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MQA creator Bob Stuart answers questions.

FrantzM

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Every sound that actually propagates in air (or water or any other medium) and we can hear, is bandwidth limited. And these bandwidth limited waves can be digitally encoded and reconstructed with mathematical perfection, so long as we sample them at more than twice the highest frequency we want to capture.

Digital audio isn't perfect, but its limitations are not theoretical. They are about the bit rates used, and the algorithms used. We're not using quite high enough bit rate to be fully transparent to all humans, and we're not using the mathematically perfect reconstruction algorithm. However, using higher bit rates and depths can account for both of these limitations.
Proofs of such ... Please?
 

MRC01

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The fact that some people under ideal conditions can discern 44-16 from higher rate formats was discussed and referenced earlier in this thread.
The second statement is based on the fact that the Whittaker-Shannon formula is the only way to get perfect reconstruction, but DACs don't use it; instead they use other algorithms like delta-sigma.
 

PierreV

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FWIW, a perfect square wave wouldn't even be a function... It's not only Shannon Nyquist that would suffer here.
 

MRC01

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A perfect square wave is a well-defined continuous mathematical function that can have a single unique value for every instant in time t. But its derivative is not, so a wave like that cannot actually exist as a sound. Thus the fact that it can't be perfectly encoded & decoded digitally is irrelevant.
 
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It can be relevant if it compresses better than a wav.

In other words, it could be an interesting academic research that might bring other, relevant, improvements.
 

MRC01

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You're correct; I used the wrong term. I did mean continuously defined, which its derivative is not. One might claim the derivative is continuously defined if you allow + and - infinity, but in any case its 2nd derivative is undefined at the transition points. Instantaneous changes don't happen in nature.
 
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Lossless compression already gets rid of redundancies in PCM.
But the format still matters.
In h264 numbers are sometimes represented by a series of "1" with a terminating "0" instead of the regular binary encoding.
That's because arithmetic compression does a better job with a series of "1"s.

Audio/video compression aren't just entropy encoding either.
They first remove redundancies based on the signal's model.
Maybe an SVG encoding will make it easier or something.

I just wrote it as an example. I don't know if it can actually help in any way at all.
But even if it doesn't, if at the end the wav file and the "SVG" take the same space.
(Edit: because in the end, they contain about the same amount of information)
Then there would be no reason not to use the SVG.
It won't help in practice, but it will be theoretically better, so its going to be a "if we can, why not?".
 
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PierreV

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You're correct; I used the wrong term. I did mean continuously defined, which its derivative is not. One might claim the derivative is continuously defined if you allow + and - infinity, but in any case its 2nd derivative is undefined at the transition points.
by convergence, or by convention (which incidentally varies from field to field) to facilitate manipulation. But let's not get down that road since everyone agrees, from every angle, that at a time t, there can't be two voltages, two sound pressures or two whatever. (now that I have said that, I sense a bybee product reference coming ;))
 

MRC01

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Along those lines I wonder how "good" lossless compression like FLAC really is. You'd have to have some mathematical ideal as a baseline for comparison. Perhaps the Shannon entropy could be such a baseline.
That is: compute the baseline for the PCM data, then apply FLAC at level 8 (or some other algorithm), and compare the size to this baseline. That would tell you how close we already are to the limits, whether it's worth any effort to improve it.
 

MRC01

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... everyone agrees, from every angle, that at a time t, there can't be two voltages, two sound pressures or two whatever. ...
That's one way to think about it. Another is the idea that it represents an infinite rate of change which can't happen in nature.
 
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Unless you use a black hole's gravitational waves to power your speakers.
Though I think you would be experiencing other problems at that point and won't be too worried about audio quality.
 

MRC01

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... everyone agrees, from every angle, that at a time t, there can't be two voltages, two sound pressures or two whatever....
Mathematically, I can define a square wave that has a distinct unique value for every time t, no need for a single time t to have multiple values:
F(t) = sign(cos(t))
Consider a transition point (say, t = pi/2). When t = pi/2, my square wave (voltage) is 0. Just before that, it's 1. Just after that, it's -1.
Thus, there are never multiple voltages at the same time. But there is an infinite rate of change, which is impossible in the real world.
 

amirm

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Along those lines I wonder how "good" lossless compression like FLAC really is. You'd have to have some mathematical ideal as a baseline for comparison. Perhaps the Shannon entropy could be such a baseline.
FLAC is not that good although the distance between good and great is very small. My team at Microsoft developed WMA Lossless with the goal of beating all the others in efficiency. You can see that ("WMAL") in this table from HA wiki: https://wiki.hydrogenaud.io/index.php?title=Lossless_comparison

1560204059421.png


That extra 1.4% of efficiency cost us in the marketplace as at the time, many CPUs were too slow to decode it in embedded platforms.

This is a bit like getting cream/butter from milk. The first pass will take out most of the fat. What is left over is very little.
 

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