formula for the zeros of a parallel connection of filters?

[Music Engineer]

What robin wants to solve is the total filter he gets when combining two filters in parallel, which probably happens to be approximately the deepest math you might encounter when working with (idealized) linear time-invariant filters. Why he actually wants to do that is beyond me as well... not that it isn't curious exercise anyway.

i originally wanted this for determining the zeros of the parallel connection of the lowpass and highpass in the crossover until it occured to me that in this special case the zeros are much easier to find - namely at the reflections of the poles in the unit circle (because we know that the sum-filter is allpass - i know, you know that, just for the record). i posed the problem in the general case because initially i wasn't aware of this simplification in my special case.

currently busy in codifying all this allpass compensation stuff - i will take a closer look at this diffeq approach when i'm done with that. although i have my solution for the concrete practical problem at hand, the general problem is nonetheless interesting enough to be investigated further and a solution to it might be really useful at some poit.

[vadarfone]

Ah, thanks a lot for the reply.

It did look mighty complex.

I will have a search through the forum and see what I can find to help me on my way. A year or so down the line, I am sure I will refer back to this thread and understand a lot more about it.

Cheers!