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Convolution homework help

  1. Feb 18, 2007 #1
    The following is all in discrete time, n is an integer

    We are given that:
    [tex] h_2(n) = \delta ( n ) + \delta ( n-1 ) [/tex]

    I want to find the convolution of h2[n]*h2[n].

    I don't really understand how to solve this properly.

    [tex] y(n) = \Sigma_{k=-\infty}^{k=\infty} (\delta(n)+\delta(n-1)) \times (\delta(n-k)+\delta(n-k-1)) [/tex]

    So the [tex] (\delta(n)+\delta(n-1)) [/tex] pulls out because it is constant.


    [tex] y(n) = (\delta(n)+\delta(n-1)) \Sigma_{k=-\infty}^{k=\infty} \delta(n-k)+\delta(n-k-1) [/tex]

    How do I even solve this?
    The book gets
    h_2(n)*h_2(n) = [tex] \delta(n) + \2\delta(n-1) + \delta(n-2) [/tex]

    I don't understand how they get this.
    Last edited: Feb 18, 2007
  2. jcsd
  3. Feb 18, 2007 #2

    D H

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    Staff Emeritus
    Science Advisor

    You are not calculating the convolution correctly.

    [tex](h_2\ast h_2)(n) = \sum_{k=-\infty}^{\infty}\cdot h_2(k) h_2(n-k)[/tex]
  4. Feb 18, 2007 #3


    I'm going to to take a walk. That was a ridiculous mistake.

    thanks man :)
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