Audio Mythbusters

[Everbeatz]

+ ovo koga ne mrzi da cita:
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Firstly all signals whether analogue or digital have an inherant noise floor.

In order to make digital signals with artificial quantisation have a noise floor that has no harmonic components and no relation to the signal itself we must statistically randomize the quantisation (i.e. dither it). In other words, what's wrong with a mathematically represented signal, and what makes it an inaccurate representation of the real world is precisely its certainty. This must be removed to accurately model reality.

If done correctly it then behaves exactly like an analogue signal.

Note that this is not simply a masking thing - this is the statistical removal of quantisation. All it does is make that particular representation harmonically accurate, regardless of the noise due to the wordlength. Therefore it cannot remove distortions from the driving signal, whether caused by quantisation in preceding processes - or any other cause.

Now if we process a dithered signal digitally then we create a new signal that requires it's own dither, regardless of what came before - and this increases the total noise of the result - just like cascaded analogue processing. In other words if we create a digital system that trully represents the real analogue world then it behaves as such in all aspects


Ok, so why do we bother with ditial signals then? Well the overwhelming advantage of a digital signal is that it's not constrained by the laws of physics. Whereas analogue circuitry has unavoidable noise caused by temperature and impedance, due to natural electronic activity - a digital signal being mathematically represented and not limited to the laws of physics and the real world, can have arbitary dynamic range and hence arbitarily low noise depending on the precision (wordlength) with which we represent it. So for instance a 48bit digital signal can have a signal to noise ratio of 288dB, which is far far greater than any possible physical signal model in the real world

This means we can make collosal signal paths, routings and processing models without the result being blighted by unavoidable build up of analogue noise from the physical world and distortions from imperfect components. We can just arbitarily add precision in the form of wider signal paths to offset the build up - this cannot be done in a physical system in the real world. So the performance we can obtain from something like an EQ plug-in running at 48bits is better than could ever be possible with any analogue system in the real universe. For a couple of hundred dollars you can have something better than could exist in the real world - ever!!


Ok to get onto the second part of one of my posts: It is obviously important that the dither itself is correct, or the signal representation will not be accurate. In the real analogue world all the uncertainty that forms the natural noise floor of an analogue signal is random - and every source is uncorrelated with every other source - i.e. they are all totally different, like every source was a new generator unlike any other sources.

If a digital system (perhaps for cheapness) tries to dither all signals by using one single noise source generator bussed around the processing to add in all places at once, (although this will still remove the quantisation just as well) - because the each dither source is effectively the same they will be correlated. Not only does this mean that they will add up by 6dB for each doubling of the number of truncations (rather then 3dB), it will also mean that for any two signals operating together (like stereo for instance) the noise produced will also be corellated.

So for instance what this means in practice is that for something like 16bit signal where the noise might be audible, the dither noise will sound statistically weighted towards the middle of the sound field (i.e. somewhat mono-ified). And in fact, if the signal level in those channels falls to complete silence the remaining dither noise on L and R might indeed be identical in the absence of anything else coming out of the channels - i.e. mono and coming from dead centre of the stereo image. So the audible 'width' of the dither depends on the music itself, how loud it is and how it is panned. We found that even with dither at 93dB down from the signal, this effect still manages to affect our perception of the stereo sound field - I was stunned when I witnessed this stuff myself.

So the issue facing designers is how to make 100's of uncorellated and completely unrelated noise sources without wasting, loads of resources. In the OXF-R3 this was originally costly, until a colleague far cleverer than some of us came up with a much more efficient method.

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"Dither makes the quantization turn into noise rather than distortion."

I have found that this fact is so very difficult for people to grasp, and I think it is because people equate accuracy with repeatability of calculation and therefore see the exactness and certainty of quantised math representation as evidence of some higher 'truth' beyond reality?

When in truth (if one steps out of the box to think about it) 'counting in discret steps' is an artifact of our minds and the way we discriminate between 'things' that we perceive - and however useful it may be, math is a human construct that we have developed to make great use of this perception. However, reality still rules despite our best efforts to quantise it - and the certainty we crave still elludes us.. Personally I have become more and more convinced there is some wider philosophical message in that - somewhere - beyond the subject of this thread.

I have sometimes met with almost manic and religious opposition to 'randomising' digital systems in my career, as though I was heretically destroying everything that was sacred about it, like an ignorant unbeliever smashing the altar with a sledge hammer. And this was most often from people far more learned than I could ever hope to be. The idea that the very certainty of it might be considered an error, has prompted people to call me a fool more than once

I once spent days trying to convince a very senior and world celebrated engineer that laboriously putting every one of 64K quantised steps of a 16 bit converter in perfect place would still not lead to a perfect result. For this I was called an idiot. What I actually did instead was add loads of noise to the input at -30dBFs, do the conversion, then subtract the noise off again afterwards. Yeah, this reduced the SNR from 96dB to around 90dB, but all the distortion evaporated like a dream - and it sounded like a dream too Even with this dramatic and obvious demonstration, it was still not accepted and instead other wild theories were proposed to explain the improvment - despite the fact that the complete loss of harmonic errors could be plotted readily on an Audio Precision test set!!

[SumAnuT]

The simple formula for this is

Noise in dB = 20 * log(Sources ^ 0.5)

So 48 of your dithered 24 bit sources added up in silence would give:

20 * log(48 ^ 0.5) = 16.81dB

The dynamic range of a dithered 24 bit signal is around -143dB

So the total dynamic range of your 48 dithered sources all added up would be

-143 + 16.81 = -126.187dB

Pe eto, receno je drugim recima ali je sustina ista. Posto se uzima da je opseg ljudskog sluha 120 dB, a kvantni sum se nalazi ispod tih 120, onda je to to?
I to samo kada bi slusao maksimalno pojacano, tj. iskoriscavao puni din opseg konvertora noda bi nivo tog suma dosegao -126 dBFS od mogucih 144 u konvertoru, sto bi u realnom svetu bilo -6 dB, dakle nase uho ne bi moglo to ni da registruje.

Ili ja opet vidim i cujem ono sto zelim da vidim i cujem?