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A convolution of a convolution

  1. Jun 8, 2010 #1
    Hi,
    can someone please give me an example of what a convolution of a convolution would look like ?

    Thanks
     
  2. jcsd
  3. Jun 8, 2010 #2

    Char. Limit

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    Gold Member

    What do you mean by "look like"?
     
  4. Jun 8, 2010 #3
    as in:
    [tex]
    f*g = \int^{\infty}_{-\infty} f(\tau)g(t-\tau) d\tau
    [/tex]

    what would
    h*(f*g) look like ?

    -Thrillhouse
     
  5. Jun 8, 2010 #4
    I should think something along these lines:

    [tex](f*g)(t) \stackrel{\mathrm{def}}{=} \displaystyle\int_{-\infty}^\infty f(x)g(t - x) dx[/tex]

    [tex](h*(f*g))(t) = \displaystyle\int_{-\infty}^\infty h(y)(f*g)(t - y) dy = \displaystyle\int_{-\infty}^\infty h(y) \left( \displaystyle\int_{-\infty}^\infty f(x)g(t - y - x) dx \right) dy[/tex]
     
  6. Jun 9, 2010 #5
    thanks pbandjay
     
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