New Xiph.Org video: "Digital Show & Tell"

[TJE]

I for one am thrilled to see Opus and Xiph in discussion, even if I can't entirely follow. This could only help shed some light on what Opus has been discussing in other threads, for those of us who have trouble judging the technical merit of his ideas.

 

[opus111]

That should be a relatively easy test to run since all you're looking for is the noise figure.

Easy test? You mean I've been looking for a Holy Grail measurement and you've been drinking from the very cup for years? Care to elucidate more on this (for me very) elusive 'noise figure' ?

Got any specific examples of music in mind?

Well I am hearing noise modulation (just like Ragnar is) on DSD so you could start with a Telarc DSD mastered RBCD if you want to measure the 'noise figure'.

 

[andy_c]

It's my understanding that noise modulation is only a problem (in principle at least) with single-bit sigma-delta conversion and that multi-bit sigma-delta converters can in principle completely eliminate it. See this Lipshitz and Vanderkooy article. Regarding optimum dither, Wannamaker's thesis on dither deals with the correlation of signal and quantization noise and how to minimize it. Here's a short excerpt ("2RPDF" = triangular PDF).

Using an argument derived from Wright [10, 11], we will now show that such 2RPDF dither is unique and optimal in the sense that it is the only zero-mean dither which renders the rst and second moments of the total error input independent, while minimizing the second moment. That is, when used in an NSD quantizing system, this dither incurs the least possible increase in the total error variance of any dither which eliminates input-dependent distortion and noise modulation.

Edit: For an example of this noise modulation, see the Stereophile review of the NAD M51 DAC. Figures 8, 9, 10 and 11 show the noise modulation in various forms (noise level depends on level of signal).

 

[opus111]

It's my understanding that noise modulation is only a problem (in principle at least) with single-bit sigma-delta conversion and that multi-bit sigma-delta converters can in principle completely eliminate it. See this Lipshitz and Vanderkooy article.

I'm aware that Lipshitz and Vanderkooy claim that but the evidence put forth to support it I don't find totally convincing. That's because they point to a noise 'floor' in an FFT as unchanging and conclude from that alone that there's no noise modulation going on. Simply because the average noise is the same does not mean that the instantaneous noise is also constant.

<edit> As regards the plots of the NAD, the engineer admits that the digital gain is set a tad high, the modulator is beginning to overload at 0dBFS - the noise modulation shown is extreme and the THD also much higher.

 

[andy_c]

I'm aware that Lipshitz and Vanderkooy claim that but the evidence put forth to support it I don't find totally convincing. That's because they point to a noise 'floor' in an FFT as unchanging and conclude from that alone that there's no noise modulation going on. Simply because the average noise is the same does not mean that the instantaneous noise is also constant.

The instantaneous value of noise is not deterministic, so it's not meaningful in terms of measurements or discussions about them. Noise by necessity is described in terms of its statistical properties, so it's necessary to have a sequence of sampled values to determine those properties. The average value of noise is typically zero (zero mean). I believe you meant to say "RMS value of noise", rather than "average noise". No credible sources regarding noise analysis in the literature actually use the terms "instantaneous noise" or "average noise".

 

[opus111]

The instantaneous value of noise is not deterministic, so it's not meaningful in terms of measurements or discussions about them.

Yet we have a chaotic digital system which is entirely a deterministic one so perhaps the word 'noise' in its traditional sense (of random noise) doesn't apply. Its still an unwanted contribution nevertheless and discussions about it are germane because its a SQ issue.

Noise by necessity is described in terms of its statistical properties, so it's necessary to have a sequence of sampled values to determine those properties. The average value of noise is typically zero (zero mean). I believe you meant to say "RMS value of noise", rather than "average noise".

No, I didn't mean to say 'RMS value of noise' rather I was pointing out that the averaged value over a time sequence long enough for an FFT to be performed (typically at least 64k points, over 1s with 44k1 sampling) is not particularly indicative of what's perceived aurally. Our ear/brain system is sensitive to much shorter durations of noise floor modulation, potentially in the region of tens of milliseconds. I'm happy to be corrected on this though.

 

[andy_c]

Yet we have a chaotic digital system which is entirely a deterministic one so perhaps the word 'noise' in its traditional sense (of random noise) doesn't apply. Its still an unwanted contribution nevertheless and discussions about it are germane because its a SQ issue.

