[sdiy] Pole Mixing

Andrew Simper andy at cytomic.com
Sun Apr 11 07:09:59 CEST 2021

```A few more notes on this stuff:

You can form any response high/low/band/notch etc from any filter core by
using the correct weights of the input and all stages used in the filter
and the resonance gain. So you can turn a 4 pole high pass into a 4 pole
low pass if you really want to. This also works with any order of filter,
so non-multimode 2 / 3 pole filters can similarly be made into multimode
filters.

For the linear 4 pole cascade, the shape of the high pass generated from a
4 pole low pass is not just the mirror of low pass, it's a kinda odd
shape, which has to do with the dc cancellation of the feedback term
(passband lowers with increasing resonance). The two pole linear versions
are symmetric, so you get the classic 2 pole high pass shape from the 2
pole low pass.

If you have non-linearities in the filter core then this cancellation of
terms to generate the different responses falls apart quite quickly, in a
similar way to not having the exact gains. So if you want a great sounding
growling and full high pass filter you're not going to get it by doing this
sort of thing, you're better off having the correct filter to start with.

Cheers,

Andy

On Sun, 11 Apr 2021 at 12:34, Andrew Simper <andy at cytomic.com> wrote:

> Also if you want to derive the frequency response yourself you solve these
> equations for hs:
>
> 0 = g (in - lp1 - k lp4) - s lp1
> 0 = g (lp1 - lp2) - s lp2
> 0 = g (lp2 - lp3) - s lp3
> 0 = g (lp3 - lp4) - s lp4
> hs = (m0 (in - k lp4) + m1 lp1 + m2 lp2 + m3 lp3 + m4 lp4) / in
>
> Cheers,
>
> Andy
>
> On Sun, 11 Apr 2021 at 12:21, Andrew Simper <andy at cytomic.com> wrote:
>
>> Hi David,
>>
>> I'm not sure you've got the correct frequency response on your page. You
>> may have better luck with this:
>>
>> (g^4 (m0 + m1 + m2 + m3 + m4) + g^3 (4 m0 + 3 m1 + 2 m2 + m3) s +  g^2 (6
>> m0 + 3 m1 + m2) s^2 + g (4 m0 + m1) s^3 +  m0 s^4) /
>> (g^4 (1 + k) + 4 g^3 s + 6 g^2 s^2 + 4 g s^3 + s^4)
>>
>> where g is the cutoff in hz, and k is the resonance feedback with 4 being
>> self oscillation, and the mixing terms are as follows:
>>
>> m0*(in - k*lp4) + m1*lp1 + m2*lp2 + m3*lp3 + m4*lp4
>>
>> Note that for the xpander uses inverting stages, I've used non-inverting
>> stages, so each other mixing terms needs to be negative, eg:
>>
>> m0, -m1, m2, -m3, m4
>>
>> Cheers,
>>
>> Andy
>>
>> On Fri, 9 Apr 2021 at 06:24, David Moylan via Synth-diy <
>> synth-diy at synth-diy.org> wrote:
>>
>>> Hi All.  I banged together a little web app to play around with filter
>>> pole mixing, of the Oberheim Xpander type.  You can mix poles in varying
>>> amounts and see the output magnitude shape as well as the transfer
>>> function.  Y axis is Db and X axis is log scale based on normalized
>>> frequency (so basically 1 equals the cutoff frequency).  Haven't done
>>> phase plot yet.
>>>
>>> If you have an interest in this sort of thing check it out:
>>>
>>> https://expeditionelectronics.com/Diy/Polemixing
>>>
>>> Cheers.
>>>
>>> --
>>> David Moylan
>>> Expedition Electronics
>>>
>>> _______________________________________________
>>> Synth-diy mailing list
>>> Synth-diy at synth-diy.org
>>> http://synth-diy.org/mailman/listinfo/synth-diy
>>> Selling or trading? Use marketplace at synth-diy.org
>>>
>>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://synth-diy.org/pipermail/synth-diy/attachments/20210411/58f8a3f8/attachment.htm>
```