Re: [music-dsp] R: R: Trapezoidal integrated optimised SVF v2
On 13.11.2013, at 12:54, Vadim Zavalishin vadim.zavalis...@native-instruments.de wrote: So, after we have modelled them all, we are not gonna need any further modelling. ;-) At that time,we should offer real-time spice to let our dear customers tinker with their virtual circuits. We’ll offer in-app purchases like “bumble bee paper wax caps” or “snake oil inductors”. Steffan -- 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
Re: [music-dsp] R: R: Trapezoidal integrated optimised SVF v2
Urs, I don't know if you're referring to music-dsp here, but this list is specifically not meant to be in the academic realm, but rather a place where people of all sorts with an interest in music and digital signal processing can chat. So I encourage you to share your results here! I'm sorry there has been unpleasantness on the list recently. best, douglas On 11/10/13 10:00 AM, Urs Heckmann wrote: We had planned to write a paper about our numerical method for the non-linear case, including a pretty fast solving algorithm that's fundamentally more precise than Newton-Raphson. But seeing how this won't be well received in the academic realm (seemingly too trivial), we might just share it in more practically oriented place (KVR dev forum). -- ... http://artbots.org .douglas.irving http://dorkbot.org .. http://music.columbia.edu/cmc/music-dsp ...repetto. http://music.columbia.edu/organism ... http://music.columbia.edu/~douglas -- 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
Re: [music-dsp] R: R: Trapezoidal integrated optimised SVF v2
On 11/9/13 6:52 PM, Andrew Simper wrote: Marco writes: Well, of course the s = (T/2)(z-1)/(z+1) conversion comes from discretizing a differential equation. but remember, that's not the only way to convert s to z. that's the bilinear way to do it. ... What I would say more about this method is that , since it is intrinsicly a biquad, you not only have to prewarp the cutoff fc but also the Q. In such Are you talking about bell filters here? For a low pass resonant filter it is hard to warp the Q since there is no extra degree of freedom to keep its gain down, so I'm not sure how prewarping the Q is possible in this case, but I'd love to hear if it can be done. Not only, but wait I could be wrong on this. I always took RBJ cookbook as a bible and he doesn't really say that the Q cant be prewarped for LPF/HPF starting from the analog Q. Maybe RBJ can correct me :) frequency warping is a consequence of using BLT. the cool thing about BLT that other methods that convert s to z do not have is that it maps the j*omega axis in the s-plane to the unit circle in the z-plane, similarly to how the *exact* transformation does (which is z = e^(s/Fs)). and the frequency mapping is strictly increasing and close to the identity function for fFs. so every bump, every feature that you see in the analog frequency response has a corresponding bump in the digital filter frequency response. but slightly (at low f) moved in frequency. at higher frequencies the effect is much more pronounced, which is why compensating for frequency warping (what we call pre-warping) is necessary. it is an effect on *frequency*, not on amplitude. if you have a 3 dB bump in the analog frequency response, there will be a 3 dB bump in the BLT-designed digital filter, but that bump might not be at the same place. so that's why the cookbook says nothing about prewarping Q. i am assuming that for a LPF, if you want to design for a resonant lip or bump of 1 dB, you want the same 1 dB bump in the digital filter. so no compensation of that parameter. but bandwidth is different. bandwidth is about frequency or log of frequency or something else (bark scale??). for every degree of freedom you have in the frequency anchor points, you can apply pre-warping and independently compensate each one regarding their relocation done by BLT. that's why it's appropriate to pre-warp bandwidth when using the BLT to convert s to z. I would love it if you are right. If RBJ can pull it off I would love to see how as it would be ultra ultra useful! pull exactly *what* off? I am however loath to use the dreaded words delay-free since they are pretty meaningless. Did you know that every single of the famous RBJ audio eq cookbook filters are delay-free? Yes, that's right, everyone using RBJ cookbook eqs and low pass filters can now happily slap on their software the hollow marketing term featuring delay-free filter technology! i have absolutely no idea what this is about. So delay-free is a pointless expression to me, it has been used to discuss or advertise delay-free feedback which, to me, still remains an impossibility for discrete-time systems. and i've seen the papers. when it all boils down to it in a real-time filter, you are defining your current output sample in terms of the current input sample and previous input samples and, if it's recursive, the previous output samples. but you cannot define your current output sample in terms of the current output sample. a more meaningful thing to mention could possibly be that (non-linear) implicit functions are being solved. For example something that has a non-linear voltage to current mapping, or something that solves for non-linearities placed in feedback loops, anything else is just linear algebra that can be solved in a single step. But even then who cares as long as it sounds good? yup. and at Fs=96kHz, you can make it sound very good. and that single-sample delay is half of what it would be at 48 kHz. -- r b-j r...@audioimagination.com Imagination is more important than knowledge. -- 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
Re: [music-dsp] R: R: Trapezoidal integrated optimised SVF v2
On 11.11.2013, at 01:33, robert bristow-johnson r...@audioimagination.com wrote: but you cannot define your current output sample in terms of the current output sample. But that, with all due respect, is what has been done for quite a while. It isn't the major ingredient of great sound, but it arguably has its perks, albeit cpu smoking ones. I agree with Andy though that the main advantage of preserving the topology is the possibility to insert the non-linearities at the right point. When using BLT, how would you insert the non-linear effects of a diode or an OpAmp into your model, where these things are desirable for a musical result? - Urs -- 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
Re: [music-dsp] R: R: Trapezoidal integrated optimised SVF v2
On 11/10/13 5:12 PM, Urs Heckmann wrote: On 11.11.2013, at 01:33, robert bristow-johnsonr...@audioimagination.com wrote: but you cannot define your current output sample in terms of the current output sample. But that, with all due respect, is what has been done for quite a while. it's been reported or *reputed* to be done for quite a while. but when the smoke and dust clear, logic still prevails. -- r b-j r...@audioimagination.com Imagination is more important than knowledge. -- 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
Re: [music-dsp] R: R: Trapezoidal integrated optimised SVF v2
i hope it's ok if i sum up the main themes here with background links, as i understand it. the thread is just such a mess... here is the state variable filter from hal chamberlin 1985 or so: http://t.co/SVJp7iAgqb pierre dutilleux wrote up a nice discretized and tuned version in dafx 1998: http://iua.upf.edu/dafx98/papers/ presumably drawing on (it can be shown that...) this much earlier AES paper, which i have not purchased https://secure.aes.org/forum/pubs/conventions/?elib=5937 andrew simper's suggestion is to integrate the capacitor functions with trapezoidal approximation, allowing for some refactoring and simplication of the dif. eq.s and faster code. http://cytomic.com/files/dsp/SvfLinearTrapOptimised.pdf there seems to be some concern about distortion introduced by the trapezoidal integration. i've tried the algo in both fixed 32 ands float, and it seems to sound and look ok to but i have not done a proper analysis either numerically or physically. has anyone else? theo vereslt seems to think the distortion would be unacceptable, and so i tend to believe that in a really high-fidelity environment it could be an issue. additionally, he seems to imply (maybe? i'm not sure) that not only is the optimization not worth it, but you can't adequately suppress artifacts during coefficient change at all (which i've always understood as the main raison for the digital SVF) without analog components (referenced switched caps as variable R's, an interesting trick), or more bandlimiting somewhere, or something. the KeepTopology paper by vadim zavalishin (http://t.co/SVJp7iAgqb) proposes modelling the SVF with digital integrators. it seems like these would follow the behaviors of the caps pretty closely and be amenable to parameter change at the cost of some expense of course... wouldn't that satisfy the purists? this last exchange seems to indicate not... but i'm not sure why. again i should just try this myself but it's a bit more work! ha. thank you all for the discussion and sorry for my noise ezra b -- 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
Re: [music-dsp] R: R: Trapezoidal integrated optimised SVF v2
Hi Ezra, A few comments: On 11/11/2013 3:19 PM, Ezra Buchla wrote: there seems to be some concern about distortion introduced by the trapezoidal integration. i've tried the algo in both fixed 32 ands float, and it seems to sound and look ok to but i have not done a proper analysis either numerically or physically. has anyone else? All single-step digital integration procedures will necessarily diverge from the analog integration. Here's a graph of the amplitude response of various integrators: https://docs.google.com/document/d/1O_38tHxkMIrSScLXULuzJAmNxYj01PxEKw50hhY4kkU/edit?usp=sharing Trapezoidal is good because it is stable but as you can see it has high-frequency roll-off compared to some others. As noted earlier Simpsons rule is not usable if you want your cutoff to go near Nyquist but is more accurate up to pi/4, which means that if you're using 2x oversampling. Trapezoidal is equivalent to the warping introduced by BLT (bilnear transform) I believe. One way to think about it is that a lowpass filter in the analog domain has gain 0 at infinite frequency, and infinite frequency maps to Nyquist after BLT/Trapezoidal -- so you will get some warping. theo vereslt seems to think the distortion would be unacceptable, and so i tend to believe that in a really high-fidelity environment it could be an issue. The usual suggestion is to oversample by 2x. Many implementations do this and it has been discussed here many times over the years. It is possible to do other tricks to match the amplitude response at 1x but the phase response can get screwed up and you really want something close to analog for both amplitude and phase responses. My take is that for synthesis it's all about your aesthetic -- if you want it to sound like an analog synth that's different from if you want it to sound good. There's whole music genres based on commodore 64 SID chips or destorted noise.. so anything goes really. additionally, he seems to imply (maybe? i'm not sure) that not only is the optimization not worth it, but you can't adequately suppress artifacts during coefficient change at all (which i've always understood as the main raison for the digital SVF) without analog components (referenced switched caps as variable R's, an interesting trick), or more bandlimiting somewhere, or something. I think the main point in the current discussion is that if you want to do *audio rate* modulation (think filter FM) then most tricks won't save you. You need a filter that can be modulated at audio rate and doesn't introduce spurious artifacts. Of course audio-rate FM will alias, but that's a separate issue that can be addressed by oversampling etc. the KeepTopology paper by vadim zavalishin (http://t.co/SVJp7iAgqb) proposes modelling the SVF with digital integrators. it seems like these would follow the behaviors of the caps pretty closely and be amenable to parameter change at the cost of some expense of course...' All filters use digital integrators. There's just a lot of different types of integrators. wouldn't that satisfy the purists? this last exchange seems to indicate not... but i'm not sure why. again i should just try this myself but it's a bit more work! ha. I can recommend the following book as a gentle and no-hype low-math introduction to numerical integration. Written by a guy who cut his teeth computing trajectories on the Apollo project: Math Toolkit for real-time programming Jack W. Crenshaw CMP Books. Cheers, Ross. thank you all for the discussion and sorry for my noise ezra b -- 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
Re: [music-dsp] R: R: Trapezoidal integrated optimised SVF v2
On 11/11/2013 12:21 PM, robert bristow-johnson wrote: but you cannot define your current output sample in terms of the current output sample. But that, with all due respect, is what has been done for quite a while. it's been reported or *reputed* to be done for quite a while. but when the smoke and dust clear, logic still prevails. I presume Urs (hi Urs!) is talking about using implicit solvers. Which some people have been using for a while. I guess it depends how you define current output sample. Is it the trial output sample that you're refining, or the sample you actually output? Seems logic could go either way. Ross. -- 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
Re: [music-dsp] R: R: Trapezoidal integrated optimised SVF v2
