Re: [Sursound] time variance...
On 2013-05-21, Dave Hunt wrote: So, there must be quite a lot going on in Focusrite's Liquid Channel. http://global.focusrite.com/mic-pres-channel-strips/liquid-channel Reputedly Focusrite license a system from Sintefex. http://www.sintefex.com/docs/appnotes/dynaconv.PDF There's altogether too much hype there. Yes, you can do what they do: characterize the short term near-LTI part of the system in steady state and then brute force apply that sample by sample in a time-variant convolution. That is a pretty powerful operation, but it's not really the form you need for compressors. I believe it's both underkill and overkill at the same time. (The input portion seems legit as far as I can tell, presuming they implemented it right.) That's because typical analog compressors are single band, which means they operate on instantaneous amplitude only. There's filtering complexity to be sure, but it's entirely in the side chain, whereas the main path is more or less just a voltage controlled amplifier. The Focusrite architecture gets it the other way around: a brutal amount of brute force processing power is being used for an operation which essentially ends up recreating a constant, more or less unity, EQ curve, while the side chain isn't being modelled at all beyond instantaneous nonlinearity. In analog compressors, and especially the better ones, the side chain which determines the eventual gain in the main one is exceedingly carefully tuned, stateful, and at longer time scales surprisingly nonlinear. It has different attack and decay time constants, it can employ slew rate limited ramps purposely, and sometimes it even has differently EQ's subbands with different constants. That is not something an architecture like Focusrite's can capture, not in analysis nor in synthesis. Mostly you're not going to notice it, of course, but a suitable mixture of steady state background, transients and silence will almost certainly show a definite difference to the original system being modelled. Additionally they say in the second link that they interpolate impulse responses linearly. That is a bad idea in itself, because it'll almost always lead to passband ripple between the endpoints, and if you're heavily into transient content like me, intermediate forms with time-variant allpass terms, muddying up the temporal structure of the signal. Combining the simulation of the nonlinear preamp and the compressor into a single, simple circuit like this buys them easy analysis, but it also makes their synthesis side unsuited to the task at hand and so nasty to analyze properly they don't even try it but resort to passing ad hoc intuitions to it. That sort of thing is Unclean. It will get the macroscopic stateless nonlinearity of the preamp more or less right, in steady state, for sparse quasiperiodic LF signals, the overall EQ curve more or less in the ballpark, and it'll capture the compression characteristic for slowly and smoothly varying envelopes. But it'll definitely not be a precise replica of any and all analog input stages. In fact I'm pretty sure you can even hear alias in the output, because when you do it the way they claim to, that first crucial coefficient of the impulse response, as a function of the input signal, will constitute an arbitrary table lookup/waveshaper of very high polynomial order. That sort of thing is very easy to drive into audible aliasing unless they employ truly exorbitant oversampling rates in the intermediate stages...which you can't really do without running into processing power and latency constraints. -- Sampo Syreeni, aka decoy - de...@iki.fi, http://decoy.iki.fi/front +358-50-5756111, 025E D175 ABE5 027C 9494 EEB0 E090 8BA9 0509 85C2 ___ Sursound mailing list Sursound@music.vt.edu https://mail.music.vt.edu/mailman/listinfo/sursound
Re: [Sursound] time variance...
On Sun, May 19, 2013 at 10:18:35AM +0200, Jörn Nettingsmeier wrote: On 05/02/2013 01:26 AM, Richard Dobson wrote: I have always understood it to mean that the behaviour is not dependent upon ~when~ the signal is injected. Thus, a plain delay is TI because everything is always delayed the same way; while a modulated effect such as a flanger (maybe using a variable delay) is not TI as exactly what comes out depends in the time something goes in. ... for practical purposes, i guess fons' definition is more useful, because then the term LTI system is strictly limited to something that can be fully described with an impulse response. Despite what I wrote before, I tend to agree with Richard. If I interpret his formulation correctly, a system is time-invariant iff, when the output for input x(t) is y(t), then the output for x(t + T) is y(t + T), for any T. It's actually quite difficult to formulate a stronger version *unless* you assume that the system is linear as well. A linear time-invariant (LTI) system is fully defined by an impulse response, or by a transfer function in the frequency domain. Now consider three cases: 1. A filter, 2. A tremolo effect, 3. A compressor. The filter is LTI, while the tremolo and compressor are not. Do they fail to be LTI because they are not linear, or because they are not time-invariant ? The tremolo fails Richard's TI criterion. But it *is* linear in a very strong sense: for any a(t) and b(t) Tremolo (a(t) + b(t)) == Tremolo (a(t)) + Tremolo (b(t)). The compressor is time-invariant according to Richard's criterion. But it isn't linear in the way the tremolo is. It could be said to be linear 'at any instant', assuming attack and release times are non-zero. But that is a somewhat problematic definition of linearity, since apart from trivial cases (pure gain) linear processes depend on the input's or output's history, and are not defined by some relation at a single instant. So it seems that a stronger definition of TI is not necesssary. Ciao, -- FA A world of exhaustive, reliable metadata would be an utopia. It's also a pipe-dream, founded on self-delusion, nerd hubris and hysterically inflated market opportunities. (Cory Doctorow) ___ Sursound mailing list Sursound@music.vt.edu https://mail.music.vt.edu/mailman/listinfo/sursound
Re: [Sursound] time variance...
