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Covolution Integration Limits Help

  1. Oct 10, 2011 #1
    I am having a little problem finding the limits of integration to this conv. just for the sake of fulfilling my curiosity. Although it is stated in the textbook but I can not do the actual integration and get the same results!


    [tex]f(x) := \begin{cases} 1 & if \ 0<x<1 \\ 0 & otherwise \end{cases}[/tex]

    [tex]g(x) := \begin{cases} x & if \ 0 < x < 2 \\ o & otherwise \end{cases}[/tex]

    the conv of the functions as in the book is

    [tex](f*g)(x) = \int_{0<u<1 and 0 < x-u <2} f(u) g(x-u) du [/tex] with limits of

    [tex]\int _{min[1,max(0,x-2)]}^{max(0,min(1,x))} (x-u) du[/tex] with also limits of

    the correct answer is:

    [tex]f*g = \frac{1}{2} \begin{cases} x^2 & if \ 0<x<1 \\ 2x-1 & if \ 1<x<2 \\ -x^2+2x+3 & if 2<x<3 \\ 0 & otherwise \end{cases}[/tex]

    the textbook is A First course in Fourier Analysis https://www.amazon.com/First-Course-Fourier-Analysis-Kammler/dp/0135787823, Page 94


    The help will be highly appreciated
     
    Last edited: Oct 10, 2011
  2. jcsd
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