Filters to Nyquist?

[Urs]

Yes, DC-blocking is one of those things. Another thing is that some designs use the transistors as diodes (grounded emitter or something?). Interestingly, some designs semm to even create a Chamberlinish SVF out of the 4 OpAmps of a Curtis Chip. I havn't had more fun with filter designs ever since "getting" the transistor ladder.

What's WDF btw?

[mystran]

Yes, DC-blocking is one of those things. Another thing is that some designs use the transistors as diodes (grounded emitter or something?).

Yeah there are plenty such variations (including 303) but those won't have the same linear response for the ladder proper either.

What's WDF btw?

Ah Wave Digital Filters...

[Z1202]

IIRC I had no trouble doing WDF discretization the trivial way (with the feedback path being the root and having the allowed single non-linearity) but that breaks down as well as soon as you want non-linear stuff in there.

Seems we have someone familiar with WDF here. Could you explain are there any practical benefits of using the WDF approach (compared to zero-delay feedback structures)? For the purposes of analog modeling, the WDF thing seems to me unnecessary overcomplicated. I never really got into that stuff, but I've got a feeling that one might even end up with exactly the same digital structure as in the TPBLT approach. Any thoughts on that?

Regards,
{Z}

[Z1202]

Yes, DC-blocking is one of those things. Another thing is that some designs use the transistors as diodes (grounded emitter or something?).

Yeah there are plenty such variations (including 303) but those won't have the same linear response for the ladder proper either.

I think that's the classical diode ladder structure, somewhat less famous than transistor ladder

[Z1202]

... differences in the ladder proper.

Could you explain what does the word "proper" mean in this context? Tried several online dictionaries, but to no avail.

Regards,
{Z}

[mystran]

... differences in the ladder proper.

Could you explain what does the word "proper" mean in this context? Tried several online dictionaries, but to no avail.

Ah, well, what I tried to say "the actual ladder ignoring the surrounding circuitry". Won't promise that was even correct usage of the word as I'm not a native speaker. It would probably have been better to say that even the linear open-loop response is different.

The thing is, if you use the transistors as diodes, you lose buffering, and you no-longer have 4 independent one-poles. But that's been discussed to death in other threads.

[mystran]

IIRC I had no trouble doing WDF discretization the trivial way (with the feedback path being the root and having the allowed single non-linearity) but that breaks down as well as soon as you want non-linear stuff in there.

Seems we have someone familiar with WDF here. Could you explain are there any practical benefits of using the WDF approach (compared to zero-delay feedback structures)? For the purposes of analog modeling, the WDF thing seems to me unnecessary overcomplicated. I never really got into that stuff, but I've got a feeling that one might even end up with exactly the same digital structure as in the TPBLT approach. Any thoughts on that?

Well, I wrote some WDF filters at some point to see if I could get anything useful out of them (and the answer turned out to be "not really"). It's really not all that complicated, but you'd probably want to automate the composition and scattering junction calculations one way or another, else your brain will probably explode (personally I just used C++ templates to compose the whole thing, which works kinda fine).

Benefits? I don't know really. You need to recalc the scattering junctions every-time impendances change which is hardly ideal, and if you analyze a filter manually you almost certainly end up with code that is much easier to deal with.

TPBLT? Haven't really tried that, but seems sensible. Stilson's ladder (was it "X1" that he called the version with a moving zero?) behaves so well that I've not spent much effort trying to fix that. Could try TPBLT for something else though.

[Z1202]

TPBLT? Haven't really tried that, but seems sensible. Stilson's ladder (was it "X1" that he called the version with a moving zero?) behaves so well that I've not spent much effort trying to fix that. Could try TPBLT for something else though.

I was playing around with Stilson's model for a while (the one with a compromise zero positioning) and remember being not fully satsified, which was one of the motivations for the TPBLT development. I'm not sure if the TPBLT ladder is sounding better or worse than the moving-zero Stilson's version. I think there must be some at least subtle differences in the amplitude response shape and more noticeable in the phase response.

FYI, regarding TPBLT, I have been doing a little bit more research (triggered by the discussion of time-variant stability which occured earlier on this forum). The subject seems rather complicated. One of the results I obtained is that the 1-pole TPBLT low/highpass (digital version of the RC-model) using canonical BLT integrator can have certain stability problems in the time-variant case if the cutoff exceeds half Nyquist (never had this occuring in practice though). Intuitively I'd expect the DF1 BLT integrator not to have that problem, but I'm not sure, this case is more difficult to analyse. Similarly, I have been able to show the time-variant stability of the 2-pole SVF in the analog case, haven't be able to analyse the same for the TPBLT version of the same filter.

