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PostPosted: Thu Jul 24, 2014 2:13 am 
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Cow

Joined: Tue Apr 01, 2014 1:47 am
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Location: Knoxville, Tn
Resolution in digital systems is usually equated with signal to noise ratio. Similarly, quantization error and quantization noise are considered synonymous.

But is this really the case? Is the error that comes from rounding solely represented by the resulting noise signal, or is it also represented as actual, possibly audible error in the audio signal? In other words, distortion, but not heard as noise?

To perhaps be more clear, in delta sigma, one gets excellent signal to noise ratio in the audio band. The actual noise resulting from the error is still there, but is inaudible to our ear due to noise shaping. What about the audio that we CAN hear? Does the signal we hear, without the noise, still have distortion due to the error and/or resolution limits of the system?

Obviously this distortion isn't in the form of noise. But shouldn't it still be there?

To use something analogous that helps me understand....

if I have a pixel matrix of black and white pixels, and I need to represent a certain shade of gray. Say, 63 percent. I switch the pixels form black to white, in such a pattern that 'disappears' to my eye. The 1-bit error of the black and white pixels is still there, it has just been shifted to a higher frequency that my eyes cannot see. Therefore, all I see is a shade of gray, not black and white pixels.

The only problem here is, my pixel matrix doesn't have enough resolution to represent 63 percent! I get something more like 62.2 percent, or some other error, depending on the exact resolution I have to work with. I can no longer see any error as noise, but if I compare the shade of gray produced by the system to the original shade I am trying to digitally represent, there is still a visible distortion there. Although I might not know it without the original reference.


So, it does seem to me that quantization distortion is indeed more than just the noise signal created. The desired audio signal seems to be proportionately distorted as well, even if we discount the noise.

Thoughts?

Thanks!

Andrew


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PostPosted: Thu Jul 24, 2014 4:51 pm 
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Muriel
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Joined: Thu Jul 26, 2007 5:45 pm
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Hi,

ball3901 wrote:
Resolution in digital systems is usually equated with signal to noise ratio.


Only in audio. Elsewhere we have SFDR and ENOB...


ball3901 wrote:
Similarly, quantization error and quantization noise are considered synonymous.


This too is not really correct but an excessive simplification. Quantisation error is clearly signal correlated and not "noise-like" in character, though the relation is non-harmonic.

ball3901 wrote:
To perhaps be more clear, in delta sigma, one gets excellent signal to noise ratio in the audio band.


Only if applying massive averaging.

ball3901 wrote:
The actual noise resulting from the error is still there, but is inaudible to our ear due to noise shaping.


It is not of course inaudible at all. If it was inaudible 120dB DNR DS would sound exactly like 120dB DNR PCM.

ball3901 wrote:
So, it does seem to me that quantization distortion is indeed more than just the noise signal created. The desired audio signal seems to be proportionately distorted as well, even if we discount the noise.


Well, let me put it that way.

If the QE is low enough (significantly below the sources noisefloor) it becomes obscured. This is often not the case for 16 Bit PCM. When I first learned about using PCM we kept 14dB headroom and 20dB footroom to avoid either overs or signals around QE band.

So 96dB theoretical DNR (I consider this number inaccurate and not "analogue equivalent" - that number would be 87dB) left us with 62dB (or 53dB) which is sufficient for most uses, but for classical gain-riding was necessary, just as with master tape grade analogue which has comparable dynamic range.

Of course, a QE of -6dB is ALWAYS WAY ABOVE any sensible noisefloor. Actually, there is most of the time more QE than signal! But no need to worry about that, magical noise shaping will make it all go away, on an AP2 screen anyway.

Ciao T

_________________
"For a successful technology, reality must take precedence over public relations, for nature cannot be fooled." Richard Feynman


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PostPosted: Thu Jul 24, 2014 6:53 pm 
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Cow

Joined: Tue Apr 01, 2014 1:47 am
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Location: Knoxville, Tn
Kuei Yang Wang wrote:

ball3901 wrote:
Similarly, quantization error and quantization noise are considered synonymous.


This too is not really correct but an excessive simplification. Quantisation error is clearly signal correlated and not "noise-like" in character, though the relation is non-harmonic.




Exactly. This seems to be a major source of confusion. DSD Zealots throw out the high in band signal to noise numbers as proof of the superior resolution of DSD.

Yet you can still be listening to a large quantization error, even with a -120db noise floor.


On a related note, I wish there was more real intellectual honesty and less zealotry in hi-fi audio. I love listening to DSD, and I can do so while still being aware of its weaknesses. As soon as I start pointing out any weaknesses, I am instantly targeted as a heretic. It is somewhat disheartening, actually. Sometimes all one wants is good, honest, non-judgemental discussion. Seems hard to find these days.


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PostPosted: Tue Jul 29, 2014 9:34 pm 
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Pig
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Real PCM and delta/sigma are not the same in this regard.

In PCM system, quantization error is made of discrete artifacts, and in that way it is closer to what is traditionally called distortion, and not noise. However it is not only harmonic distortion either, even though harmonically related components are mostly dominant ones.

If you go down the level range, and use only 4 - 5 bits, you can easily hear how quantization error actually sounds like.

Quantization error is fully signal related. It implies also that some waveforms and frequencies produce more, and some produce less of spurious signals. In that way, signals related to sampling frequency do not produce quantization artifacts at all, say clean sinewave 11025 kHz sampled at 44.1 kHz and properly reconstructed (filtered) remains clean sinewave - nothing but sinewave indeed. But it still may have an "error" in the amplitude domain, since its actual level must be approximated to the closest possible one. That's where your observation on 63% vs. 62.2% comes into place.

The first thing that changes this is dither, as it increases resolution in the amplitude domain, at the expense of added noise (real wideband noise).

Another thing is that, even if we can prefer PCM to DSD or any kind of delta/sigma modulation, and even if most of the music is still stored as PCM, we in fact have no choice here, as probably the most of the music we are listening today has gone through some delta/sigma modulation during recording process. The reason is simple: pure PCM A/D converters practically disappeared. (I know people still avoiding any digital processing, and using the old PCM ADC with no oversampling, but this is really rare.)

So delta/sigma appears unavoidable, and things there are different.

But firstly, please note that raw delta modulators that suffer from both so-called slope overload and granular noise, and hence bring both highly signal related and relatively random noise artifacts, were never used in the audio. Delta/sigma converters, which are ubiquitous, almost entirely randomize spurious signal, turning it into what is really noise, and shaping the noise to move it out of audible range.

Yet, the term "error" is very generic one, and above said doesn't imply that steady state noise is fully able to describe delta/sigma modulators, nor does it mean that there are no other errors in their performance, especially because they are "dynamic systems". And, as far as I'm concerned, this topic is still quite open. Because, for instance, we know that their transient behavior is not consistent, yet you won't find much about this problem though.


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