change convolution function if signal is above threshold? 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
Is there a name for such a kind of filter?


No. (Ok, there probably is, but it's not commonly used)

The point is that your filter is not a linear system, and thus has properties that make it unsuitable for most applications. Hence, I'd neither heard of someone using it, nor of someone giving it a name.