Just for the lulz...here's a first simple model I cooked up using mystrans method. It's a 2-pole lowpass filter with nonlinear feedback, inspired by the Korg MS stuff.

This filter has some sweet spots (I really dig the sound of its self-oscillation), but it needs work. The differential equations I used as a starting point are:

dy1/dt = f*(in - y1 - g(r*y2))
dy2/dt = f*(y1 - y2 + g(r*y2))

where 'r' is resonance, 'g()' is the nonlinear function. Certainly additional equations are needed to improve the sound, I keep it as simple as possible. Any suggestions welcome!

The code:

Last edited by Richard_Synapse on Thu May 24, 2012 7:13 am; edited 1 time in total

Damn you Richard - that was exacly the structure that I was desperately trying to solve, you shouldn't make it look so easy

I got stuck on the notion that there is dual feedback from the output - thus 2 diffent denominators!

Now my head really hurts.

That's exactly the 2-pole filter I use in my synth!


This is not strictly in accordance with your equations. Your code realizes a filter with the resonance gain r pre-saturator, while your equations have r at the output of g().

You don't need solve the whole feedback loop for both integrator outputs. Instead, just solve for y2, then all inputs for the first lowpass stage are available and you can compute y1 in the traditional way (probably cheaper).

True- fixed



Yeah, I just copy+pasted straight from Maxima.

Richard

so, where does this system come from? is this an RLC-circuit or mass-spring-damper system (which are, if i'm not mistaken, mathematically the same thing)?

I got it from Antti Houvilainen's thesis:
http://www.dsprelated.com/showabstract/139.php
(Figure 4.4, page 28 )

cool. now that i'm finished with Vadim's book, i needed something new to read anyway. THX.

I got the rough concept from the Stinchombe paper about the MS10/20. It's not really a MS filter though, the resemblance is just that the output is clipped then fed back into the first capacitor. In the ladder filters the output gets fed back to the input, but this doesn't seem to work well for a two-stage 12dB filter (maybe there's a way but I haven't seen it yet).

Richard

You can copy-paste the solution for one output, then remove that output from the set of equations/unknowns and resolve. This will give you rest of the unknowns in terms of what's already solved.

That typically results in less work. It's not really ideal, and I already have a method for generating better code, but it's still very much work-in-progress.

ah - OK, thanks. yes, this must then be the same filter as in Antti's thesis.

For two sided RC model:


  V1 -> ---R---o----C--- <- V2
               |
               v Vout


We observe that voltage over the resistor Vres = V1-Vout and voltage over the capacitor is Vout-V2 (ie Vout = Vcap + V2, Vres = V1-Vcap-V2), so we have

footnote: I'm "measuring" voltages over the components "backwards" from right to left; this is safe as long as it's consistent and saves a bunch of negations.. it makes perfect sense if you think of Vres and Vcap as voltage drops over the components

 dVcap/dt = (V1-Vcap-V2)/(R*C)
  Vout = Vcap + V2


Discretize (for example) as:

 yOut = vCap + f*(v1-yOut-v2) + v2
 vCap += 2*f*(v1-yOut-v2)


Observe that in the special case of v2 = 0, this is just the usual low-pass. In the special case of v1 = 0, the output is v2+lp(-v2) which for one-pole is clearly valid high-pass and "vCap" here is just the voltage over capacitor (ie Q/C where Q is the charge stored) and no-longer a ground-referenced absolute voltage (yOut is still ground referenced).

That depends on on which Korg chip your talking about; for the people who haven't yet read Tim's excellent paper, the first version was a Sallen-Key design, the second was an OTA design. The Sallen key had diode limiting in the feedforward path, and the OTA version had the diodes in the feedback path.

In my honestly moronic opinion - your filter looks closer to a Sallen-Key than an OTA. So maybe - for variation - you could move the TanhXdX, and maybe even add the asymmetrical resonace that Tim refers to.

Andrew

Yeah, I built the Sallen Key version in PSpice, the OTA version I haven't looked at yet. Soundwise the SK version is a matter of taste, however, I only like the self-resonance so I ended up with a mix of both structures. When a signal is driven through the Korg35 chip, it seems to affect both the cutoff and resonance, which is truely weird. Not really a fan of that...also an authentic model of that will be a lot harder to derive.

Richard

Now that's the beauty of digital, we decide what's cool or not

they're both the same sallen-key structure. the ota version just uses otas instead of transistors for the trans-conductive elements and does away with the a-symmetrical buffer. the result is that the revised version (in the ms-20 r2) is all odd-harmonic, while the ms-10, ms-10 r1, and ms-20 are balanced even-harmonic with the clipper in the signal path.

the best filter of all is the transistor based without clipping in the feedback path.

http://soundcloud.com/aciddose/resszor
http://soundcloud.com/aciddose/resszorb

(pad mixed in, only the ramp + res sound is of interest.)

the frequency modulation is due to direct modulation of the current through the transistors. the effect is identical to subtracting the signal from the base voltage - you're just changing the VBE.

the feedback is NOT modulated. there is a significant dc offset and the clippers are applied to the dc-biased signal. this results in the clipping having more effect on one side than the other. solution? apply an a-symmetrical clipping.

http://soundcloud.com/aciddose/ressy-pulse