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

[soundmodel]

But you get the output for each frequency for which you have the impulse response? Then a time-varying filter is just about mixing the output of each of such?

Not exactly, because a static system and dynamic system behaviors are generally different. E.g. imagine a delay. If you vary the delay time, you'll hear a changing pitch. Now try to achieve the same effect by merely crossfading between different delays instead. Smth tells me you won't be very successul. And we're still in the linear case, not even talking about nonlinearities (compare the sound of mixing pre- and post-distortion).

Well, I still talked about filters. I think it's true that the Nebula filters do not capture time-variant behavior (that is, if the filter changes with time). But rather it's giving a static image on each frequency, which is still sounds quite convincing.

I think their dynamic models like delays and reverbs use some other related technique. They also have choruses and phasers, so certainly there's some depth to this.

Some info: https://www.soundonsound.com/reviews/ac ... o-nebula-3

I think the "Capturing Your Own Kernels" tool basically reveals what their techniques are. "Dynamic captures require you to decide on the number of levels and the dB step between them".

Also:

https://www.soundonsound.com/techniques ... dio-nebula

[Z1202]

TBH at this point I don't care too much what exactly Nebula does, and they might be using quite a lot of advanced tricks to overcome the generic limitations of the convolution or whatever approach they are using. What's important however, is that a system generally does care about how did it come to the current state not only with respect to the previous input signal, but also with respect to the system parameters. This simply cannot be captured if you are simply crossfading the static responses, because the memory about the system parameters is thereby obliterated.

If you want to do what Nebula does, maybe you should phrase your questions differently (but I'm personally more interested in direct emulation approaches, won't be of much help here, but maybe other would).

PS. And there are way less differences between delays and filters than it might seem, delay is actually "just" a particular kind of an allpass filter.

[soundmodel]

The question is about how do the ways to capture analogueness in these methods compare?

I wonder what's in something like u-he Satin. It sounds analogue, but it's probably not about captured impulse responses.

[Z1202]

The question is about how do the ways to capture analogueness in these methods compare?

Solving differential equations tries to build a direct emulation of what's happening in the analog world. Everything else (AFAICT) tries to do something else, which is mathematically supposed to produce an "equivalent" result. However all those definitions of "equivalence" (AFAIK) make a number of assumptions, which hold only to an extent. E.g. we assume that the system is LTI (whereas often it's not). Respectively your model is only as good as your idea of "equivalence" holds in your particular use case.

I haven't heard of any of such "equivalent" model which is 100% equivalent (that is, without any reservations) to the direct solution of differential equations and I'm not sure if that's even possible. Time-varying nonlinear differential equations are simply too complicated to reason about. I could be missing smth, of course.

The reason a number of such "equivalent" approaches exist is, among other things, that in many cases it might be pretty difficult or plain impossible to figure out the "right" differential equations. So people try to circumvent that, but it's a tradeoff, which might work or might not, depends on the specific case.

[soundmodel]

I don't think it's convincing to attempt to discover an authentic DE for a component anyways. Thus the impulse response -based methods seem more reasonable, which is again why I thought direct forms mean that they include analogueness, since they can base on impulse responses that have them. I don't think the SVF method in the Cytomic papers gives any kind of clue about how to include analogue non-linearities, but OTOH I think u-he discussed somewhere regarding the development of Repro that the gold standard of analogue synth models would be to implement all the components in SPICE. But that the computational cost is too high for it to be played in real-time.

So can the SVF get analogueness merely by adding more component terms to it?

[Urs]

The question is about how do the ways to capture analogueness in these methods compare?

I wonder what's in something like u-he Satin. It sounds analogue, but it's probably not about captured impulse responses.

It's got, among other things, a model of "magnetic tape recording and playback" based on formulas, patents and whatever public and not-so-public information we could get on the topic. Much of the material were books from the mid of the previous century - think 1950ies - which were only ever published in German language (lucky us for speaking it!) and which were salvaged from closed down manufacturers and which somehow found their way into our hands in form of copies or originals (some of them written on typewriter).

(In other words: Nothing captured from impulse responses...)

