# Coefficients for Oberheim Variations of a VA Ladder Filter

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TheWaveWarden
KVRist
Topic Starter
267 posts since 10 Apr, 2020
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
KVRian
1443 posts since 12 Apr, 2002
5.5 of VAFilterDesign (rev 2.1.2) contains an explanation of the principles.

TheWaveWarden
KVRist
Topic Starter
267 posts since 10 Apr, 2020
Exactly what I was looking for! Thanks!

earlevel
KVRian
608 posts since 4 Apr, 2010
TheWaveWarden wrote: Wed Aug 25, 2021 8:51 amFrom 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.
My audio DSP blog: earlevel.com