Hmm wouldn't be far from this Oid to make a Oberheim 12db Filter?
https://www.kvraudio.com/forum/viewtopic.php?p=8194407
"I'm implementing a VA LadderFilter following Will Pirkle's synth book. A cascade of four VA one-pole filters is used to achieve the filter. However, there's a twist. From what is called Oberheim Variations, more filter responses (LP, BP, HP, each 2-pole or 4-pole) are achieved.
It is done by taking the outputs of each cascaded stage separately as well as the input and mixing them together following a set of coefficients A through E. So the equation goes like:
output = A * (input + feedback) + B * LPF1 + C * LPF2 + D * LPF3 + E * LPF4
I have the coefficients for the above mentioned filter types, but I recon there is more to be discovered.
The book references a research paper by Välimäki and Huovilainen, where these coefficients are taken from. However, the paper doesn't explain how the coefficients came to be.
A further reference points towards a service manual for the Oberheim Xpander. There's several relevant information on pages 26 and 27, but I don't see the connection between the provided information and the coefficients I already have.
So I was wondering if anybody could point me in the right direction, how to obtain the rest of the coefficients. I am particularly after the 3- and 1-pole versions, notch-filters and allpass-variants."
So the only missing piece in the puzzle are the A-E coeficients.
From the KVR Thread:
5.5 of VAFilterDesign (rev 2.1.2) contains an explanation of the principles.
https://archive.org/details/the-art-of-va-filter-design-rev.-2.1.2
Here is also a c++ example of an Oberheim Filter:
https://github.com/ddiakopoulos/MoogLadders/blob/master/src/OberheimVariationModel.h
My math is not so good to understand this