Good read Sampo, thanks for taking time to think and write clearly. Reminds me of that feeling when understanding Godel/Russell, of once solid ground feeling unsound beneath me.
It's a reminder that the ways we "see" things is just one map, one set of tools. There's many ways to decompose and reconstruct signals, some of them more useful or immediate than others. To the broader question. Forgive my liberty with an analogy from computing. When we look at software it's tempting to think that this is the _only_ way things can be. We mistake human constructs for ground truths. Possible languages rest on possible hardware, like von Neumann/Harvard architecture, which rest on choices of number bases/states. So what would be the point in disrupting that stack, of going and moving the whole foundations? One might be the discovery of a new medium for computing. What we get with quantum computing is new possibilities, and the need for new ways of formulating problems. Another reason is more human and greedy. It's "intellectual property". When space runs out in one domain, and nobody seems able to push things forward in that space, there's always the option of ripping up the old rules and moving to an adjacent space. The problem with doing that is you put a barrier between your new technology and the rest of the world. I have not heard this MQA encoded sound, but it seems that's the intention - to claim a broad set of patents to monopolise/restrict encoding and then the main schtick seems to be selling special decoder hardware that can "cast" streams (dubious when folks like to make up their own language to describe decoding). Am I completely misunderstanding this? My worry then with YAPAF (Yet another proprietary audio format) is that we'll end up with landfills full of once expensive decoder boxes in much the same way as thousands of tons of ASIC bitcoin mining gear is being buried right now. I's still dealing with the legacy of DAT formats in my studio. And yet another unneeded format that will complicate future curation of audio files. The performance of MQA would need to be something really special for such a departure from established signal norms to be worthwhile. cheers, Andy On Sun, Jan 30, 2022 at 08:01:30PM -0800, Ethan Duni wrote: > Very interesting and perceptive take as usual Sampo! > > On Sat, Jan 29, 2022 at 8:05 PM Sampo Syreeni <de...@iki.fi> wrote: > > > > > You just cannot have compact support in > > the time and frequency bases at the same time; this is in fact the most > > basic form of the uncertainty principle (a mathematical theorem about > > Fourier transforms, and not an empirical physical thingy, as some seem > > to think). > > > > IMO the physics part is the realization that (wavefunctions of) certain > physical quantities (position/momentum, time/energy) can be related as > Fourier transform pairs (and the associated scaling with Planck's > constant). Once you make that assumption, uncertainty relationships follow > immediately from the properties of the FT, as you say. > > > > Furthermore do note that such bases can only be discretely > > shift-invariant, not continuously. That's because of one of the basic > > classification theorems in functional and harmonical analysis: every > > shift-invariant subspace of an L^2 (by slight modification, an L^1 one) > > space is spanned by some combination of quadrature sines and cosines. So > > essentially everything truly linear and time-invariant comes out of the > > bandlimited sampling framework. This implies that MQA, while linear in > > its sampling step, is not time-invariant, and it cannot be; it'll > > necessarily lead to intermodulation products related to the sample rate, > > just as if you amplitude modulated the signal before sampling with some > > harmonic combination of sinewaves having to do with the rate. > > > > This is a very helpful perspective, thanks for this. > > > > (since a product of minimum phase filters > > is minimum phase, and the phase response of a minimum phase filter is > > wholly determined by amplitude response, multiplying two all-pass > > minimum phase filters has to be idempotent). > > > > Wait, what? Isn't a minimum-phase allpass necessarily trivial? Or was that > your point? > > > > [MQA] utilizes a set of basis functions which > > are not bandlimited, so that it can theoretically reconstruct things > > like hihgly time-localised transients which bandlimited sampling cannot. > > But that's then at the cost of not being able to perfectly reconstruct > > bandlimited signals; the finite innovation framework works to prove this > > too, in its contrary, because the proof is entropically as tight as the > > original Shannon one. "There is no free lunch." > > [...] > > In the case of > > MQA, the assumption is a signal which decomposes nicely in a > > time-variant basis composed of recurring polymial splines of some kind. > > > > The latter model is not well suited to *anything* but time-domain work. > > As I said above, it'll necessarily lead to intermodulation distortion. > > If that can be held below the masking threshold, fine, it might not be > > noticeable. > > > Also very helpful perspective; this puts things in a much clearer context > for me. > > > > That stuff is much easier to do within the conventional critically > > sampled + quantizer + dither + lossless statistical compression > > framework. [...] How you do it is, you brickwall and sample > > conventionally, at a very high rate. (If you want to go as far as that > > 1MHz bound I mentioned from analogue work, you bring in a coherent, > > higher frequency but lower precision converter to fill in.) You apply > > your favourite apodising LTI filter, delta-sigma-method and whatnot, to > > arrive at a phase and amplitude spectrum to your liking. It will now > > typically be something headily bottom-sided in frequency, which you then > > quantize with well-thought-out dither; apodization takes out ringing, > > and the system remains fully translation invariant even on the > > continuous side time, > > > I find the translation invariance appealing intuitively, but is there a way > to quantify its importance in audio terms? > > > > So we rewind our transducers for lots of extremely thin wire, and go > > from permanent magnets as the stator to high amperage electromagnets. In > > the whole Tesla range, not Gauss. Still, the mechanical range isn't > > enough: too much mass and tensile strength, so that the speaker/phone > > vibrates at too-high-Q, and doesn't respond adequately outside its > > natural range. What is there to do? > > > > Well, let's elevate the driving force/voltage, then, and shorten the > > cables to where negative feedback regains control authority to within > > less than a quarter of a cycle @1MHz. > > > > I seem to remember this led to there being something like 10A going > > through the headphones' stators, and upwards of 5000V through a finely > > wound moving coil. Per ear. > > > > I enjoyed this story a great deal, reminds me of my undergrad intern days :P > > E
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