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Convolution - prove commutative

  1. Sep 30, 2006 #1
    anyone know how to prove that it is commutative...

    as if f *g = g*f
  2. jcsd
  3. Sep 30, 2006 #2


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    Try a change of variables.
  4. Oct 1, 2006 #3


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    You might want to start with the definition: the convolution of f and g is
    [itex]f*g(x)= \int_0^\infty f(x-t)g(t)dt[/itex] and, of course, [itex]g*f(x)= \int_0^\infty g(x-u)f(u)du[/itex] (I have intentionally used a different variable of integration here). Hmm, in one you have f(x-t) and in the other f(u). Does that substitution benndamann33 mentioned leap to mind?
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