How Do You Calculate Convolution with the Sign Function?

[PhysicsGirl90]

Hello all,

I am having some trouble calculating a convolution. For the question, and my attempt at a solution, please take a look at the pic. Can someone please point me in the right direction?

 

[vela]

I didn't check your work closely. If it's correct, you probably want to now look at two cases separately: t<0 and t>0.

The other suggestion I'd have is to try using $\tau-t$ as the argument of sgn instead of the exponential. It might make the integral easier to analyze.

 

[PhysicsGirl90]

Ok, I will try it and see what i get

 

[rude man]

Tried it that way, got 2exp(-t) -1