four-pole state variable filters

[Martin Czech]

> 3. you can't change any of the filter coefficients independently in a casaded
> design - i really don't know if this is good or bad?

Beeing a two pole you have only two parameters for the poles, and two for
the zeros.  They are quite easy to understand, this could be an advantage
(of course if we set the coefficents for s^0 to 1.0, this is the normal
way to write it down)
> 
> here's a more general question, related to 3:
> 
> - in a standard 2-pole SVF design, changing the resonance of the filter
> changes the coefficient of s ( right? ).  what does the resonance do in a
> 4-pole filter? does it just change the coefficient of s^3? what about s^2 and
> s?

Yes this is related, in a general 4 pole structure that i tryed to
describe in my last mail cincerning this topic you have accordingly 3
parameters for the zeros (ok, maybe four, if you add a direct signal-in
tap) and 3 parameters for the poles.  This is not so easy to grasp
what they are doing. Perhaps a clever implementation could bring more
meaningfull parameters. The three pole parameters are the coefficients of
the related linear differential equation and thus control pole location,
ie. also resonance.  The math gets quite ugly, you have to find the zeros
of an third order polynome, I think there is no analytical method to do
this, you have to use numeric solutions ...

And I think, tracking of the integrators is an issue,too. One could
adapt the capacitor values for each individual ota. If the otas are
driven with op-amp current mirrors, they should track.

OTOH a cascaded two pole version gives easy to grasp parameters, but
has certainly problems for high resonance applications where tracking
is very important. Since each filter (as a seperate module) has it's
own expo converter, the tracking will be worse, as you have allready mentioned.

Why not combine the two ideas: drop the seperate module approach for
the two two poles, if they are on the same pcb, they can be controlled
by the same current generator in the way I desvcribed it above for the
four pole. But they still have the cascaded two pole form, so meaningfull
parameters are combined with good tracking.

The switching problem you have mentioned is not so bad: only these
configurations make sense: lp->lp, hp->hp, bp->bp , no->no. I doubt if
any other bp configurations make any audible difference. lp->hp gives
a kind of bp, but this is allready there, so no need.

Maybe it is not so stupid to use two two poles with the same current
source, independend mode switches and a chaining switch. This could give
parallel as well as serial configurations.  A parallel thing could be
used as frequency splitter... 
And maybe an additional feedback path could be added for the serial form,
from the last stage back to the input.


Just some ideas. 

m.c.