Let's say I have a signal $s(t)$ and two filters $f_1(t)$ and $f_2(t)$, I also have a threshold $A$.
Now I define $a_1(t)$ as $a_1(t) = \min(s(t),A)$, then I do the convolution of $a_1* f_1$.
Now I also define $a_2(t)$ as $a_2(t) = \max(0, s(t)-A)$, (ie. whatever is above $A$) then I do the convolution of $a_2*f_2$.
The total result $a$ is $a=a_1*f_1+a_2*f_2$.
Is there a name for such a kind of filter?
Basically, I do some convolution filter on some part of the input, and some other convolution on the remaining part of the input, then add the results
This can also by generalized with more than 2 filters, or continuous thresholds and continuously parametrized convolution functions