[Z1202]

• The only "analog" thing about DFs is that they have a good transfer function. But so does any BLT-based digital filter. ZDFs generally do an even better job here, due to better numerical properties. With sufficiently high FP precision all BLT-filters sound completely identical in the LTI case, DFs or not.
• DFs are not "based on impulse responses". They are based on transfer functions, which have a 1:1 relationship to the responses. But those are typically the "ideal theoretical responses", not the ones which "capture the analogueness". If "analogueness" of some particular unit is contained in impulse response, you might be able to capture it by convolution (but not with DFs in general, as DFs have only a limited set of impulse responses that they can generate). But you have to be sure that you're not trying to pick up nonlinear effects this way, the result won't be consistent across different input signals. Sometimes you could be lucky and capture enough "analogueness" just in the LTI properties and maybe even be able to represent it by a small number of DFs, but you can't expect this to work in all cases. Also, as mentioned, any other BLT filters will do an equally good, if not a better job here.
• DFs cannot accommodate nonlinearities. More strictly speaking they, of course, can, but it's extremely difficult if possible at all to map those against analog nonlinearities, since the filter structure is totally different. ZDF filters do not have this problem either.
• DFs cannot accommodate analog time-varying behavior, which is part of "analog" sound
• SPICE works by solving DEs. The engineer's role would be to identify which parts of DEs are essential for the sound and which not, thereby optimizing the computational costs.
• I'd not recommend SVF as a starting point to try to experiment with nonlinear effects. It's a simple filter, but it "doesn't like being messed with". A Moog ladder is a much better starting point here.

[soundmodel]

• I'd not recommend SVF as a starting point to try to experiment with nonlinear effects. It's a simple filter, but it "doesn't like being messed with". A Moog ladder is a much better starting point here.

Why?

Why can't one just sum new independent terms to a functional and well-behaved SVF?

[hugoderwolf]

Superposition principle is one of those many things that only work with linear systems.

[mystran]

"Analogueness" in my opinion is about modelling analog artifacts (eg. non-linear behaviour) while avoiding digital artifacts. IMHO you're basically wasting your time if you're trying to find "analogueness" in transfer functions, because the relevant stuff is outside the scope of LTI theory.

Well, apart from the part that BLT squeezes the frequency response, which makes the use of 2x oversampling almost mandatory for actual "analog" frequency response, especially at high frequency and resonance.

Well.. right.. but you generally need (a lot) more than 2x for "analog" to prevent aliasing.

[mystran]

• I'd not recommend SVF as a starting point to try to experiment with nonlinear effects. It's a simple filter, but it "doesn't like being messed with". A Moog ladder is a much better starting point here.

Why?

Basically stick the wrong type of non-linearity in a random place in an SVF and it will lose BIBO stability. Because of the way it is based on global rather than local feedback this is rather easy to do... so in order to really do anything much beyond the diode bypass thing, you sort of need to jump into the deep end and start thinking about voltage supply limits... where as with a number of other filters (moog, sk) you can do random things and get usable results and build your intuition about how things affect the sound.

[soundmodel]

• I'd not recommend SVF as a starting point to try to experiment with nonlinear effects. It's a simple filter, but it "doesn't like being messed with". A Moog ladder is a much better starting point here.

Why?

Basically stick the wrong type of non-linearity in a random place in an SVF and it will lose BIBO stability. Because of the way it is based on global rather than local feedback this is rather easy to do... so in order to really do anything much beyond the diode bypass thing, you sort of need to jump into the deep end and start thinking about voltage supply limits... where as with a number of other filters (moog, sk) you can do random things and get usable results and build your intuition about how things affect the sound.

Is the background for these observations discussed in some paper possibly?

Or you mean because the Moog for example seems to have things more modularized, whereas the SVF seems sort of like a fully connected thing.

[Z1202]

Is the background for these observations discussed in some paper possibly?

I'm not sure whether there are enough details to justify writing a paper about that. It's pretty trivial, once you start getting into the details of how these filters operate. In the Moog filter, the resonance is created by feeding more signal back (although inverted once), which results in both signals being in phase at the resonating frequency. So, more feedback = more resonance. In SVF the feedback is a combination of 90- and 180-degrees phase shifted signals, and the resonance is controlled by adjusting the amount of the 90-degress phase shifted signal, but... in the opposite direction: less feedback = more resonance. This picture is pretty difficult to think about intuitively, and this "less feedback = more resonance" relationship is even not the most braindamaging part. Why are things this way? Because of the math, which is not too complicated but even not counter- but simply non-intuitive.

I'd even say that having a differential system, where the nonlinearities have an easily intuitively understandable effect, is rather an exception. So one should ask not why "SVF is so difficult", but why "Moog ladder is so easy".

[soundmodel]

I'd even say that having a differential system, where the nonlinearities have an easily intuitively understandable effect, is rather an exception. So one should ask not why "SVF is so difficult", but why "Moog ladder is so easy".

Does this suggest that one should still look for something more than ZDF/TPT?

[mystran]

I'd even say that having a differential system, where the nonlinearities have an easily intuitively understandable effect, is rather an exception. So one should ask not why "SVF is so difficult", but why "Moog ladder is so easy".

Does this suggest that one should still look for something more than ZDF/TPT?

Not necessarily. You can apply trapezoidal integration (=ZDF/TPT) to Moog ladder just fine.