convolution procedure question

mudcat

Hello. I need help with understanding one part of the convolution procedure. This doesn't involve any particular homework problem, but I'll use the following problem as an example:




I have 2 questions. If anybody can help me, I would greatly appreciate it.

1. When x(0-T) crosses the rectangle part of h(T), I understand the reasons for the integrals with the limits of t-1 to 0 and 1 to t-3. Can anyone confirm that the integral from 1 to 0 happens because x(0-T) is larger on the x plane than h(T)?

2. I don't remember how to obtain the inequalities of T for each respective integral (1 < t < 2, 2 < t < 3, etc. ) This eludes me. Please help. Thanks.

Mark44

The image is not showing, so we have no clue as to what the problem is.

Why are you writing x(0 - T)? Isn't that the same as x(-T)?

mudcat

Sorry, that should have been (t - T). Here's the corrected image, I hope: