Can I conclude from this that the perceived issue is a problem of specific implementation rather than fundamentals? Thanks very much for your help.
Chris
I'm not yet clear myself that it is merely an implementation issue. Which is why I'm eagerly awaiting the reply from Bob Adams. It might just not be possible even in theory to control the probability density function of the noise in the noise shaping feedback loop so as to guarantee zero noise modulation.
What is an implementation issue would be techniques for rendering the noise modulation less audible. Designers do realise its an issue, I'm not clear how big an issue they consider it to be. The datasheet for the ESS DAC for example merely notes that their DAC is better than others - they don't claim to have totally licked the problem. As far as I recall they admit to 6dB noise floor variation with DC level and claim that others are as bad as 20dB.
I'm totally lost now. It seemed that you were building up to a big deal about citing your quote from those days as proof that you understood dither ... or maybe your goal was just to show that you were aware of it? I mean, you asked us all at least twice to get ready for this before finally delivering the quote itself.
I totally take issue with the phrase "pretty accurate" considering that the quote you cited does not seem to show a full understanding of dither. Maybe you mean that it was an 'accurate' summary of the collective misunderstanding of a particular group of people?
In other words, dither adds resolution below the LSB, and therefore your statement that dither does not improve the accuracy of the system is incorrect. Perhaps I am taking liberties with the terminology, though. My position is that certain low-amplitude signals can be completely lost without dither, and thus the change in accuracy is infinite when those signals can be resolved again with dither added.
Maybe I should state my assumptions since I'm losing track. I get the impression that your position is that dither is a bad thing; and even that dither is not what it claims to be; and further that many people who 'understand' dither find that it is not necessary. Am I lost?
Beyond the question of the shape of the dither spectrum (uniform/rectangular, triangular, Gaussian) is the question of it's amplitude. My take-away from the Vanderkooy, et al, papers is that the amplitude should be 2 LSB. Their point against 1-bit digital is that there is only 1 LSB in the system, so how can you even mathematically have a 2 LSB dither amplitude? Their proof of the 2 LSB amplitude requirement was fairly convincing; at the very least they comfortably proved that the dither amplitude should be greater than 1 LSB to be fully effective. Thus, 1-bit sigma-delta seems mathematically excluded from the set of perfectly-dithered digital systems. That's not to say that what's happening in 1-bit sigma-delta converters is not a form of dither, just that it is an insufficient dither (or perhaps excessive, depending upon your point of view).
It's interesting to consider the minimum bit depth. A 2-bit digital system would have 4 distinct PCM values. Assuming 2 LSBs of dither, that's leaves little room for the signal; basically 0 dB S/N to avoid clipping. With 3-bit, you reach maybe 9 dB S/N; 4-bit 17 dB S/N; 5-bit 23 dB S/N; 6-bit 30 dB; 7-bit 36 dB; 8-bit 42 dB; etc. I may have the math wrong on those, but the point is that the coding system can resolve the difference between the undithered signal and the dithered signal.
P.S. TPDF (2nd order) is the minimum, but I have wondered whether higher orders might sound better, particular taking the order to infinity to achieve Gaussian distribution.
The usual 2V, but that is meaningless anyway.
The way I would express it is that with a peak SPL of 104dB at the listening position (which is a common and convenient point to use) and a crest factor of 14dB (which is common in acoustic music) the average SPL would be 90dB, which is substantially louder and a large scale classical orchestra in a large hall.
In this case the highest peaks see the nonlinearity that causes 0.2% 2nd order HD (and practically nothing else!) and signals around the average would see around 0.04% 2nd HD.
That is of course the source only, Speakers, possibly power amplifiers and certainly human ears add many times this level of distortion...
Ciao T
Let's adopt SY's working definition of 'resolution' and test this claim. To save backtracking the thread he says (paraphrasing slightly) that resolution means ability to resolve two quantities.
So its clear that adding dither noise actually makes it less possible to resolve two quantities sampled by the ADC - those numbers coming out are now wiggling about more, not less. The increase in resolution is only apparent if we lower the bandwidth - i.e. average over more than one sample. Only then we get the benefit of dither in terms of increased resolving power. Its then prudent to ask - is the increased resolution really the result of the dither or of the bandwidth reduction? Or some combination of both?
