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DSD vs PCM resolution


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Could you describe how calculated this values? What conditions you took?

 

SNR? It is straight from the Shannon-Hartley theorem, channel capacity for 44.1k-base DSD64 is 2822400 bps and you need to take into account Nyquist-Shannon sampling theorem so you need to use 40000 as bandwidth usage for 0 - 20 kHz utilization.

 

Same equation gives 106.20 dB SNR for RedBook for 0 - 20 kHz (you have that 2.05 kHz band for noise) or 96.33 dB SNR for 0 - 22.05 kHz band. For 0 - 22.05 kHz band DSD64 the SNR figure is 385.32 dB (exactly same as 64-bit integer PCM would give).

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What I would like to get is the value of say dI/I (I being the volume or intensity of the signal) for the smallest quantization step, for a frequency of 1KHz, for both a loud signal and one 30dB lower, for both DSD and PCM. Four numbers.

 

 

Just kind of blathering here, don't know if this is helpful or even makes sense: I wonder whether thinking of DSD in terms of "smallest...steps" is a useful concept. The (very) general idea is more a running average over time, which allows the (average) result to adjust in far smaller increments than the individual steps. I suppose you could make an analogy to pixels on a screen that can switch between black and white far, far too rapidly for the switching to be seen, and by varying the amount of time each spends as black or white you can get nearly any shade of gray you want.

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I suppose you could make an analogy to pixels on a screen that can switch between black and white far, far too rapidly for the switching to be seen, and by varying the amount of time each spends as black or white you can get nearly any shade of gray you want.

 

This is how pixel intensity on plasma (and many LED) displays work, the intensity is controlled using PWM. Then the intensity is integrated using phosphorus or similar fluorescent coating on the screen (for LED it's just a parallel capacitance).

 

With DSD, the overall properties mostly depend on the oversampling (for DDC) and modulator implementation.

 

Because DSD is not simple delta-modulation, but instead has also the sigma in it, response to the bit stream changes is exponential.

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Hi Jud,

 

Yes. We can't consider both PCM and DSD as "steps". Due it is form of storing of signal only. Digital form.

 

We should consider restored analog signal only. It's filtered "steps" for PCM and DSD.

 

Best regards,

Yuri

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Just kind of blathering here, don't know if this is helpful or even makes sense: I wonder whether thinking of DSD in terms of "smallest...steps" is a useful concept. The (very) general idea is more a running average over time, which allows the (average) result to adjust in far smaller increments than the individual steps. I suppose you could make an analogy to pixels on a screen that can switch between black and white far, far too rapidly for the switching to be seen, and by varying the amount of time each spends as black or white you can get nearly any shade of gray you want.

Yes, this is the gist of it. I watched the video you posted and the key insights on how to go about doing the math are there, I just need some time to think about it (currently very busy with work).

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SNR? It is straight from the Shannon-Hartley theorem, channel capacity for 44.1k-base DSD64 is 2822400 bps and you need to take into account Nyquist-Shannon sampling theorem so you need to use 40000 as bandwidth usage for 0 - 20 kHz utilization.

 

Same equation gives 106.20 dB SNR for RedBook for 0 - 20 kHz (you have that 2.05 kHz band for noise) or 96.33 dB SNR for 0 - 22.05 kHz band. For 0 - 22.05 kHz band DSD64 the SNR figure is 385.32 dB (exactly same as 64-bit integer PCM would give).

 

Miska, thank you for additions. I want analize it more later.

 

Me also interest: why you suppose 24 steps (24 ones) of DSD for maximum amplitude achieving? What DAC's filter features there?

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SNR? It is straight from the Shannon-Hartley theorem, channel capacity for 44.1k-base DSD64 is 2822400 bps and you need to take into account Nyquist-Shannon sampling theorem so you need to use 40000 as bandwidth usage for 0 - 20 kHz utilization.

 

Same equation gives 106.20 dB SNR for RedBook for 0 - 20 kHz (you have that 2.05 kHz band for noise) or 96.33 dB SNR for 0 - 22.05 kHz band. For 0 - 22.05 kHz band DSD64 the SNR figure is 385.32 dB (exactly same as 64-bit integer PCM would give).

