[sdiy] Pole Mixing

David Moylan dave at expeditionelectronics.com
Sun Apr 11 14:34:44 CEST 2021


A bit hard to follow here, Andrew. Your main transfer function looks the 
same to mine if g=1, except that you have the k term included in the 
denominator but not the numerator.  In general, my denominator looks 
like yours with the k term, and in the numerator the feedback only 
changes the term on s^0 which goes from

a - b + c - d + e;

to

(a * (1 - k)) - b + c - d + e;

David Dixon shared his Excel spreadsheet with me, so verify with that as 
well.

Dave


On 4/11/21 12:21 AM, Andrew Simper 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 <mailto: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
>     <https://expeditionelectronics.com/Diy/Polemixing>
>
>     Cheers.
>
>     -- 
>     David Moylan
>     Expedition Electronics
>     sonic adventures!
>
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-- 
David Moylan
Expedition Electronics
sonic adventures!

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