[music-dsp] R: R: R: Trapezoidal integrated optimised SVF v2
Hi Andrew, you misinterpreted my words :) I know you are not intentionally hiding anything. The computation are intrinsically hidden themselves because of the nature of your approach (solving directly the differential eqs instead using the ABCD matrixes). All the coeffs involved in input, output and state vars belong to some matrix, which is why I say it's a statespace-like algo. AFAIK the transient suppressor technique is a nice analysis of the problem and suggest a fix (btw which is expensive). I am not aware of anything that worked fine to keep a a given filter timevarying with theoretically no artifacts, even if I am working on something about recently (just got some ideas and I cant wait to test them). Laroche suggested an analysis to understand if a filter is BIBO stable during transients, but I remember in his paper he says that's not the glitch-free problem test (of course). M. -Messaggio originale- Da: music-dsp-boun...@music.columbia.edu [mailto:music-dsp-boun...@music.columbia.edu] Per conto di Andrew Simper Inviato: domenica 10 novembre 2013 13:18 A: A discussion list for music-related DSP Oggetto: Re: [music-dsp] R: R: Trapezoidal integrated optimised SVF v2 On 10 November 2013 18:43, Marco Lo Monaco marco.lomon...@teletu.it wrote: if you look at Yeh's work you can have an idea. The (D)KMethod is a generalization/extension of the state space ABCD approach to analog systems. Vadim's and Andrew are basically the same thing and the inversion is hidden in the calculation of the coeffs and also takes benefit of the order 2 size of matrix A (which is very simple to invert). I didn't mean to hide anything from you :) I have mentioned MNA or modified nodal analysis, and in all the links to qucs it shows how to add entries to the matrices involved in the solution of the circuit equations. Here is a direct link to the MNA matrix formulation: http://qucs.sourceforge.net/tech/node14.html There is also a lot of good work made by the finnish guys (Valimaki et al) about the usage of the so called transient suppressors. Transient suppressors just screams to me of an underlying problem that should be fixed. Without telling too much (sorry I cant :) ) if I have time I will show the similarity and the matrix inversion problem analyzing the SVF via a statespace approach similar to Andrew's. I am unfortunately fully loaded of work, but as I get some free time I will try to publish a pdf. My 0.02EUR ;-) Marco No rush on any of this, whenever you get a chance it would be appreciated. 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
[music-dsp] Analog versus digital systems
Hi all,
Of course I'm aware of it this work probably won't give m a (bit late)
YUP existence in SanFrancisco or a well paid Berkeley professorship that
I like, but at least I don't really run the risk of looking like a
dumb-*ss when playing the unpaid professor a bit in this territory, and
hopefully cut down some Non-Giant Redwood trees that appear to create
more pollution than oxygen.
First, a repeat of what I've tried to communicate a number of times, as
it were to discourage the idea of taking interesting mathematical truths
from (lame or interesting) digital signal processing effects in music,
let's first consider the theoretical basics that defy all ignoration:
(A)
{Digital System} -- {Digital Sample stream} -- {Digital to Analog}
-- {Analog signal}
, versus:
(B)
{Analog System} -- {Analog Signal}
The main differences are on a short list:
(1) The only way in which the two analog output signals of graph (A)
and (B) are going to be (almost or perfectly) the same is when somehow
the digital system creates very well made samples (which *CAN* come from
simply playing back accurately sampled form of some frequency limited
signal), and the Digital to Analog convertor is very high quality (or to
achieve actual mathematical perfection: is a perfect reconstruction type)
(2) The digital system implemented as a filtering of any kind of
combination of FIR/IIR tap-connections is normally not coming close to
making analog-equivalent signals, by far, unless it is big, and there
explicit measures being taken (extremely high sampling frequencies and
vertical resolution, tuning of the DA-convertors always-present
transient behavior, medium long averaging effects control (hard problem)
seriously long sinc-based integral corrections (computationally intensive)).