On 9 November 2013 22:21, Marco Lo Monaco marco.lomon...@teletu.it wrote: Hi Marco, First up I want to thank you for your considered and useful observations Marco, I appreciate where you are coming from and how you can clearly communicate your ideas. This makes it possible for me to reply to your points and offer observations in return which are hopefully helpful to not only you, but anyone reading this thread. Hi Andrew, I think it's useful for everyone, and especially those wanting to handle non-linearities or other music behaviour. Yes, but people who are working in this field and doing virtual analog have known these tricks for at least 10 years ago. :) Here is a direct quote from my first email, and similar quotes will be found in all initial emails from me, and references to reinforce just how not new this stuff is: Please note there is absolutely nothing new here, this is all standard circuit maths that has been around for ages, and all the maths behind it was invented by people like Netwon, Leibnitz, and Euler, they deserve all the credit and came up with ways of solving not just this linear case but also the non-linear case. Even if this is old news, there are plenty of people struggling along with algorithms that don't sound as good and they aren't aware of alternatives. I'm trying to raise the level of dsp here by pointing out what to me is obvious and helpful, I'm not pretending to have invented anything. You don't need the laplace space to apply all these different discretization (numerical integration) methods, they all come from the time domain and can be derived pretty quickly from first principles. Well, of course the s = (T/2)(z-1)/(z+1) conversion comes from discretizing a differential equation. Using Laplace is simply more handy IMHO. Mainly because once you have your state space model (or TF) representation you can choose (via a CAS tool) to discretize it at best. Moreover modeling an analog network with s-domain impedence sometimes is quicker/easier. But I understand it's only a routine behavior and it's a matter of tastes. I remember I have once modeled 50eqs linear system via KVL/KCL always remaining in the continuos domain and because I wanted to see different behavior I chose the Laplace representation. If I had to solve several times those linear system with different integration rules I would have gone nuts :) Please note you only have to solve the numerical integration equations once to generate a linear equivalent model of the form ic = gc vc - iceq, then you put that linear equivalent model into your Computer Algebra System (CAS) to solve things. So although it may be more handy for you at the moment to do things via the laplace domain there are compelling reasons not to, even in the case where you don't modulate the filter at all like an eq. In noise performance tests I've done (I don't know how to prove this analytically, but if you do then please go ahead and work it out and share it with us!) using direct integration on an svf delivers better results (rms error) than any other filter realisation I've tried which operates via the laplace transform (DF1, DF2, DF2T, Ladder (not moog), Direct Wave, etc etc). Here are some plots of the previous method I posted which is almost identical to the one in the newer pdf, the ladder structure is the only one to come come close but it falls down on some of the tests. I suggest if you are not convinced to repeat the tests yourself (or even come up with new ones) and share the results: http://www.cytomic.com/files/dsp/SVF-vs-DF1.pdf What I would say more about this method is that , since it is intrinsicly a biquad, you not only have to prewarp the cutoff fc but also the Q. In such Are you talking about bell filters here? For a low pass resonant filter it is hard to warp the Q since there is no extra degree of freedom to keep its gain down, so I'm not sure how prewarping the Q is possible in this case, but I'd love to hear if it can be done. Not only, but wait I could be wrong on this. I always took RBJ cookbook as a bible and he doesn't really say that the Q cant be prewarped for LPF/HPF starting from the analog Q. Maybe RBJ can correct me :) I would love it if you are right. If RBJ can pull it off I would love to see how as it would be ultra ultra useful! You can do all the same warping no matter if you go through the laplace space or directly integrate the circuits, and it doesn't matter what realisation you are using, in particular you can have a look at my previous workbook where I matched the SVF to Roberts RBJ shapes: I would love to see it, if you have the chance. I missed adding the link here, sorry about that, here is the old version with the bell shape mapped, you can use the same method on the new version I just didn't bother adding it to the new pdf (you match all the RBJ shapes with algebra exactly)
