Coefficients for Oberheim Variations of a VA Ladder Filter

[TheWaveWarden]

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.

[Z1202]

5.5 of VAFilterDesign (rev 2.1.2) contains an explanation of the principles.

[TheWaveWarden]

Exactly what I was looking for! Thanks!

[earlevel]

From what is called Oberheim Variations, more filter responses (LP, BP, HP, each 2-pole or 4-pole) are achieved.

"Oberheim variations"—funny...the idea was actually taken from Electronotes...but yeah, I don't think it had been implemented in a production synth before the Xpander.