Should I be interested in something else than TPT/ZDF filters at this point of time?

[soundmodel]

Should I be interested in something else than TPT/ZDF filters at this point of time?

Based on what I've gathered it seems like ZDF filters are the best compromise for musical applications. Some others do work, but they don't seem to have a good balance for the needs in musical applications like guarantees for stability in time-varying use.

Here it was SVF:

www.dafx14.fau.de/papers/dafx14_aaron_w ... s_for_.pdf

But here it's almost all TPT/ZDF:

https://www.native-instruments.com/file ... _2.1.0.pdf

These particular forums also seem to be pushing towards ZDFs in many discussions.

Whereas in e.g. here:

http://dafx14.fau.de/papers/dafx14_aaro ... s_for_.pdf

they still talk about audible clicks when changing coefficients of Direct Form II structures.

[JustinJ]

Should I be interested in something else than TPT/ZDF filters at this point of time?

Based on what I've gathered it seems like ZDF filters are the best compromise for musical applications. Some others do work, but they don't seem to have a good balance for the needs in musical applications like guarantees for stability in time-varying use.

Here it was SVF:

www.dafx14.fau.de/papers/dafx14_aaron_w ... s_for_.pdf

But here it's almost all TPT/ZDF:

https://www.native-instruments.com/file ... _2.1.0.pdf

These particular forums also seem to be pushing towards ZDFs in many discussions.

Whereas in e.g. here:

http://dafx14.fau.de/papers/dafx14_aaro ... s_for_.pdf

they still talk about audible clicks when changing coefficients of Direct Form II structures.

For most cases I'd recommend using Andy Simper's SVF from here:

https://cytomic.com/files/dsp/SvfLinear ... mised2.pdf

If you go to the last page you'll see everything you need to replace conventional RBJ biquads DFI and DFII. These filters don't have any problems (i.e. blowing up) under extreme modulation and they're a breeze to implement. There's no reason to use the old DFI and DFII biquad stuff anymore.

Equally, the filters in The Art of Filter Design will do you well.

Then, for filters with analog modelling, saturation etc...that's a whole different ball game.

[soundmodel]

Yes, I don't know why many synths seem to have other models still though. Maybe it's for historical reasons. E.g. Camel Audio's Alchemy had: 31 different filter types including 18 analog modelled filters.

I don't know, but my perception has been that many SVF implementations I've heard in synths have been "bland" sounding compared to supposed BLTed analog models. They sound clean, but that's not always desirable. But I thought the SVF or the ZDF or both can also implement non-linearities easily. But I don't think I've actually heard such filter.

Yes, in the Native Instruments paper it says:

This results in digital filters having nice amplitude and phase
responses, nice time-varying behavior and plenty of options for nonlinearities.

[mystran]

I don't know, but my perception has been that many SVF implementations I've heard in synths have been "bland" sounding compared to supposed BLTed analog models. They sound clean, but that's not always desirable. But I thought the SVF or the ZDF or both can also implement non-linearities easily. But I don't think I've actually heard such filter.

This TPT/ZDF business is usually more or less just trapezoidal integration. With frequency prewarping this is BLT, but done on the "topology" rather than transfer function; hence "topology preserving" as we integrate the ODE directly in it's original form. If you just take a linear "analog" filter and apply trapezoidal integration this way, you get a numerically robust filter that modulates in a clean way. It will sound "bland" though if we leave it at that.

If you want to model the saturation and/or distortion found in many analog filters, then essentially you need to build a circuit model of whatever level of sophistication, then apply numerical integration to that circuit model. If we choose trapezoidal integration and prewarp, then we essentially have a BLT again, but now applied to the equations describing the more sophisticated model. In a sense, it's still the same basic TPT/ZDF business, but applied to a more specific circuit rather than just an abstract linear topology. There are older "analog modelled" filters that attempt to model the non-linearities without using trapezoidal integration, but the integration scheme and the model being integrated are sort of orthogonal concepts.