 

The Shannon-Harley theorem gives an upper bound. It says it's impossible to exceed this bound. However, it doesn't prove that practical implementations exist that can match the bound. In practice, the bound can be fairly closely approached by complex modulation schemes as used in some modems, but these do not correspond to legal DSD modulators because they typically generate random signals and use complex error correcting coding, not something that can be decoded to analog with a low-pass filter.

 

A second question is how one measures the noise. This is not so difficult in traditional PCM. Where there is noise shaping and non-linear feedback it is possible for there to be artifacts that have low power averaged over a long period, but when averaged over a shorter period (appropriate to the ear's temporal response) these artifacts may be audible.

 

It would be helpful if you could describe the performance of your modulator(s) and how you measure this.

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A second question is how one measures the noise. This is not so difficult in traditional PCM.

 

There are different methods measure SNR.

 

1. As example, take sine and filter band (first band) about it (measure signal energy - S). And filter pure noise band (same weight) about first band - it's noise energy N.

 

After made S/N. It will SNR.

 

For more correct result need take SNR for several frequencies into signal band.

 

2. If signal fill full its band, we can measure energy noise N before signal switch ON.

 

But last method suitable for ideal modulator and input signal only. Due signal can have own level of noise (in useful band) during transmit mode. Or due some modulator distortions.

 

This method is not recommended.

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Bonjour,

 

This is slew rate. I care about min deviation for a 1KHz signal - 1mS - not a 176KHz signal.

 

Slew rate is down to the filter that integrates. As the Modulators for DSD are between 6th order (Grimm/Putzney) and 8th Order (Weiss Saracon) with 7th order the purple book spec. a very high order filter with in effect a 20kHz lowpass is implied. This will severely impact the slew rate. How bad, I do not see the 24 Samples to slew from maximum negative to maximum positive...

 

Anyways, what I calculated was the smallest step that can be in theory expressed for a 1mS (single 1kHz sinewave cycle) signal (as you asked for 1kHz). For DSD we have 2822 possible 1's and zeros in 1mS. So the system at maximum can express 2822 values in this time. This gives the 11mV cited (normalised to 0dBFS = 2V).

 

As DSD is often compared to quad speed PCM and claimed to be equal or superior I decided to use this as comparison.

 

Here is the rub. PCM has time domain granularity of X (Sample rate) and amplitude domain granularity of Y (Wordlength) and within limitations of analogue circuitry can be as precise as either analogue linearity or noise or wordlength allow (whichever term is dominant).

 

The same is of course true of DSD or Sigma Delta modulation, but here the amplitude domain granularity is very low (only two values instead of 2^wordlength).

 

There are corollaries. DSD resolution is frequency dependent. At DC it is essentially infinity (limited by noise and nonlinearity). At halve the sample rate it is in effect zero. Simple modulators would show a straight line between zero and infinity, more complex ones can reshape the noisefloor considerably.

 

If sample rate and wordlength suffice than a simple lowpass low order filter after the PCM DAC suffices to deliver a 1kHz sinewave that for each 1mS shows a "perfect" wavelet.

 

The same is of course true of Sigma Delta, however with only DSD128 and DSD64 available for testing one can safely say that these sample rates are insufficient.

 

If you want to compare DSD resolution to PCM resolution just a Non-Oversampling ladder DAC and a DSD solution, make test tones for both and look at the signal with an oscilloscope.

 

One look suffices to declare "Sigma Delta" to be severely broken to any old analogue engineer who used to test linear analogue circuits.

 

Salud M.I.

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Bonjour,

 

SNR? It is straight from the Shannon-Hartley theorem, channel capacity for 44.1k-base DSD64 is 2822400 bps and you need to take into account Nyquist-Shannon sampling theorem so you need to use 40000 as bandwidth usage for 0 - 20 kHz utilization.

