everyone.
Could someone explain me how to properly deal with limits in two-dimensional convolutions?
Namely, I need to convolve two "Step waves":
$$ H(t - |x|)*H(t - |x|)$$
I am trying to write it down like:
$$ \int\limits_{R^2} H(t-|x|)\cdot H(t - \tau - |x - \xi|) d\xi d\tau$$
Obviously, the first part is non-zero only if $t>|x|$, which is true in the upper quarter of the plane. But I am struggling to deal with the second part...
is it just
$$ \int\limits_{t-x}^{t+x}\int\limits_0^t (\tau-\xi) d\xi d\tau $$ ?
Doesn't seem so. I am misunderstanding something here.
Please, help.