SVF as such is just a topology. It can be implemented in various ways. An "analog modelled" SVF is often a model of SEM-1A filter (or something very similar) if not otherwise labelled, though for example Wasp filter is also an SVF, but drastically different in how it behaves, thanks to different non-linearities.

Now.. the question.. should you bother with something other than trapezoidal filters? For the most part, for regular utility filters the linear trapezoidal SVF is numerically great, modulates fine and not significantly more expensive than direct forms (which are not great numerically). For analog models these days, I'd go with trapezoidal as well, even though this means a bit of difficulty with non-linearities, because we're solving an implicit system; theoretically we need to use Newton or some other iterative scheme to get accurate results, but in practice this method or some slight variation can often work reasonably well in simple cases, especially when you're oversampling anyway to avoid aliasing. That said, even if Newton is iterative, it can often be made to converge pretty fast (eg. 1-2 iterations average) with oversampling, so don't dismiss it if you can't get good enough results from non-iterative methods.

Beyond TPT/ZDF though, polyphase FIR filters are useful for oversampling/resampling and all-pass lattices (or lattice-ladders) can be handy for things where you want to use longer delays... and perhaps something else too, though I can't immediately think of an example. Like trapezoidal filters, all-pass lattices are kinda well behaved numerically, though it's the "non-normalized" variant that is numerically better I guess, where as the "normalized" version handles modulation better. More generally understanding all-pass networks (of which traditional FDN and figure-8 reverb designs are specific examples) is useful if you're into reverb design.

If you're specifically thinking about synth filters though... trapezoidal (aka. TPT/ZDF) is probably what you want... with a whole continuum of different levels of "circuit modelling" accuracy to choose from.

[soundmodel]

I don't have the experience for this one, but do "from analog" direct forms give any auditory benefits over more stable structures?

I think this paper http://www.dafx14.fau.de/papers/dafx14_ ... s_for_.pdf suggests that not only are SVFs more nice numerically, they'd also be sonically superior.

But "good sounding" is a bit complex topic. Sometimes what sounds shitty is good.

Do you know any examples where there's an SVF and a direct form implementation of nearly the same filter?

[JustinJ]

Do you know any examples where there's an SVF and a direct form implementation of nearly the same filter?

The SVF link I provided gives direct replacements for direct form RBJ biquad filters.

[soundmodel]

If synth makers just told what design they use ...

It's so dumb to go like "wow, maybe this has good filters, since they sound like one" and then realize it's "just the usual SVF and personal bias".

[Richard_Synapse]

This would be interesting to know in some cases, but not generally, ihmo. The best digital emulation of analog filters, in theory, would be a circuit model run through SPICE, with all the analog components modeled in it. If you route audio through such a model, however, you'll find it is still a model, not reality. In some cases, it can be far from realistic. So far that a simplier model tweaked to match the analog hardware can be preferable.

Richard

[Z1202]

If you route audio through such a model, however, you'll find it is still a model, not reality. In some cases, it can be far from realistic.

Normally a model not matching the reality indicates (in physics or in DSP) that we are outside the applicability range of the model and a better model is needed (or the model that we're trying to apply is wrong/buggy to begin with), not that the idea of using a model is inferior per se.

So far that a simplier model tweaked to match the analog hardware can be preferable.

As a practical shortcut, sure. But by the same token one might stay away from modelling completely and tweak just some DSP algorithm to sound close to reality. A practical approach is usually a mixture of the two, since tweaking a dissatisfactory DSP algorithm might take longer than tweaking a model, but in either case, as a researcher I would be left we a deep dissatisfaction, still not understanding why a particular circuit sounds the way it does. Usually it just means one was reluctant to take a deeper look.

[mystran]

If you route audio through such a model, however, you'll find it is still a model, not reality. In some cases, it can be far from realistic.

Normally a model not matching the reality indicates (in physics or in DSP) that we are outside the applicability range of the model and a better model is needed (or the model that we're trying to apply is wrong/buggy to begin with), not that the idea of using a model is inferior per se.