 

Same equation gives 106.20 dB SNR for RedBook for 0 - 20 kHz (you have that 2.05 kHz band for noise) or 96.33 dB SNR for 0 - 22.05 kHz band. For 0 - 22.05 kHz band DSD64 the SNR figure is 385.32 dB (exactly same as 64-bit integer PCM would give).

 

Quel dommage. This Theorem gives LIMIT VALUES and not for coding using either single bit modulators or binary weighted PCM.

 

What is it with Sigma Delta proponents that makes them always inflate their numbers well past ridiculous?

 

You would have to state the order of noise shaper you apply to derive a meaningful number.

 

Using just single bit modulation at 2.822MHz and no noise shaping gives 25.8dB SNR for 0 - 22.05kHz. Unless we specify he noise shaping applied in detail, we cannot make any determination about SNR except by experiment.

 

This is even worse than that graph that pretends to compare DSD and 24 Bit PCM and omits to account for some 39dB FFT Gain in the noisefigures for DSD, which would have to be applied to PCM in this Graph to show apples for apples noisefloor...

 

DSD_PCM.jpg

 

If we apply this correction, well, this is what should have been presented:

 

Untitled.jpg

 

Suddenly DSD does not look so impressive. Archimago has been investigating this whole DSD vs. PCM Malarkey in some detail, including generating test signals in the digital domain and analysing them there.

 

Here is what he ended up with:

 

Noise%u00252BPCM%u00252Bvs.%u00252BDSD.png

 

Very instructive, very good blog, excellent research and good expermriments, if you want to know what happens technically:

 

Archimago's Musings: ANALYSIS: DSD-to-PCM 2015 - foobar SACD Plug-In, AuI ConverteR, noise & impulse response...

 

I'll let everyone draw their own conclusions on how much veritas is in the rantings and ravings and number inflation that makes Enron look tame by comparison is there with the Sigma Delta proponents. I shall go for a triple-triple down to the Dep and see if there is enough coffee in that, it strikes me as more gainful.

 

Salud M.I.

Magnum innominandum, signa stellarum nigrarum

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Bonjour,

 

Very instructive, very good blog, excellent research and good expermriments, if you want to know what happens technically:

 

Archimago's Musings: ANALYSIS: DSD-to-PCM 2015 - foobar SACD Plug-In, AuI ConverteR, noise & impulse response...

 

 

Another good and realistic look at DSD vs. PCM:

 

Craigman Digital - PCM vs DSD

 

Salud M.I.

Magnum innominandum, signa stellarum nigrarum

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Bonjour,

 

 

 

Quel dommage. This Theorem gives LIMIT VALUES and not for coding using either single bit modulators or binary weighted PCM.

 

What is it with Sigma Delta proponents that makes them always inflate their numbers well past ridiculous?

 

You would have to state the order of noise shaper you apply to derive a meaningful number.

 

Using just single bit modulation at 2.822MHz and no noise shaping gives 25.8dB SNR for 0 - 22.05kHz. Unless we specify he noise shaping applied in detail, we cannot make any determination about SNR except by experiment.

 

This is even worse than that graph that pretends to compare DSD and 24 Bit PCM and omits to account for some 39dB FFT Gain in the noisefigures for DSD, which would have to be applied to PCM in this Graph to show apples for apples noisefloor...

 

[ATTACH=CONFIG]20139[/ATTACH]

 

If we apply this correction, well, this is what should have been presented:

 

[ATTACH=CONFIG]20140[/ATTACH]

 

Suddenly DSD does not look so impressive. Archimago has been investigating this whole DSD vs. PCM Malarkey in some detail, including generating test signals in the digital domain and analysing them there.

 

Here is what he ended up with:

 

[ATTACH=CONFIG]20141[/ATTACH]

 

Very instructive, very good blog, excellent research and good expermriments, if you want to know what happens technically:

 

Archimago's Musings: ANALYSIS: DSD-to-PCM 2015 - foobar SACD Plug-In, AuI ConverteR, noise & impulse response...

 

I'll let everyone draw their own conclusions on how much veritas is in the rantings and ravings and number inflation that makes Enron look tame by comparison is there with the Sigma Delta proponents. I shall go for a triple-triple down to the Dep and see if there is enough coffee in that, it strikes me as more gainful.