(3) Reconstructing an analog signal from samples that isn't a
retarded subset of all possible signals, will require a DA convertor
design which has a serious signal delay, for all known normal and
industrial Audio convertors. So to prevent some very measurable (by over
see-ably simple traditional measurement techniques at the level of the
THD of a very moderate transistor radio) distortion, serious measures
would have to be taken, like outside the scope of this list. Even making
sure those distortions don't become multi-fold ugly and even a potential
danger to the hearing of the customers isn't easy (and thus far never
has been discussed, even though these distortions are almost incredibly
ugly, and host of unrealistic monitors have been invented which are
supposed to smooth some of this over, apparently through lack of
awareness of the impossibility to approach per-sample sinc functions by
any resonance or other mechanical or switching amp trick).
(4) It is quite possible to create a computer simulation of an
electronics circuit, like a Moog filter, even with serious accuracy, and
to state the output of such simulation in the form of a sequence of
equidistant digital samples with accurate vertical quantization. Even
this does not preclude you from having to take equal relevant care of
the above, except for point (2).
There, that's a few New things, apparently for those not blessed with
either the intelligence, means or geographical or time opportunity to
follow a good EE university (or for most of this: bachelor level)
Sophomore year equivalent.
Of course going a bit further in the better EE education (say second or
third year of a serious education), you may want to practice yourself in
creating computer models of interesting non-linear electronics circuits,
and see if you computer simulations on the basis of these models and
some form of circuit-to-signal strategy, be it based on the frequency
domain or not, turn out to be accurate, and maybe invent some fun games
with this, like a Virtual Prophet-5 that everybody can run on their
home computer for free, or things equally thrilling and educational!
I had done some (extremely low budget) preparatory work because of my
much longer standing personal interests for this (like owning various
synthesizers and samplers with digital filters like the TG500 in the
80s), see eg http://theover.tripod.com/so1.html and
http://theover.tripod.com/switch.html , written before the year 1999.
Ir. T. Verelst
http://www.theover.org/Synth
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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] Analog versus digital systems
Theo, please stop with the insults. On 11/10/13 9:55 AM, Theo Verelst wrote: Of course I'm aware of it this work probably won't give m a (bit late) YUP existence in SanFrancisco or a well paid Berkeley professorship that I like, but at least I don't really run the risk of looking like a dumb-*ss when playing the unpaid professor a bit in this territory, and hopefully cut down some Non-Giant Redwood trees that appear to create more pollution than oxygen. -- ... 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] Trapezoidal integrated optimised SVF v2
On 09.11.2013, at 01:57, Tom Duffy tdu...@tascam.com wrote: To paraphrase, all are good enough if the frequency is low ( pi/3); Simpsons is the best, but blows up above 0.8 pi Note that Andys approach uses trapezoidal integrators just as that - integrators. While the whole structure of the SVF looks like a 2nd order biquad, it isn't one. The z-1 sections are all in branches parallel to the signal path. The blow up problem of classical digital implementations of SVFs (e.g. Chamberlin) stems from the unit delay in the feedback path. This unit delay isn't present in Andy's approach and thus there is no blow up problem anywhere below Nyquist. The obvious advantage of Andy's approach is the numerical accurateness. Unlike biquads which require double precision floating processing from 2nd order and up, Andys filters don't suffer much from rounding errors. This should be obvious because the biquad filter coefficients (if you really want to call them that - I really prefer Andy's term) of the integrators are 1.0f The thing about the recent approaches to eleminate the unit delay in the feedback path is the vastly improved stability, the much closer match of phase response towards analogue equivalents and the true independence of cutoff and resonance that make these filters sweepable. The drawback of these approaches is the higher computational effort, which has become less of an issue for realtime processing on desktop computers in recent years. - 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] Trapezoidal integrated optimised SVF v2