I think here we go pretty deep into philosophical questions about what it means for a model to "match reality" and what the "applicable range" actually means in practice. Do we model the variation of junction temperatures, do we model thermal noise? There's obviously more, but these are very obvious examples of things that are clearly observable in analog gear with the naked ear, yet I wouldn't necessarily label it a problem if the SPICE model doesn't pickup a nearby GSM signal.

So far that a simplier model tweaked to match the analog hardware can be preferable.

As a practical shortcut, sure. But by the same token one might stay away from modelling completely and tweak just some DSP algorithm to sound close to reality. A practical approach is usually a mixture of the two, since tweaking a dissatisfactory DSP algorithm might take longer than tweaking a model, but in either case, as a researcher I would be left we a deep dissatisfaction, still not understanding why a particular circuit sounds the way it does. Usually it just means one was reluctant to take a deeper look.

Emphasis mine. More generally, I feel like the question should never be "what method is the best one" but rather "what methods can I use, perhaps together, to get the results I want" or "how can I improve the algorithm so that I can tweak it do what I want."

[Z1202]

Do we model the variation of junction temperatures, do we model thermal noise? There's obviously more

We might not be able to model everything, because the rabbit hole can go infinitely deep (although, maybe not necessarily), but I'd say that (from the researcher satisfaction perspective) we model whatever processes are responsible for the important features of the generated sound. Now which features are important is subjective, but only to an extent, there's still quite an objective aspect to it. As a general reference, I'd say if there are no musicians or sound designers that can tell the difference (both in a mix and outside!) or care about it, we're good.

[Z1202]

As an example, consider the "leakage" of the input signal of a Moog filter into its control signal. We could try to tweak a model by introducing an explicit leakage path and tune it to sound reasonably close to reality, or we can realize how the leakage emerges from a detailed enough model of the filter's nonlinearities (where we find that there is no true leakage, this is just a side effect of how the saturation works in this filter). It's the latter that I'm talking about.

[mystran]

The best digital emulation of analog filters, in theory, would be a circuit model run through SPICE, with all the analog components modeled in it. If you route audio through such a model, however, you'll find it is still a model, not reality. In some cases, it can be far from realistic.

Not going to argue here, but just wanted to remind that something to remember with Spice is to pick realistic components as well. At least in LTSpice I've sometimes seen very idealized behavior when I was lazy and just used generic "NPN" transistors without picking a model (which I'd guess just gives Ebers-Moll with some very average parameters), yet by actually choosing some specific transistor (even if that's just a generic 2n3904) suddenly more interesting behaviour would emerge.

Same thing with opamps.. a generic one that doesn't have voltage rail or gain-bandwidth limits is not going to behave like any real opamp in any real circuit. Pick a more realistic model somewhere in the general ballpark of what you want... and suddenly things start to behave a lot more realistically. The key point here is not that you necessarily always need a model for the exact component, but you might sometimes want "real" components rather than the most generic, idealized thing that Spice can give you.

[Richard_Synapse]

Not going to argue here, but just wanted to remind that something to remember with Spice is to pick realistic components as well. At least in LTSpice I've sometimes seen very idealized behavior when I was lazy and just used generic "NPN" transistors without picking a model (which I'd guess just gives Ebers-Moll with some very average parameters), yet by actually choosing some specific transistor (even if that's just a generic 2n3904) suddenly more interesting behaviour would emerge.

Sure, I was implying the proper model per individual component (or the closest/best replacement if there is none). I would never simplify to generic components unless it turns out it does not matter.

Richard

[JustinJ]

Does anyone know if any research has been done on creating (musical) filters purely from a digital non-modelling perspective?

That is, coming up with filters that sounds really good, say, for synths but not trying to mimic an electronic component based filter. I'm not talking about vanilla SVF or usual TPT, but filters with interesting character. It seems like a lot of emphasis is on modelling yesteryears analog filters.

Say, take the MS20 with its classic 'bite' or something like Steiner-Parker. Now I want to come up with filter with similar aggressiveness but from a bottom up digital implementation and for it to have its own character.