 

Salud M.I.

 

Old argument on these pages.

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Bonjour,

 

 

 

Quel dommage. This Theorem gives LIMIT VALUES and not for coding using either single bit modulators or binary weighted PCM.

 

What is it with Sigma Delta proponents that makes them always inflate their numbers well past ridiculous?

 

You would have to state the order of noise shaper you apply to derive a meaningful number.

 

Using just single bit modulation at 2.822MHz and no noise shaping gives 25.8dB SNR for 0 - 22.05kHz. Unless we specify he noise shaping applied in detail, we cannot make any determination about SNR except by experiment.

 

This is even worse than that graph that pretends to compare DSD and 24 Bit PCM and omits to account for some 39dB FFT Gain in the noisefigures for DSD, which would have to be applied to PCM in this Graph to show apples for apples noisefloor...

 

[ATTACH=CONFIG]20139[/ATTACH]

 

If we apply this correction, well, this is what should have been presented:

 

[ATTACH=CONFIG]20140[/ATTACH]

 

Suddenly DSD does not look so impressive. Archimago has been investigating this whole DSD vs. PCM Malarkey in some detail, including generating test signals in the digital domain and analysing them there.

 

Here is what he ended up with:

 

[ATTACH=CONFIG]20141[/ATTACH]

 

Very instructive, very good blog, excellent research and good expermriments, if you want to know what happens technically:

 

Archimago's Musings: ANALYSIS: DSD-to-PCM 2015 - foobar SACD Plug-In, AuI ConverteR, noise & impulse response...

 

I'll let everyone draw their own conclusions on how much veritas is in the rantings and ravings and number inflation that makes Enron look tame by comparison is there with the Sigma Delta proponents. I shall go for a triple-triple down to the Dep and see if there is enough coffee in that, it strikes me as more gainful.

 

Salud M.I.

 

The last chart you show was pulled by Archimago from the PS3SACD Forum. In turn it was pulled by the poster on that forum from a page that now comes up 404 Not Found. This is not the sort of provenance I personally look for when searching for probative, informative material.

One never knows, do one? - Fats Waller

The fairest thing we can experience is the mysterious. It is the fundamental emotion which stands at the cradle of true art and true science. - Einstein

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Using just single bit modulation at 2.822MHz and no noise shaping gives 25.8dB SNR for 0 - 22.05kHz. Unless we specify he noise shaping applied in detail, we cannot make any determination about SNR except by experiment.

 

You cannot even do delta-sigma modulation without noise shaping.

 

Suddenly DSD does not look so impressive. Archimago has been investigating this whole DSD vs. PCM Malarkey in some detail, including generating test signals in the digital domain and analysing them there.

 

It all depends on what modulator you use...

 

Very instructive, very good blog, excellent research and good expermriments, if you want to know what happens technically:

 

And very limited scope. Of course it is nice to do experiments in digital domain, but it is much more useful to measure actual DAC outputs what I've been doing. I'm still waiting to see a PCM ladder DAC that has -144 dB THD+N with 24-bit input.

 

Almost systematically my measurements have shown that you get practical performance improvements using DSD instead of PCM. Such as lower IMD, for which there are clear technical reasons too.

 

For example iFi iDSD Micro:

44100/32 input ("Standard" digital filter): THD+N=0.00678%, IMD=0.00114%

DSD256 input: THD+N=0.00257%, IMD=0.00086%

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When we compare PCM and DSD we can compare

 

[DSD sample rate + noise shaping] vs. [PCM bit depth].

 

PCM sample rate don't impact to quantization noise. Except we apply noise shaping like DSD.

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The Shannon-Harley theorem gives an upper bound. It says it's impossible to exceed this bound. However, it doesn't prove that practical implementations exist that can match the bound.

 

Yes, that's why I said it is theoretical limit... People started to talk about theoretical limits.

 

From theory perspective the calculations I gave are valid.