Hi Douglas, No worries, I couldn't have started my business without this list, it was an important factor in my career - for the very reason that it isn't strictly academic. I would love to give back if it's of anybody's help. (if we ever find the time to write that damn paper ;-) Thanks, - Urs On 10.11.2013, at 16:03, douglas repetto doug...@music.columbia.edu wrote: 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 -- 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] Time Varying BIBO Stability Analysis of Trapezoidal integrated optimised SVF v2
With reference to my previous message: It looks like there is a change of basis matrix T that can be used to satisfy Laroche's Criterion 2 (time varying BIBO stability at full audio rate), at least for k 0. T: [ 0, 1] [ 1, -1/1 ] This matrix requires k 1/1 but it seems that the lower bound on k can approaches zero as the 2,2 entry approaches zero from below. Hopefully I'm not imagining things. Ross. On 11/11/2013 2:58 AM, Ross Bencina wrote: Hi Everyone, I took a stab at converting Andrew's SVF derivation [1] to a state space representation and followed Laroche's paper to perform a time varying BIBO stability analysis [2]. Please feel free to review and give feedback. I only started learning Linear Algebra recently. Here's a slightly formatted html file: http://www.rossbencina.com/static/junk/SimperSVF_BIBO_Analysis.html And the corresponding Maxima worksheet: http://www.rossbencina.com/static/junk/SimperSVF_BIBO_Analysis.wxm I had to prove a number of the inequalities by cut and paste to Wolfram Alpha, if anyone knows how to coax Maxima into proving the inequalities I'm all ears. Perhaps there are some shortcuts to inequalities on rational functions that I'm not aware of. Anyway... The state matrix X: [ic1eq] [ic2eq] The state transition matrix P: [-(g*k+g^2-1)/(g*k+g^2+1), -(2*g)/(g*k+g^2+1) ] [(2*g)/(g*k+g^2+1),(g*k-g^2+1)/(g*k+g^2+1)] (g 0, k 0 = 2) Laroche's method proposes two time varying stability criteria both using the induced Euclidian (p2?) norm of the state transition matrix: Either: Criterion 1: norm(P) 1 for all possible state transition matrices. Or: Criterion 2: norm(TPT^-1) 1 for all possible state transition matrices, for some fixed constant change of basis matrix T. norm(P) can be computed as the maximum singular value or the positive square root of the maximum eigenvalue of P.transpose(P). I've taken a shortcut and not taken square roots since we're testing for norm(P) strictly less than 1 and the square root doesn't change that. From what I can tell norm(P) is 1, so the trapezoidal SVF filter fails to meet Criterion 1. The problem with Criterion 2 is that Laroche doesn't tell you how to find the change of basis matrix T. I don't know enough about SVD, induced p2 norm or eigenvalues of P.P' to know whether it would even be possible to cook up a T that will reduce norm(P) for all possible transition matrices. Is it even possible to reduce the norm of a unit-norm matrix by changing basis? From reading Laroche's paper it's not really clear whether there is any way to prove Criterion 2 for a norm-1 matrix. He kind-of side steps the issue with the norm=1 Normalized Ladder and ends up proving that norm(P^2)1. This means that the Normalized Ladder is time-varying BIBO stable for parameter update every second sample. Using Laroche's method I was able to show that Andrew's trapezoidal SVF (state transition matrix P above) is also BIBO stable for parameter update every second sample. This is the final second of the linked file above. If anyone has any further insights on Criterion 2 (is it possible that T could exist?) I'd be really interested to hear about it. Constructive feedback welcome :) Thanks, Ross [1] Andrew Simper trapazoidal integrated SVF v2 http://www.cytomic.com/files/dsp/SvfLinearTrapOptimised2.pdf [2] On the Stability of Time-Varying Recursive Filters http://www.aes.org/e-lib/browse.cfm?elib=14168 -- 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] Trapezoidal integrated optimised SVF v2
as a longtime lurker, it's really nice to see this list heating up again, and to see mr. simper's comments finally make it through. cytomic is wonderful stuff and i for one certainly appreciate the sharing. there's a non-technical thread of discussion interleaved here, which is about education and theoretical accuracy and so on. it's wearisome and frequently insulting. creative technology has never advanced solely by cleaving to strict numerical perfection, and will not do so in the future. there are other fora for talking about DSP applications in automotive or medical technology or other truly critical problem domains. [or even AD/DA design, loudness limiting, other low-level and certainly important problems.] but in music, we can afford to play around and follow the ears anyways, please post more, everyone! mr heckmann, your synth is lovely and i look forward to hearing any advice you have or things you've learned, and i'd love to read that paper. thanks again, and all the best ezra buchla On Sun, Nov 10, 2013 at 10:48 AM, Urs Heckmann u...