Accuracy is rather orthogonal to resolution so John's pretty sound on that point.
Circular, but bless you for quoting me accurately.
I somewhat disagree that the dithering process yields higher resolution at the expense of bandwidth, at least as I understand the term "bandwidth." When you average over several cycles of the signal, you still get the level and frequency correct, e.g., if in a dithered 44.1 system you look at 10ms worth of 1kHz, you'll get the same amplitude number that you'd get for 10ms of 22kHz if the two signals' true amplitude is equal. Perhaps we mean two different things by "bandwidth"?
Circular, but bless you for quoting me accurately.
Bless you back for pointing out my shortcomings in expressive power
Somewhat disagree means somewhat agree too?
You appear to be jumping across domains. Let's talk time domain - if there's a 20kHz sinewave coming in, and I take 2 samples and average them, I most certainly will never get an average of two which indicates the peak amplitude of the original sine. The averaging is in effect a low-pass filter.
Yes, mine's the normal one
But if you take (for example) 10 samples, you know amplitude and frequency of the signals to a greater precision, right up to the Nyquist limit. I think you're defining bandwidth as "reciprocal of number of times per second I can take a group of samples and decode what signals are in there" rather than "highest frequency that can be recorded and played back," the sense in which I understand it.
I'll admit that I'm looking at the situation from a potentially unique point of view. But I will reiterate: If a low-amplitude signal completely disappears without dither, but can be discerned in the PCM with dither, then that is an infinite improvement in accuracy!
You describe a technique above which is one of many available, but not the only one. i.e. It is possible to use oversampling to gain bit depth. When that technique is employed, you do, indeed, trade bandwidth for traditional accuracy. But dither is entirely orthogonal to that, as well.
I think SY is doing a better job at explaining this than I have. If you ignore the exact value of the sample below 1 LSB (or 2 LSB), you still have periodic signals with a frequency and amplitude. No averaging is necessary to glean the amplitude and frequency of the input signal. However, without dither, input signal components below 1 LSB in amplitude completely disappear. With dither, you have those low amplitude (sub 1 LSB) input signals plus noise (at 2 LSB), but we know that the human hearing system can still distinguish faint pitched signals in the presence of Gaussian noise, and thus no averaging is needed. In fact, beyond the addition of dither, no further processing is necessary (other than DAC) for the human hearing system to perceive low level signals that would be lost completely without dither.
I realize that it is pushing the definition of accuracy a bit to claim that dither increases the accuracy of a multi-bit digital sampling system. However, given that it can easily be demonstrated that certain low level signals completely disappear without dither, but are preserved with dither, I think it's fair to say that some sort of improvement has been made.
Ha! What you say is literally true, but SY never suggested that you add them together. He stated that you should 'take' them, as in look at them, or maybe convert them to analog and listen to them. There is information in those 10 samples to be gleaned in ways other than summing them together.
Hi,
Not quite.
1lsb Dither @ 16 bit equals 0.03% Fuzzy distortion @ 0dBfs and 30% Fuzzy distortion at -60dBfs. This may or may not be inoccous or even beneficial, the noise levels in MOST (but not all) recording chains will at best be comparable and analogue systems do not rally do better
Now if I have a 5 Bit DAC which I somehow fake to produce (say) 126dB dynamic range under certain measured conditions (but not in reality) I have around 6% Fuzzy distortion @ 0dBfs and 6000% Fuzzy distortion at -60dBfs.
So I am not conflating things, I am merely ignoring the quantitative domain, as it is not directly applicable to the argument.
Dither at ANY level adds "fuzzy distortion", if such is perceived as "neutral", "beneficial" or "disbeneficial" will clearly depend on a number of factors of which quantity is one, but not the only determinant.
We can theorise endlessly where the audible "fuzzy distortion" in low bit, heavily DS Noise shaped systems comes from, I beleive I personally at least have eliminated IM in the Analogue Stage as the only factor, a theory I favoured in the 90's somewhat.
However, I believe we can find agreement in the point that all else being equal there is less of this quality the greater the actual number of real bit's (in the sense of multi-bit DAC/SAR ADC) is and the lower the applied amount of noiseshaped dither, down to a point (like 16 Bit noisefloor) wehere we may or may not part company.
I believe there is something on this in one of Lipshitz/Vanderkoy papers.
