

  1. Apr 14, 2010 #1
    1. The problem statement, all variables and given/known data

    Let f,g be two continuous, periodic functions bounded by
    [tex]
    [-\pi,\pi]
    [/tex]

    Define the convolution of f and g by

    [tex]
    (f*g)(u)=(\frac{-1}{2\pi})\int_{-\pi}^{\pi}f(t)g(t-u)dt.
    [/tex]

    Show that
    [tex]
    (f*g)(u)=(g*f)(u)
    [/tex]

    3. The attempt at a solution

    I think the way I'm supposed to do this is by interchanging variables, but I'm stuck. If I let k=t-u and try to switch the variables around, I end up with (-1/2pi) times the integral of g(k)f(k+u)dk. Am I doing this wrong? Is there a better way to solve this?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Apr 14, 2010 #2
    can you check the integral of f(t)g(t-u) or f(t)g(u-t)
     
  4. Apr 14, 2010 #3

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Are you sure you stated the problem correctly? Shouldn't the integrand in the convolution be f(t)g(u-t)? That might help.
     
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