@u-he.com wrote: Hi Douglas, No worries, I couldn't have started my business without this list, it was an important factor in my career - for the very reason that it isn't strictly academic. I would love to give back if it's of anybody's help. (if we ever find the time to write that damn paper ;-) Thanks, - Urs On 10.11.2013, at 16:03, douglas repetto doug...@music.columbia.edu wrote: 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 -- 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] Analog versus digital systems (Ezra Buchla)
... a) of course we all know about the sampling theorem and sync interpolation. truly! b) though i enjoy reading ASM synth code, i don't see anything here that is interesting. ... I'm sorry to say, but while of course I don't feel all too much of it, and of course that isn't a reason to use my free speech necessarily for placing a correction, but that little snippet is quite insulting, given the story thus far. So outside of rethoric, that is a technical/scientific insult of the first order that you're trying to force my direction. I don't really take the insult, and am glad there's serious discussion, and people feeling inspired to share maxima code, etc. and apparently not overwhelmed or something, so they post about what interests them, so on the average, I am glad about the results. I don't feel like scientifically defending the quotes I few simple quotes I posted. As a serious remark about the content of many of the musical and signal processing subjects: it's a great idea to use well known *analog* synthesizer designs as the basis for (partial) digital simulation, which I though already before people like Dave Smith were writing award winning software to that effect, and which interested me long before the advent of a number of software companies that occupy themselves with the subject. As the suggestion is from some of my quotes, it would be good to have a potent, 64 bit circuit simulator which allows audio output, and explicit (parts with curves for parameter changes) or implicit (driven sources in the network, OTAs in replacement circuits, etc) time dependencies, possibilities for storing/continuing network states, and a choice of accuracy feedbacks that I've been hinting at, and which clearly isn't understood by most, which doesn't make me continue. Also, I've suggested signal improvements, but they won't work without some fundamental changes to the most used algorithms, which I would prefer to be applied to some musical software, preferably Open Source. Those things are very audible, and it surprises me that people who may feel the need for improvements are so numb. Must be some limited musicians trying to rule the show, which in broader circles, which also can benefit from DSP for musical purposes is getting in demand. Just saying. Sounds like a simple statement of truth to me, and I think I'm qualified to judge that, so if you feel a bit humble, don't confuse that with feeling insulted. I do feel slandered, regulaly, and that *is8 a real issue for me, and the law. T.V. -- 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] Analog versus digital systems (Ezra Buchla)
i'm sorry mr. vereslt, i do apologize for insulting you. to be honest, i made a mistake with the e-mail and thought this was still under that other thread. and so i tried to read your code, [ which if course is very interesting and informative to me (since i am not nearly at your level as an engineer), it shows some fundamental aspects of high-resolution sample reconstruction rendered in a highly-efficient way ] - but it is not so directly relevant to coefficient changing within the filter, is it? if it is, can you put the relationship a little more plainly so that dummies like me could understand? for example, would you bandlimit an SVF coefficient change signal using sinc or something? perhaps by offline-processing it and using buffer playback? is this stuff only relevant at 64 bits (high vertical resolution)? what if we obtain much greater processing efficiency at 32? switched capacitors is interesting to me too because i have been thinking a lot about tunable sampling rates. this schematic itself is old news though, is it the precise behavior of these integrators while changing the clock rate that you wand to point out? you see, i really respect your intelligence and erudition on this stuff, so i woud love to hear more explanation, just without being so angry. i have of course read the code on your website before now, but still need to know more specifically what part you refer to. i mean to try and starve troll in all of us, i am glad that your pursue correctness aggressively, it is a benefit for all. and so telling you that i'm from a certain area of the world that you make fun of, and so is dave smith for that matter, and that it is easier to pay attention when the tone is more civil. thank you for reminding me of it as well. sincerely, and thanks, ezra b On Sun, Nov 10, 2013 at 3:31 PM, Theo Verelst theo...