It's not a deterministic system in the strict sense, because dither has been added. I'm assuming we're still talking about the Lipshitz article regarding A/D conversion - multi-bit vs. 1-bit.

No, I didn't mean to say 'RMS value of noise' rather I was pointing out that the averaged value over a time sequence long enough for an FFT to be performed (typically at least 64k points, over 1s with 44k1 sampling) is not particularly indicative of what's perceived aurally. Our ear/brain system is sensitive to much shorter durations of noise floor modulation, potentially in the region of tens of milliseconds. I'm happy to be corrected on this though.

When talking about the added dither, its average value is zero, but its RMS value is not. Average=DC. "Average value" of a signal is not meaningful when describing dither. RMS is.

Our ear/brain system is sensitive to much shorter durations of noise floor modulation, potentially in the region of tens of milliseconds. I'm happy to be corrected on this though.

Maybe that's true, maybe not. Where did this claim come from? What data is there to support it? If there is data, it might be interesting to find a way to test it.

 

[opus111]

It's not a deterministic system in the strict sense, because dither has been added. I'm assuming we're still talking about the Lipshitz article regarding A/D conversion - multi-bit vs. 1-bit.

No, you introduced that, I'm still talking about the original topic - my quibble with Monty about transparency of DACs. Do you know that the dither was introduced on a true random basis? I would suggest in simulation it normally is not (due to the relatively large inconvenience of providing hardware-based randomness), it would be the output of something like a pseudo-random bit sequence generator, entirely deterministic.

When talking about the added dither, its average value is zero, but its RMS value is not. Average=DC. "Average value" of a signal is not meaningful when describing dither. RMS is.

OK, I accept your point here. When I was talking about averaging I was hinting at the term (short or long) of the averaging window.

Maybe that's true, maybe not. Where did this claim come from? What data is there to support it? If there is data, it might be interesting to find a way to test it.

There's observation that I hear it, and observation is always primary in science. Data would be secondary to observation - how to turn my (and others') observations into data - any suggestions?

Incidentally if you're maintaining your assertion (based on the Lipshitz paper already cited) that in a multibit modulator, noise modulation can be entirely eliminated, what's your hypothesis to explain the data already cited here? That 14dB noise modulation in the DAC part of Monty's chip?

 

[andy_c]

No, you introduced that, I'm still talking about the original topic - my quibble with Monty about transparency of DACs. Do you know that the dither was introduced on a true random basis? I would suggest in simulation it normally is not (due to the relatively large inconvenience of providing hardware-based randomness), it would be the output of something like a pseudo-random bit sequence generator, entirely deterministic.

Yes, of course. Random number generators are deterministic and have a period that's non-infinite. Knuth has studied this in detail. I'd suggest reading Knuth's works, and not just for deconstruction purposes, but for actual useful information - assuming of course that one's purpose is to do something useful.

There's observation that I hear it, and observation is always primary in science. Data would be secondary to observation - how to turn my (and others') observations into data - any suggestions?

It's not easy. Your claim gave the impression that someone had done controlled experiments. But I see that no such experiments were done, so what you're talking about is a conclusion with no real basis in fact.

Incidentally if you're maintaining your assertion (based on the Lipshitz paper already cited) that in a multibit modulator, noise modulation can be entirely eliminated, what's your hypothesis to explain the data already cited here? That 14dB noise modulation in the DAC part of Monty's chip?

One might imagine that there could conceivably be a difference between "can be" and "is".

 

[opus111]

Yes, of course. Random number generators are deterministic and have a period that's non-infinite.

So why the distraction from the point then? You originally were claiming that because noise was random what I was saying wasn't meaningful. But now you admit that the noise isn't random. Have you indeed learned something new here?

Knuth has studied this in detail. I'd suggest reading Knuth's works, and not just for deconstruction purposes, but for actual useful information - assuming of course that one's purpose is to do something useful.

Your recommendation is noted.

Your claim gave the impression that someone had done controlled experiments.

You're responsible for your own impression, I of course have made no claims about 'controlled experiments'.

But I see that no such experiments were done, so what you're talking about is a conclusion with no real basis in fact.

