Andy, FYI besides the KMethod, DePoli/Borin/Sarti et alias always in the 1990s also formulated the W-method which was the dual of KMethod but using the wave digital filter theory by Fettweis. AFAIK is not so easily used because of the increased complexity of nonlinearities adaptors involved (you have shear AND rotation transformations). To me KMethod is much more attractive and it is the be biggest step forward in the last 2 decades to approaching non linear simulation, especially regarding it's robust formalism and elegant math in it. Moreover using KCL/KVL is naturally straightforward when dealing with analog schematics. Using tables seems attractive but for MIMO systems (with order greater than 2) it is not feasible (memory and finding algorithms are an issue). Unfortunately if you have a timevarying element (i.e. a potentiometer) you have to invert a matrix (H), which is good only at control rate, not audio rate. Pls note that when modeling a tone stack, the KMethod degenerates in the state-space classic approach, which is equivalent to yours (C=F=0). I consider Yeh's work very good since the first time I read it years ago. I personally don’t think that automatic systems (DK) will be the panacea of nonlinear modeling (even if everybody here is dreaming of a realtime spice). Very often only a human can see patterns in circuits and find shortcuts to simplify things. Moreover there are so many other dicretization schemes to be investigated (multistep). IMHO the very "big leap ahead" was the KMethod formalism/theory by Borin/DePoli, an extension of StateSpace one, and I guess that in the future we will see more papers to come, even if I admit that lately the computer music group of University of Padova has been changing their research targets.
Regards, Marco -----Messaggio originale----- Da: music-dsp-boun...@music.columbia.edu [mailto:music-dsp-boun...@music.columbia.edu] Per conto di Andrew Simper Inviato: mercoledì 13 novembre 2013 07:12 A: A discussion list for music-related DSP Oggetto: Re: [music-dsp] R: Trapezoidal integrated optimised SVF v2 On 10 November 2013 18:12, Dominique Würtz <dwue...@gmx.net> wrote: > Am Freitag, den 08.11.2013, 11:03 +0100 schrieb Marco Lo Monaco: > I think a crucial point is that besides replicating steady state > response of your analog system, you also want to preserve the > time-varying behavior (modulating cutoff frequency) in digital domain. > To achieve the latter, your digital system must use a state space > representation equivalent to the original circuit, or, how Vadim puts > it, "preserve the topology". By starting from an s-TF, however, all > this information is lost. This is in particular visible from the fact > that implementing different direct forms yields different modulation > behavior. Yes, modulation behaviour is a very important point to me. > BTW, in case you all aren't aware: a work probably relevant to this > discussion is the thesis of David Yeh found here: > > https://ccrma.stanford.edu/~dtyeh/papers/pubs.html > > When digging through it, in particular the so-called "DK method", you > will find many familiar concepts incorporated in a more systematic and > general way of discretizing circuits, including nonlinear ones. Can't > say how novel all this really is, still it's an interesting read anyway. > > Dominique Thanks very much for this link! I have read most of these papers in isolation previously, but missed David Yeh's dissertation https://ccrma.stanford.edu/~dtyeh/papers/DavidYehThesissinglesided.pdf which contains a great description of MNA and how it relates to the DK-method. I highly recommend everyone read it, thanks David!! I really hope that an improved DK-method that handles multiple nonlinearities more elegantly that it currently does. A couple of things to note here, in general, this method uses multi-dimensional tables to pre-calculate the difficult implicit equations to solve the non-linearities, but as the number of non-linearities increases so does the size of your table as noted in 6.2.2: "The dimension of the table lookup for the stored nonlinearity in K-method grows with the number of nonlinear devices in the circuit. A straightforward table lookup is thus impractical for circuits with more than two transistors or vacuum tubes. However, function approximation approaches such as neural networks or nonlinear regression may hold promise for efficiently providing means to implement these high-dimensional lookup functions." Also note that also in section 2.2 some basic "tone stack" circuits are discussed, which contain 3 capacitors 2 pots and a resistor, which are trivial enough to solve using direct integration methods. Yeh notes that WDF can only handle serial or parallel connections of components, not arbitrary ones like in the tonestack, and says specifically (page 26): "Passive filter circuits are typically suited to implementation as a wave digital filter (WDF) (Fettweis, 1986). This approach can easily model standard components such as inductors, capacitors, and resistors that are connected in series and in parallel. However, the tone stack is a bridge circuit, which falls into a category of connections that are neither parallel or series (Fränken et al., 2005). A bridge adapter with 6 ports can be derived (Fränken et al., 2005; Sarti and De Sanctis, 2009), but in general, for a 6-port linear sys- tem, there are 6 × 6 input/output relationships that must be computed. Efficient, parametric implementations for these circuits are not currently obvious." And then goes ahead and solves the circuit using regular symbolic circuit math and implements it with a DF2 T 3 pole filter, not WDF nor the (D)K-method. So all up this shows real promise, but it's not quite there yet. All the best, Andy -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
