When solving convolution integrals, the logic seems to be in defiance of the basic shifting property of equations. I'm confused.
This is the summary of the concept: Having been given $h(T)$, we'll define an $h(t-T)$, where $t>0$ creates a shift to the right, and $t<0$ means a shift to the left.
However that seems in total contradiction of how shifting should work! Normally, if you have $y(x), y(x-k)$ results in a shift of $k$ to the right. $h(t-T)$ equals $(h(-(T-t))$. So, if $t$ is positive, first we shift $h(T)$ to the right, and then we reverse $h(T-t)$ (delays are supposed to happen BEFORE reversals in the OOP), making a positive $t$ a shift to the LEFT.
Please help me reconcile this methodology - the contradiction mixes me up every time. The methodology seems constant for all books and lecture notes I could find online, so I don't know why I seem to be the only one with a problem. Verbal explanation from book
