[sdiy] Pole Mixing

Tom Wiltshire tom at electricdruid.net
Fri Apr 9 19:19:26 CEST 2021


I’ve not heard one in the flesh, but it’s been said that the resonance on some of the Xpander filer modes is somewhat underwhelming, and this could be why.

Building the same structure with a 3320 filter instead of a 3372 makes more sense and gives you free access to the dry signal and therefore no need to do the cap switching trick (although that’s still an efficient way to generate a pile more responses cheaply).

Tom


> On 9 Apr 2021, at 17:50, David Moylan via Synth-diy <synth-diy at synth-diy.org> wrote:
> 
> 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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