[sdiy] Pole Mixing

David Moylan dave at expeditionelectronics.com
Fri Apr 9 18:50:14 CEST 2021

Working out the algebra to handle the feedback signal made me realize 
something about the Xpander implementation.  Rather than including a mix 
of the true dry input signal needed for certain modes, the Xpander 
switches the first integrator essentially into a buffer.   This makes 
the mix from the first integrator section a "dry" signal and the rest of 
the transfer function is then 3 pole based.   That means the feedback 
signal in that structure, for those modes, is also a 3 pole low pass 
signal instead of the 4 pole low pass when the integrator is engaged.

Makes me curious about how that will effect the transfer functions with 
feedback applied.   Will maybe have to set up a new page dedicated to 
the exact Xpander structure after I get this feedback signal worked out 
for the original app. Down a rabbit hole...

On 4/9/21 10:00 AM, Richie Burnett wrote:
> Taking the feedback from after the 4th pole makes all of the responses 
> become 4th order when feedback is applied.  So even something 
> otherwise simple like a 1-pole low-pass filter can display resonance 
> when feedback is applied in this way.
> -Richie,
> -----Original Message----- From: David Moylan via Synth-diy
> Sent: Friday, April 9, 2021 2:19 PM
> To: synth-diy at synth-diy.org
> Subject: Re: [sdiy] Pole Mixing
> Thanks, Tom.   In practice, I do find quite a few interesting. LP1 +
> Notch sounds great.  And just being able to switch between LP4, LP2, LP1
> is also useful.  I don't get a lot of mileage out of the HP only modes,
> usually want some LP too, but that makes HP3+LP1 mode interesting.
> Though I agree, in the universe of all possible transfer functions the
> list is relatively small.  It also begs the question "how many of these
> could be approximated with 2 state variables in series?".   But that
> ignores the feedback paths which I haven't worked into the equations
> yet.  In the Xpander the feedback is always from the LP4 tap like it
> would be for standard low pass filter and I think I remember someone,
> maybe David Dixon, pointing out that it has interesting effects on the
> curves as resonance is increased.
> If you click on the slider in question you should be able to use arrow
> keys to step in .1 increments.  I thought that was fine enough to get
> close to some desired curve, after that get out the pencil and paper or
> a soldering iron!  All of the presets except the 20db LP shelf use
> integers anyway, seems almost necessary to get the cancellations
> required to make interesting curves.
> On 4/9/21 5:34 AM, Tom Wiltshire wrote:
>> Absolutely agree, that is a fantastic piece of work.
>> It makes all sorts of things about pole-mixing more obvious, 
>> including how few of the combinations are actually interesting, and 
>> as Richie said, how sensitive some of the combinations are.
>> If you’re still working on it, would it be possible to add boxes to 
>> type in the coefficients as an alternative to the sliders? Getting 
>> specific values with the little sliders is quite fiddly.
>> Thanks very much for this though - really great.
>> Tom
>> ==================
>>         Electric Druid
>> Synth & Stompbox DIY
>> ==================
>>> On 8 Apr 2021, at 23:24, 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
>>> sonic adventures!
>>> _______________________________________________
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David Moylan
Expedition Electronics
sonic adventures!

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