 

In practice, the bound can be fairly closely approached by complex modulation schemes as used in some modems, but these do not correspond to legal DSD modulators because they typically generate random signals and use complex error correcting coding, not something that can be decoded to analog with a low-pass filter.

 

Complex DSD modulators are not so far from modems and are actually more complex than modems use in their fairly low power DSP chips. For example it has been shown that practical ninth order modulator can reach 190 dB SNR for audio band at DSD64 rate. Ninth order modulator is still far from a "brickwall" modulator that would come closer to the theoretical limits. I know how 4G/LTE radio modem and signaling works and it is pretty simple in the end, but afterall it needs to be implementable on a $100 phone that doesn't drain the battery in an instant. While developing modulator to run for audio in a computer I don't need to care how much computational power it is going to take, I can focus purely on the technical performance.

 

For DSD256 and higher rates I trade a bit of bandwidth for pushing audio band noise floor down way below 24-bit PCM equivalent levels.

 

Sure, I can generate make 128-bit PCM at arbitrary rate in a computer and say it looks nice in digital domain analysis. But it doesn't have anything to do with real world performance what comes out of the DAC. While the real world performance is what I'm interested in.

 

A second question is how one measures the noise. This is not so difficult in traditional PCM. Where there is noise shaping and non-linear feedback it is possible for there to be artifacts that have low power averaged over a long period, but when averaged over a shorter period (appropriate to the ear's temporal response) these artifacts may be audible.

 

That is one area where on-chip modulators fall short. But in particular those non-linear feedbacks in PCM DAC analog sections cause elevated IMD figures. Another much bigger problem with PCM are the band limiting filters required to reach nice figures which causes much more audible temporal artifacts than any modulator behavior.

 

And a lot of 16-bit RedBook material certainly use noise shaping to improve perceived dynamic performance. You also need to note that you rarely encounter "pure" PCM outside of theory these days, because all new audio ADCs and almost all DACs are delta-sigma design and the PCM you see is just result of (often poor) decimation from the original ADC's SDM format.

 

It would be helpful if you could describe the performance of your modulator(s) and how you measure this.

 

I rather describe it through measurements with real world D/A converters, because that is what matters.

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PCM sample rate don't impact to quantization noise.

 

In a way it does, if you keep inspection bandwidth the same, but increase sampling rate (oversampling). Every doubling of sampling rate gives you one extra bit worth of dynamic range in the same bandwidth, because the quantization/flat dither noise spreads throughout the Nyquist band.

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In a way it does, if you keep inspection bandwidth the same, but increase sampling rate (oversampling). Every doubling of sampling rate gives you one extra bit worth of dynamic range in the same bandwidth, because the quantization/flat dither noise spreads throughout the Nyquist band.

 

Level noise for upsampled PCM signal will lower. But energy of noise (what impact to dynamic range of analog part) is constant independent of sample rate.

 

So we win nothing.

 

However, if we upsample and filter useful range (0 ... 20 kHz - called above as inspection bandwidth), we get profit - lower energy noise (energy beyond 20 kHz was eliminated).

 

I.e. more upsampling grade - less remain of noise energy.

 

It's like noise shaping and filtering noise into DAC for DSD.

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However, if we upsample and filter useful range (0 ... 20 kHz), we get profit - lower energy noise (energy beyond 20 kHz was eliminated).

 

I.e. more upsampling grade - less remain noise energy.

 

It's like noise shaping and filtering noise into DAC for DSD.

 

Yes, that part is done by the analog reconstruction filter in the DAC, or alternatively digital filter in digital domain to higher word length, or FFT of the full band, but use only the FFT bins in the wanted pass-band for analysis (which is again equivalent of filtering).

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Bonsoir,

 

 

Old argument on these pages.

 

 

An old argument is not a wrong or technically incorrect argument, unless it has been shown to be so. Kirchhoffs law is very old but still valid.

 

 

The last chart you show was pulled by Archimago from the PS3SACD Forum. In turn it was pulled by the poster on that forum from a page that now comes up 404 Not Found. This is not the sort of provenance I personally look for when searching for probative, informative material.

 

 

You may wish to look at the whole article.

