We have $f(t)$, $h(t)$ and we want to compute the convolution of these two functions.
So we will have a dummy variable τ for the product: $f(\tau)h(t-\tau)$ as we know...
Why we are not permitted to consider this:
if: $h(t - \tau) = h(-\tau-(-t))$ is true
then $h(t - \tau)$ is constructed like this:
invert $h(\tau)$
shift $h(-\tau)$ on the right for a constant (-t). If t > 0 then the function will be shifted on the left by t.
Instead of the steps above we say:
a. $\phi(\tau) = h(-\tau)$
b. $\phi(\tau - t) = h[-(\tau-t)] = h(t-\tau)$
which means the opposite from steps 1-2:
first we invert $h(\tau)$ for having $h(-\tau)$ and then shift $h(-\tau)$ by $t$ having: $h(t-\tau)$.
In this case if t > 0 we obtain right shift instead of left shift from steps 1-2.
It seems that the difference is among different constructive steps but which ones?
Thanks in advance.