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Convolution of exp(-mod(x))

  1. May 22, 2013 #1
    1. The problem statement, all variables and given/known data
    Prove that the convolution of [itex]e^{-\left|x\right|}[/itex] is [itex](1-x)e^{x}[/itex] for x<0 and [itex](1+x)e^{-x}[/itex] for x>0

    2. Relevant equations



    3. The attempt at a solution

    I plug through the integral in the standard way and take the limits as x tends to positive and negative infinity etc. But, I keep getting that the convolution is zero?

    Any help would be greatly appreciated.
     
  2. jcsd
  3. May 22, 2013 #2

    Dick

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    Science Advisor
    Homework Helper

    You're doing f*f, right? You don't need to take limits in x. You just need to write down the integral and carefully work out what the absolute values are on each interval. Show your work. How did you get 0?
     
    Last edited: May 22, 2013
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