I personally, based on my experiences in fields outside electronics and audio and based on intuition would suggest that GAUSSIAN and not TRIANGULAR are required. As Dither is at best Triangular but Johnson noise is Gaussian it is not reasonable to directly equate these two BTW, as some have been doing here.
This is a very reasonable and logical thesis, however it may or may not be true. However is a darn sight better than the flat out denial and assertion of orthodox dogma "all dither at all levels is only good" one usually gets in thesehere parts...
Ciao T
Not quite.
1lsb Dither @ 16 bit equals 0.03% Fuzzy distortion @ 0dBfs and 30% Fuzzy distortion at -60dBfs. This may or may not be inoccous or even beneficial, the noise levels in MOST (but not all) recording chains will at best be comparable and analogue systems do not rally do better
Now if I have a 5 Bit DAC which I somehow fake to produce (say) 126dB dynamic range under certain measured conditions (but not in reality) I have around 6% Fuzzy distortion @ 0dBfs and 6000% Fuzzy distortion at -60dBfs.
So I am not conflating things, I am merely ignoring the quantitative domain, as it is not directly applicable to the argument.
Dither at ANY level adds "fuzzy distortion", if such is perceived as "neutral", "beneficial" or "disbeneficial" will clearly depend on a number of factors of which quantity is one, but not the only determinant.
We can theorise endlessly where the audible "fuzzy distortion" in low bit, heavily DS Noise shaped systems comes from, I beleive I personally at least have eliminated IM in the Analogue Stage as the only factor, a theory I favoured in the 90's somewhat.
However, I believe we can find agreement in the point that all else being equal there is less of this quality the greater the actual number of real bit's (in the sense of multi-bit DAC/SAR ADC) is and the lower the applied amount of noiseshaped dither, down to a point (like 16 Bit noisefloor) wehere we may or may not part company.
I believe there is something on this in one of Lipshitz/Vanderkoy papers.
I personally, based on my experiences in fields outside electronics and audio and based on intuition would suggest that GAUSSIAN and not TRIANGULAR are required. As Dither is at best Triangular but Johnson noise is Gaussian it is not reasonable to directly equate these two BTW, as some have been doing here.
This is a very reasonable and logical thesis, however it may or may not be true. However is a darn sight better than the flat out denial and assertion of orthodox dogma "all dither at all levels is only good" one usually gets in thesehere parts...
Ciao T
Hi,
Would that include perchance the presence of one or several corpora delicere?
Ciao T
Would that include perchance the presence of one or several corpora delicere?
Ciao T
Chris,
This is the real question in this.
Given that real noise shaping loops and real converters are subject to non-ideal behaviours that cannot in practical implementations be eliminated, the answer to your question may be in idealised principle affirmative, but in reality negative.
Ciao T
This is the real question in this.
Given that real noise shaping loops and real converters are subject to non-ideal behaviours that cannot in practical implementations be eliminated, the answer to your question may be in idealised principle affirmative, but in reality negative.
Ciao T
Vinyl Digitizing
Agreed, at 96kHz and higher sampling rates, there is plenty of data for the software to analyze to properly deduce the parameters of the noise. I have not evaluated any recent impulse noise subtraction software like the CEDAR at any sample rate over 48kHz, due to the fact that the incoming customer masters I have had to deal with were already sampled at that rate.
The de-clickers available in inexpensive software packages like Sound Forge, Audition, etc. are inadequate and have significant side-effects, even when applied to high sampling rate recordings. I don't have the $$ to buy any of that really nice software for my home use!
Howie
Howard Hoyt
CE - WXYC-FM
UNC Chapel Hill, NC
www.wxyc.org
1st on the internet
Agreed, at 96kHz and higher sampling rates, there is plenty of data for the software to analyze to properly deduce the parameters of the noise. I have not evaluated any recent impulse noise subtraction software like the CEDAR at any sample rate over 48kHz, due to the fact that the incoming customer masters I have had to deal with were already sampled at that rate.
The de-clickers available in inexpensive software packages like Sound Forge, Audition, etc. are inadequate and have significant side-effects, even when applied to high sampling rate recordings. I don't have the $$ to buy any of that really nice software for my home use!
Howie
Howard Hoyt
CE - WXYC-FM
UNC Chapel Hill, NC
www.wxyc.org
1st on the internet
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