MS 20 filter a 3-pole?

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I just read this:

http://www.willpirkle.com/Downloads/AN-5Korg35_V3.pdf

And he seems to suggest that it is a 3-pole filter, in the buffered version it is basically a non-resonant LP sent to a 'regular' sallen-key and the output is tapped from the first pole. This doesn't make much sense...where does he get that extra pole from?

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That didn't make sense for me either when I read this the first time :D

The thing is that Will Pirkle has tried to find a way to get more or less directly the "digital simulation scheme block" from the "analog circuit scheme block". So, he looked for the analog signal path and replaced all the obvious analog blocks with digital blocks (the Sallen-Key being here two serial 1-pole lowpass filters and a 2 pole band pass filter in the feedback or a one pole lowpass filter is the block scheme is optimized). Then, he uses a strategy he developed, using the TPT stuff and a trick he detailed in his articles, to simulate the whole block scheme without delay in the feedback loop. One of the interesting things he did is to add a "feedback" output in the TPT simulation structures, allowing him to mix combinations of TPT filters in a feedforward and a feedback path.

If you try to write the transfer function of the whole block scheme, you will see that it will be a 2-pole digital filter thanks to simplifications that will occur, and that it is equivalent to what you get with a standard discretization method.

The main interest of that method for him was also that it gives an easy way to insert a "naive" non linearity in the block scheme, since it is following the analog circuit path with the cost of an "extra pole". However, you will see that things become more complicated if you try to use a "not naive" non linearity, or if you try to model another circuit with this method where the "analog blocks" are not simple lowpass or highpass filters.

I tried in the past to apply the same method on a Twin-T topology synth filter. I had not simple at all 2-poles analog blocks, for which the whole TPT stuff is useless since you need to use a TPT SVF structure with gains on the LP/BP/HP outputs, which breaks its main strength when the parameters are modulated. Then I was stuck when I was trying to have a not naive non linearity instead of a simple waveshaper in the signal path, with zero-delay feedback + good behaviour on time-varying cases... So I dropped Will Pirkle's method and used something else instead...

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It's just a regular 2-pole and could be implemented canonically with 2 states just fine. For some reason he wants to split the LP and HP zero-configurations of the first pole into separate implementations, but that doesn't really make any difference if the 1-poles themselves are assumed linear (as is the case for his model).

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Thanks for the explanations Mystran and Wolfen, that makes sense. Think I'll buy the synth book in-anyway, it looks useful, and his 'half-ladder' is pretty sneaky and smart, but I would have called it 3/4 ladder :clown:
Wolfen666 wrote: I tried in the past to apply the same method on a Twin-T topology synth filter. I had not simple at all 2-poles analog blocks, for which the whole TPT stuff is useless since you need to use a TPT SVF structure with gains on the LP/BP/HP outputs, which breaks its main strength when the parameters are modulated.
Coding a drum machine? Btw, I think you could make a TPT SVF with multiple inputs - that might be a little more stable(?). I just googled the Twin-T topology, saw a nodal analysis - it looks hairy :eek:

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Yes I think I questionned people about that a while ago, I discovered the uses of a few other digital filter structures. However, I still need to do some R&D to have everything working as expected in nonlinear + time-varying cases. I will probably talk about that again when I will be done ;)

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