[sdiy] Pole Mixing (with Resonance)

David Moylan dave at expeditionelectronics.com
Fri Apr 9 22:47:56 CEST 2021

Got a resonance slider added.  I had to attack the math a few different 
ways, but finally got the proper cancellations and looks very simple in 
retrospect.  Definitely ruins the HP modes. :)

On 4/9/21 2:03 PM, David Moylan via Synth-diy wrote:
> Hi Brian.  This was inspired by the Xpander/Matrix filter but is more 
> of a general exploratory tool at this point.  I think most of the 
> names overlap but there are definitely some not implemented on the 
> Obies, such as HP4 and the double notch curves.  Those require all 4 
> poles plus a dry signal and the Obies don't have that capability.  The 
> curves are calculated on the fly from the theoretical transfer functions.
> I'm in algebra hell right now trying to work the math out to handle 
> the feedback signal.  It would be a lot easier with no dry signal but 
> once you start mixing that in you get different denominators that have 
> to be resolved and suddenly I'm looking at 8th order polynomials :(
> On 4/9/21 1:53 PM, Brian Willoughby wrote:
>> This is excellent! Thank you for sharing this online.
>> As a Matrix-12 owner, I appreciate the list of presets that cover the 
>> available modes. It looks like you've even included some modes that 
>> aren't available in the Oberheim. Is that correct?
>> Did you use impulse response measurements to obtain the frequency 
>> response?
>> The reason I ask is that I wrote a macOS CoreAudio application that 
>> can load various AudioUnit plugins and measure their frequency 
>> response by simply feeding a short, 1-sample impulse into the plugin 
>> and doing a Fourier transform on the result. This only works for pure 
>> LTI (Linear Time-Invariant) plugins, but it's spot-on for those that 
>> fall into the category (i.e. no distortion or envelope-controlled 
>> dynamics).
>> Brian
>> On Apr 8, 2021, at 15:24, David Moylan 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

David Moylan
Expedition Electronics
sonic adventures!

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