transfer function order (was Re: filter waveform question)

[jhaible]

> Sorry I cannot resist, forgive my the following math outbreak:

Great descriptions, both yours and Ingo's.

> Our music circuits (filters) use only very little of the possible 
> pole/zero arrangements. 

The typical N buffered stages + one feedback loop filters can be described
as "polygon filters", because of their special pole locations.

> On the other hand it can be shown, that any H(s) can be reproduced
> by chaining or parallel use of second order filters (state variable),
> and first order sections (simple RC high or lowpass).

This is right for (ideal) linear filters. In the real world, with things
like
nonlinearity, headroom, and so on, they can sound very different.
Just think about two 2-pole sections in series. You will typically have
one high Q and one low Q partial filter. Which one will be the first stage
?
How does the second stage filter the distortion products, when the
first stage is (ever so slightly) overloaded ?

JH.