Regards,
{Z}

[mystran]

TPBLT? Haven't really tried that, but seems sensible. Stilson's ladder (was it "X1" that he called the version with a moving zero?) behaves so well that I've not spent much effort trying to fix that. Could try TPBLT for something else though.

I was playing around with Stilson's model for a while (the one with a compromise zero positioning) and remember being not fully satsified, which was one of the motivations for the TPBLT development. I'm not sure if the TPBLT ladder is sounding better or worse than the moving-zero Stilson's version. I think there must be some at least subtle differences in the amplitude response shape and more noticeable in the phase response.

If you mean by "compromise zero" the version that just picks a static compromise, the version that moves the zeroes with linear relationship depending on poles behaves significantly better. You need some low-order poly to correct tuning of the poles (though, to be fair, at 2x oversampling the error without correction is about similar to what you'd expect from an analog, haha) but other than that you have close to constant self-oscillation gain.

Anyway, regarding small differences, I won't sign that small differences in actual response are hugely important. Even the particular tanh-approximation you'd use (for transistor ladder) can change things enough to give a larger audible difference.

[Z1202]

Anyway, regarding small differences, I won't sign that small differences in actual response are hugely important. Even the particular tanh-approximation you'd use (for transistor ladder) can change things enough to give a larger audible difference.

Generally I agree. However there are differences which keep things "musical" and those which aren't. IMHO, large differences which keep the "musical" sound are much more acceptable than small differences which don't. So it's all relative and, to an extent, subjective.

Edit: wanted to add, regarding TPBLT vs other methods, the beauty of TPBLT is that you exactly know in advance, how much off is your frequency response compared to the analog prototype, and no parameter prewarping (besides the cutoff) is necessary. So, it's a quick way to reasonable quality results

[aciddose]

Well, I have recently obtained 6 analogue synths that should technically sound very similar because all of their filter models would end up exactly like Antti's model. Ok, some use 4-OpAmps-On-A-Chip, some are discrete transistor circuits. Still, they all sound very, very different. There's still a lot of variety to be explored within the model.

there are many things over-looked due to stupid assumptions made by dsp people who don't fully understand electronics.

one major thing is that in the transistor and diode versions it's assumed that any complex non-linearity cancels out due to the differential amplifier - not true.

nobody discusses the reason for the biasing in the transistor version and the resulting difference in the diode version, and it's also assumed currents are equal in both - not true.

noise isn't considered in either circuit and the non-linear response of the output buffer is simplified to tanh - retarded.

nobody discusses the frequency dependence or hysteresis of the biasing circuit, the buffer, the feedback path.

there is no discussion of changes in supply voltage/current leading to changes in circuit parameters, nor that they are also dependent upon what the circuit is doing at any particular moment.

nobody mentions the simple fact that you can drive with different levels into the filter with little consequence to the apparent result, but which is actually significant.

i'd say the best thing you could look into is the fact that:

1) the conductivity of each stage is not equal compared to the others
2) the conductivity of each side is not equal to the other
3) the differential amplifier is not well approximated with tanh and is not perfectly balanced / symmetric
4) capacitance is different between each stage
5) the differential amp input is non-linear and contributes the most to over-all non-linearity / limiting of feedback (not the buffer, the base of the integrator chain)
6) many sums of non-linearity are fed into highpass filters before being fed into more non-linearity.
7) input currents (signal) significantly change the conductivity and biasing of the over-all circuit (frequency modulation)
8) highpass filters built with electrolytic capacitors can exhibit high frequency losses

[mystran]

Anyway, regarding small differences, I won't sign that small differences in actual response are hugely important. Even the particular tanh-approximation you'd use (for transistor ladder) can change things enough to give a larger audible difference.

Generally I agree. However there are differences which keep things "musical" and those which aren't. IMHO, large differences which keep the "musical" sound are much more acceptable than small differences which don't. So it's all relative and, to an extent, subjective.

The thing though, is BLT still wraps things near Nyquist a lot, and I'm personally not sure if that is musical change at all. Whether it's relevant with whatever internal samplerate you need for other reasons is another question.

[Z1202]

The thing though, is BLT still wraps things near Nyquist a lot, and I'm personally not sure if that is musical change at all. Whether it's relevant with whatever internal samplerate you need for other reasons is another question.

So do Euler-like methods, and usually way more than BLT (at the same SR). Besides, BLT fully preserves the relationship between amplitude and phase responses, which might be important in transients. Personally, I think at 2x oversampling the frequency axis distortion by BLT is quite acceptable. Notably, it's the same 2x oversampling which might help the time-variant stability issues I mentioned earlier.

[Z1202]

and I'm personally not sure if that is musical change at all.

In my experience it's quite tolerable musically. YMMV