If we have two functions: $\displaystyle f(t)$ and $\displaystyle g(t)$.

When taking the convolution we replace t with$\displaystyle \tau$ let's say for$\displaystyle f(t)$, so we didn't change it.

The fun ends when for the other function we write $\displaystyle g(t-\tau)$. If we have on the abscissa now $\displaystyle \tau$, so when we add the minus sign inside then we reflect the function across the $\displaystyle x = 0$.

Now we must move the function to the far left. So if I understand correctly we write $\displaystyle \infty$ instead of $\displaystyle t$ when integrated, because we move it to the left. Because if we have function $\displaystyle h(x+\infty)$ then we move it to the $\displaystyle \infty$ in the left direction.

But what about$\displaystyle \tau$?