'Such' here doesn't seem to me to be pointing to any specific experimental design. The rest of your reasoning here is nonsensical. Perhaps some background reading in the philosophy of science might come in handy?

 

[xiphmont]

So why the distraction from the point then? You originally were claiming that because noise was random what I was saying wasn't meaningful. But now you admit that the noise isn't random. Have you indeed learned something new here?

'random enough' is what gets the desired properties. Here's the entire random number generator most of our tools use to generate TPFD:

static unsigned int rngseed = 22222;
static inline unsigned int fast_rand() **
  rngseed = (rngseed * 96314165) + 907633515;
  return rngseed;
}

That is sufficient to achieve complete noise decorrelation beyond what I can measure. There's no point to getting fancier, and infinite period isn't necessary.

Easy test? You mean I've been looking for a Holy Grail measurement and you've been drinking from the very cup for years? Care to elucidate more on this (for me very) elusive 'noise figure' ?

A test to extract the THD+N signal? That's straightforward depending on how picky you need to be, and how much control you have. If you can provide both the DAC and the ADC a common, high quality clock, and don't mind measurements being referenced to the ADC, this is indeed straightforward and I've written all the code before. Even if you can't, I expect we can still make it work, but I'd need to write code to track and compensate clock perterbations. I've not done that before, but I expect I can.

Splitting the THD out from N... trickier. I'd have to ask around, I'd bet gmaxwell could do it. He would probably even have a better way of getting THD+N than I do, my thinking tends to be rather 'modular' I know how to construct a solution by solving the problem one block at a time, Xiph has a few folks who are better at solving a problem in one fell swoop that makes me say 'Daaaaaamn.'

 

[xiphmont]

Incidentally if you're maintaining your assertion (based on the Lipshitz paper already cited) that in a multibit modulator, noise modulation can be entirely eliminated, what's your hypothesis to explain the data already cited here? That 14dB noise modulation in the DAC part of Monty's chip?

Uhh... ~ 4dB of actual noise modulation, plus the harmonic distortion products near 0dBFS.

 

[opus111]

A test to extract the THD+N signal?

No, a test which extracts the noise generated by the modulator when the stimulus is music. Seems to me that we'd need a way of nulling out the original (music) signal leaving only the modulator's contributions. Having played with 'Diffmaker' I know its too flawed in its means of looking for a null, so we need another approach. Ripples in digital oversampling filters prior to the modulator will limit the depth of null attainable, as will any departure from linear phase - some systems have IIR filter sections preceding the modulator.

If you wanna do this as an analog-analog null test then there's a time delay built in in the digital system - how to compensate for this in the analog path?

Where does your 4dB figure arise?

 

[xiphmont]

No, a test which extracts the noise generated by the modulator when the stimulus is music. Seems to me that we'd need a way of nulling out the original (music) signal leaving only the modulator's contributions.

That is what I was suggesting, extracting the THD+N contribution of modulation. By my thinking, we'd need to compensate for FR, phase, delay and possibly aliasing near nyquist. We'd then have THD+N, and could watch for input-correlated changes over a sliding window... though I supect it's still mostly just going the see the harmonic distortion from nonlinearity appearing and disappearing below the overall noise floor.

Ripples in digital oversampling filters prior to the modulator will limit the depth of null attainable, as will any departure from linear phase - some systems have IIR filter sections preceding the modulator.

If the ripples change, that indicates changes in phase and FR. Where phase is 0 degrees and FR=0dB, there's no change to the Gibbs ripples. Compensating both is straightforward so long as they're time invariant. And if they're not, we'd notice.

If you wanna do this as an analog-analog null test then there's a time delay built in in the digital system - how to compensate for this in the analog path?

I was suggesting doing it digitally. It would be referenced to an ADC, but that doesn't seem like a showstopper.

Where does your 4dB figure arise?

the approximate change in the FFT noise floor, not the total broadband THD+N value.

 

[opus111]

That is what I was suggesting, extracting the THD+N contribution of modulation. By my thinking, we'd need to compensate for FR, phase, delay and possibly aliasing near nyquist. We'd then have THD+N, and could watch for input-correlated changes over a sliding window... though I supect it's still mostly just going the see the harmonic distortion from nonlinearity appearing and disappearing below the overall noise floor.

