[sdiy] New filter project 8 pole / dual 4 pole morphing filter

[Theo]

This is a multifunction VCF idea I've been sitting on for quite a while.
The analogue part is already on a PCB and the digital part will follow soon
after.
However some help on the math side, especially the filter transfer functions
would be greatly appreciated.

It is a  combination of two 4 pole multifunction VCF but with e-pot based
output mixers.
This makes it possible to "morph" from one filtermode to an other by
cross-fading between the mixer settings needed.
Using the two filters in series (with same "pan" and "cutoff" settings)
allows up to 8 pole filter functions.
For a block diagram of the contraption please see;
http://members.home.nl/tidal/Morhp%20filter%20block%20diagram.gif

The filter is build on two PCBs.
PCB one holds two Vactrol based VCFs and the Cutoff CV inputs/led steering
for the Vactrols.
On the second PCB there is a ATmega8 AVR uC and a bunch of e-pot ICs.
The internal ADC of the AVR handles the CV input for:
- Resonance, morph & pan of both filters ( 6 CV inputs)
- Serial/Parallel and Ext-input level for the second filter (2 CV inputs)
The AVR also handles a small LCD, 4 buttons and encoders for manual
parameter control.

If there is enough interest I will make the PCBs and schematics available
later on when the proto is finished.

I've already calculated the mixer setting needed for all possible;
- Low-pass
- High-pass.
- Symmetric & asymmetric Band-pass
- 2 pole Notch & 4 pole Notch

My question what other filter functions are useful and what are the transfer
functions.
Other Notch and All-pass functions come to mind,
maybe there are even more filter types beyond these?

A search through the literature wasn't very helpful.
Either only basic LP, HP and BP functions where given
or just one formula describing every possible transfer function in the
complex plane.
The latter being far over my head.

First there are the Notch functions:
Going from the 2 and 4 pole Notch transfer functions my guess is that,

6 pole Notch would be:  (S^6 + 3S^4 + 3S^2 + 1) / (1+S)^2

and 8 pole Notch : (S^8 + 4S^6 + 6S^4 + 4S^2 + 1) / (1+S)^2

Is this right??
Also do there exist 3 pole, 5 pole and 7 pole notch functions, similar to
asymmetric BP?
What are the transfer functions of there?

Then there are the All-pass filters, what are the transfer functions for
these?
Again help would be appreciated.

Regards,
Theo