[sdiy] Pole-mixing, Highpass filters, and switching the first stage off

[Andrew Simper]

On 6 September 2014 07:00, Richie Burnett <rburnett at richieburnett.co.uk> wrote:
>
> I think you can do that Tom.  Switching out the first capacitor (really this just reduces the capacitance here and moves the first pole way up to a very high frequency,)  is really just another way of getting access to the raw input waveform whilst using only a 4 input mixer.  This is instead of having to have a mixer with five weighted inputs instead of four.  The price you pay is that you can't achieve a 4-pole HPF response though, unless you mix the input with a weighted mix of the 4 separate pole outputs.


Just remember that when using the pole mixing you are basically
creating an FIR out of the poles, so this is easiest with alternating
polarity for each tap, including the input.

Yep spot on. This means that when the first stage is bypassed you get
the input, but now your only have 3 one pole low passes with feedback,
so you need more feedback gain to get resonance self oscillating. It
looks like the Oberheim engineers figured this was the best approach
to double the number of responses from the 8 inputs of the multiplexer
to 16.

>
> The "pole-mixing" is a cheap way to get multi-mode responses but the high-pass and band-pass responses are a little funky looking when resonance is introduced, because of the way the poles split as feedback is applied. Not really what you would expect them to look like on paper, but good enough for making music ;-)


Here are some plots I did to show the difference between a true 4 pole
cascade (4 1 pole high pass cascaded with feedback) and a 4 pole
generated from pole mixing:
http://www.cytomic.com/files/dsp/cascade-hp4-vs-lp4hpxtaps.pdf


>
> Also you can get strange responses like a "1st order 6dB/oct" filter with adjustable resonance.  Of course a 1st order filter technically cannot be resonant at all because that requires pairs of poles, and the response is really 4th order as soon as any feedback is applied around the loop. Pspice, Multisim or MATLAB are great for graphing all of these different responses!
>
> -Richie,


You can get 6 dB out of a 2 pole SVF or 2 pole Sallen Key as well
quite easily. For the SVF just sum the band with the high or low to
make the high or low 6 dB instead of 12, for the Sallen Key either
feed the input to the second state, or take the output from the first
stage.

All the best,

Andy


PS: sorry for the double up, I posted the first email in html format.


>
>
> -----Original Message----- From: Tom Wiltshire
> Sent: Friday, September 05, 2014 11:19 PM
> To: synthdiy diy
> Subject: [sdiy] Pole-mixing, Highpass filters,and switching the first stage
> off
>
>
> Hi All,
>
> I've got a question about pole-mixing filters of the Oberheim Xpander/Matrix
> type. Olivier Gillet gives a nice explanation of the concept:
>
> http://mutable-instruments.net/static/documentation/pole_mixing.pdf
>
> and the schematic..
>
> http://mutable-instruments.net/static/schematics/Shruthi-Analog-PoleMixing-v02.pdf
>
> Olivier's filter does the same as the original Xpander filter and switches
> out the first stage for some of the responses.
>
> The point of this seems to be to allow access to the input signal directly,
> since now the output of the first stage is just the input (or the input
> inverted, anyway) which is required for the high pass filters.
>
> The question is this - given that we're just adding poles into a mixer, why
> not just add a resistor directly from the input, instead of going to all
> this trouble of switching the first stage out?
> What am I missing? Is my assumption about the purpose of the switch wrong?
>
> Thanks,
> Tom
>
>
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