# Covolution Integration Limits Help

1. Oct 10, 2011

### Fayez

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!

$$f(x) := \begin{cases} 1 & if \ 0<x<1 \\ 0 & otherwise \end{cases}$$

$$g(x) := \begin{cases} x & if \ 0 < x < 2 \\ o & otherwise \end{cases}$$

the conv of the functions as in the book is

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

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

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