On 2013-05-20, Fons Adriaensen wrote: So it seems that a stronger definition of TI is not necesssary. At the same time there is a definite point to compressors being kind of time-variant and only weakly nonlinear. They certainly don't behave like a distortion pedal or anything like that. I guess one way to look at it would be to consider the difference between the whole system as a mathematical operator on the one hand, and the constituent parts of its implementation on the other. In the case of LTI systems the difference is easily neglected because of the strong circuit invariants, including commutativity. Numerical effects like noise accumulation, representable range and coefficient quantization are pretty much the only thing fundamentally separating the two, there, and they have little to do with time. But as soon as you go to time-variant and especially (memoryful) nonlinear systems, any invariants you might have to aid in the analysis are much weaker, they don't compose easily, and so you can't factor out the internal dynamics of the system the way we do with LTI circuits. Suddenly it does matter whether parts of the system can be locally approximated as, say, slowly time-variant linear systems, like all dynamics processing can. That sort of thing is especially important when there's nonlinear feedback involved, because then you'll pretty much always be relying on such properties to prove stability and convergence. That goes for Dolby A decoders and Pro Logic II type active steering alike, to mention just two recent topics. Or the other way around, it'll bite you even in the case of fully linear but time-variant circuits with feedback: it's a well known DSP nit that the stability of such filters even under well-behaved coefficient modulation cannot be straight-forwardly deduced from the steady state system function(s), but is intimately tied to the actual circuit topology implementing the filter. So, once you contrast the system and its implementation, suddenly it's no longer generally the case that (approximate) time-invariance of (some of) the parts implies the same of the whole, or the other way around, both properties are still very important for the analysis even if only to quantify how much they're lacking (cf. the analysis of modulation artifacts in compressors), and though the two concepts aren't fully comparable, for the most part applying approximate linearity and/or time-invariance to the exploded circuit constitutes a more fine grained, or stronger, approach. -- Sampo Syreeni, aka decoy - de...@iki.fi, http://decoy.iki.fi/front +358-50-5756111, 025E D175 ABE5 027C 9494 EEB0 E090 8BA9 0509 85C2 ___ Sursound mailing list Sursound@music.vt.edu https://mail.music.vt.edu/mailman/listinfo/sursound
[Sursound] time variance...
On 05/02/2013 01:26 AM, Richard Dobson wrote: On 01/05/2013 23:52, Sampo Syreeni wrote: ... Still, do give me your definition of time-invariant. Perhaps there are stronger definitions I haven't heard of yet, and which can be useful in e.g. more fine grained analysis. I have always understood it to mean that the behaviour is not dependent upon ~when~ the signal is injected. Thus, a plain delay is TI because everything is always delayed the same way; while a modulated effect such as a flanger (maybe using a variable delay) is not TI as exactly what comes out depends in the time something goes in. i guess that's pretty much sampo's definition. but according to him, a compressor is time-invariant because it only depends on previous states of the input signal, so the result will be the same regardless of when you begin injecting the signal. iiuc, fons would consider this a time-variant system, because its behaviour at any single point in time is not constant (it depends on previous input according to RMS circuit, previous gain reduction and attack/release times). so i guess the conceptual difference is whether the system's behaviour depends only on the input signal, or on some external factor, like modulation. for practical purposes, i guess fons' definition is more useful, because then the term LTI system is strictly limited to something that can be fully described with an impulse response. -- Jörn Nettingsmeier Lortzingstr. 11, 45128 Essen, Tel. +49 177 7937487 Meister für Veranstaltungstechnik (Bühne/Studio) Tonmeister VDT http://stackingdwarves.net ___ Sursound mailing list Sursound@music.vt.edu https://mail.music.vt.edu/mailman/listinfo/sursound