@telfort.nl wrote: ... a) of course we all know about the sampling theorem and sync interpolation. truly! b) though i enjoy reading ASM synth code, i don't see anything here that is interesting. ... I'm sorry to say, but while of course I don't feel all too much of it, and of course that isn't a reason to use my free speech necessarily for placing a correction, but that little snippet is quite insulting, given the story thus far. So outside of rethoric, that is a technical/scientific insult of the first order that you're trying to force my direction. I don't really take the insult, and am glad there's serious discussion, and people feeling inspired to share maxima code, etc. and apparently not overwhelmed or something, so they post about what interests them, so on the average, I am glad about the results. I don't feel like scientifically defending the quotes I few simple quotes I posted. As a serious remark about the content of many of the musical and signal processing subjects: it's a great idea to use well known *analog* synthesizer designs as the basis for (partial) digital simulation, which I though already before people like Dave Smith were writing award winning software to that effect, and which interested me long before the advent of a number of software companies that occupy themselves with the subject. As the suggestion is from some of my quotes, it would be good to have a potent, 64 bit circuit simulator which allows audio output, and explicit (parts with curves for parameter changes) or implicit (driven sources in the network, OTAs in replacement circuits, etc) time dependencies, possibilities for storing/continuing network states, and a choice of accuracy feedbacks that I've been hinting at, and which clearly isn't understood by most, which doesn't make me continue. Also, I've suggested signal improvements, but they won't work without some fundamental changes to the most used algorithms, which I would prefer to be applied to some musical software, preferably Open Source. Those things are very audible, and it surprises me that people who may feel the need for improvements are so numb. Must be some limited musicians trying to rule the show, which in broader circles, which also can benefit from DSP for musical purposes is getting in demand. Just saying. Sounds like a simple statement of truth to me, and I think I'm qualified to judge that, so if you feel a bit humble, don't confuse that with feeling insulted. I do feel slandered, regulaly, and that *is8 a real issue for me, and the law. T.V. -- 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] Trapezoidal integrated optimised SVF v2
On 11/8/13 6:47 PM, Andrew Simper wrote: On 9 November 2013 08:57, Tom Duffytdu...@tascam.com wrote: Having worked with Direct-Form I filters for half of my career, I've been glossing over this discussion as not relevant to me. It depends if you value numerical performance, cutoff accuracy, dc performance etc etc, DF1 scores badly on all these fronts, nope. and this is even in the case where you keep your cutoff and q unchanged. you can, for a lot fewer instructions than a lattice or a ladder or an SVF, do a DF1 with noise shaping with a zero in the quantization noise TF at z=1 that obliterates any DC error. infinite S/N at f=0. in a fixed-point context, this DF1 with noise shaping (sometimes called fraction saving), has *one* quantization point, not two, not three. you can also rewrite equations to get rid of the cosine problem, which is at the root of problems regarding cutoff accuracy. you do it by replacing, in your equations, every occurrence of cos() with this: cos(2*pi*f0/Fs) -- 1 - 2*( sin(pi*f0/Fs) )^2 as you can see, even if you have floating point, all of the information concerning f0 is in the difference that cos() is from 1. so, assuming f0Fs, even floating point doesn't help. all of the information concerning f0 is in the mantissa bits that are falling offa the edge as f0 gets lower and lower. double precision floats *do* help out here, but it's a numerical problem. and all of the designs using tan(pi*f0/Fs) have their own numerical problems regarding ranging, which is why i would suggest to move away from using tan() as soon as possible in your coefficient math. you'll get something a little different, but pretty strongly related to the standard DF1. -- 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 11/9/13 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