Cool, and I suspect it will show predominantly noise modulation as the dominant broadband error. Which is what experiments are for, to falsify (or not) hypotheses

If the ripples change, that indicates changes in phase and FR. Where phase is 0 degrees and FR=0dB, there's no change to the Gibbs ripples. Compensating both is straightforward so long as they're time invariant. And if they're not, we'd notice.

Not a showstopper, I agree. Not sure what you mean by 'referenced to an ADC' though.

the approximate change in the FFT noise floor, not the total broadband THD+N value.

OK well this kinda provides validation for my hypothesis - estimating the noise modulation from the FFT sucks.

<edit> OK its sunk in better what you plan to do now - digitize the output of the DAC with the ADC. Hence 'referenced to an ADC' - I'm a bit slow at grasping. But the noise modulation contribution of the ADC will be added in to the picture too then - are we interested in separating out the two effects? Or will you use an SAR type ADC to be sure of getting no ADC noise modulation? Plenty of decent parts available at ADI but they'll need a decent AAF.

P.S. Thorsten Loesch has already done a similar experiment, using a Cirrus DAC - I think his null was of the order of 60dB but only after extensive modifications beyond the manufacturer's stock evaluation board. I could find a link if you'd like to hear of that from the horse's mouth.

 

[xiphmont]

Cool, and I suspect it will show predominantly noise modulation as the dominant broadband error. Which is what experiments are for, to falsify (or not) hypotheses

What I meant was that it will not distinguish between the two as formulated, so that's problematic.

OK well this kinda provides validation for my hypothesis - estimating the noise modulation from the FFT sucks.

Those figures were measuring steady state signals. I think you're barking up a weird tree, at least in this case.

the noise modulation contribution of the ADC will be added in to the picture too then

Yes.

are we interested in separating out the two effects?

if there's an effect to be separated, yes. Easy tests first.

Or will you use an SAR type ADC to be sure of getting no ADC noise modulation? Plenty of decent parts available at ADI but they'll need a decent AAF.

I don't think it will necessarily need to be as perfect an AAF as you think. Software is a powerful thing, and pre-render / analysis need not be done realtime.

I'm... not sure exactly what I'm signing up for here. Hm. First, sleep.

 

[Ethan Winer]

the board software is changing curly brackets to asterisks... Syntax errors: not my fault!

You can force the forum software to leave what you type verbatim with the [code ] and [ /code ] tags (but don't use the spaces):

{whatever}
{more special stuff}

The Code tags also retain blank spaces rather than close them up:

FOR X = 1 TO 10
   PRINT X;
NEXT

I sometimes use Code tags for ASCII art because it leaves spaces alone.

--Ethan

 

[xiphmont]

You can force the forum software to leave what you type verbatim with the [code ] and [ /code ] tags

Oh yay, thanks.

 

[Orb]

Xiph/Opus.
Just to throw in an alternative approach-perspective Keith Howard did some analysis of dithering back in 2006 (this is not the article I am looking for with regards to more recent investigations he has done regarding 24-bit/noise level/dithering/etc).
His approach-article was in the context (if read whole article from page 1 but not important) of audibility-behaviour of dither relating to 24-bit recordings truncated to 16-bit so not quite the same thing I accept and has certain large noticable caveats:

What I did for this was to generate five different noise signals—all with the same RMS amplitude but different PDFs—and add them to a piano recording ripped from the European Broadcasting Union's Sound Quality Assessment Material (SQAM) CD. In this track the inherent noise level is about –85dBFS, so the noise was added at an amplitude about 20dB greater in order to swamp it.

Varying the PDF of the added noise was achieved by summing together different numbers of random-number generators, from 2 to 5 (all this was done in software, and the processed files burned to CD-R for the listening comparison). As fig.6 shows, adding the output of two random-number generators results in noise with a triangular PDF; increasing the number of random-number generators further makes the noise more Gaussian in nature; ie, it has a PDF shaped more like the bell curve of the normal distribution. Gaussian noise is what we experience of analog processes, and might therefore be more natural to the ear than TPDF noise, whose PDF is like nothing we normally encounter in nature.

http://www.stereophile.com/content/contingent-dither-page-3
Cheers
Orb

 

[Gregadd]

http://en.wikipedia.org/wiki/Sampling_rate

By definition a sampe is incomplete.Look at the graph and you will see the gaps.