 

 

The chart seems correct though. You can easily download RMAA and to the same experiment for 16/44.1 and 24/96 test tones. And the DSD64 trace closely matches that shown by Andreas Koch for DSD together with the (deliberately?) incorrect graphing of the PCM Formats shown above. So this chart shows "canonical SACD DSD" and "standard PCM" correctly according to all applicable theories.

 

Had you been looking at the excellent articles on this site you would be able to see how many other modulators compare. Much useful info and no "CD is good enough" BS like Xiph.

 

 

You cannot even do delta-sigma modulation without noise shaping.

 

 

I was not referring to Sigma Delta modulation, just to single bit, which can absolutely and positively be done without noiseshaping. Check out any decent book on basic electronics to find such systems described in detail.

 

 

It all depends on what modulator you use...

 

 

Absolutely. Analogue Domain modulators have severe stability issues, are prone to creating idle tones. As that is what is used as ADC it is what should be matter of debate.

 

 

If we are debating PCM to DSD conversion, this process must be lossy, UNLESS we employ a theoretically perfect modulator with a noise-free bandwidth greater than the noise-free bandwidth than the source. As for 32/44.1 this bandwidth is 22.05kHz at the minimum 128 FS Sigma Delta would have to be used.

 

 

And very limited scope. Of course it is nice to do experiments in digital domain, but it is much more useful to measure actual DAC outputs what I've been doing.

 

 

Considering that you have a tendency to measure at several MHz, rather than in the audio band I would have to question the point of your measurements. Even dogs do not hear past 100kHz. Now if you instead actually showed audio band measurements scaled to be comparable to the tests JA does at Stereophile (you can still at several MHz for addition) there may be some use tour measurements. Currently I fail to see any value to humans who have very limited HF hearing.

 

 

I'm still waiting to see a PCM ladder DAC that has -144 dB THD+N with 24-bit input.

 

 

I'm still waiting to see a Sigma Delta DAC that has -144 dB THD+N with 24-bit input or 1-Bit input. At 2V 0dBFS level this is the same as the noise of a 50 Ohm resistor.

 

 

Almost systematically my measurements have shown that you get practical performance improvements using DSD instead of PCM. Such as lower IMD, for which there are clear technical reasons too.

 

 

For example iFi iDSD Micro:

44100/32 input ("Standard" digital filter): THD+N=0.00678%, IMD=0.00114%

DSD256 input: THD+N=0.00257%, IMD=0.00086%

 

 

There is a clear technical reason mes ami. Your measurements compare a system that is in effect 4 times oversampled (DSD256) to one that is not, or one might say apples to oranges. One would expect around 6dB improvement from that, I'd say your test results are within experimental error limits. You should have used 176.4k/32 not 44.1k/32 to compare to DSD256, or DSD64 to compare to 44.1k/32.

 

 

In a way it does, if you keep inspection bandwidth the same, but increase sampling rate (oversampling). Every doubling of sampling rate gives you one extra bit worth of dynamic range in the same bandwidth, because the quantization/flat dither noise spreads throughout the Nyquist band.

 

 

This is incorrect. Every doubling of sample rate lower noise by 3dB (1/2 Bit) not 6dB (1 Bit). Please look up any basic text that deals with oversampling for confirmation.

 

 

For example: Understanding Delta-Sigma Modulators | Analog content from Electronic Design

 

Salud M.I.

Magnum innominandum, signa stellarum nigrarum

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An old argument is not a wrong or technically incorrect argument, unless it has been shown to be so.

 

I think I have shown it couple of times already? But it is really boring to look at same URLs over and over again over the years while you fail to reproduce any of your own study results that would show that you have actually researched the subject yourself.

 

You can easily download RMAA and to the same experiment for 16/44.1 and 24/96 test tones.

 

I have a license for RMAA but it is too buggy and not very good for my taste. And it only knows about PCM.

 

I was not referring to Sigma Delta modulation, just to single bit, which can absolutely and positively be done without noiseshaping.

 

Non-Sigma-Delta 1-bit is not relevant to this discussion in any shape or form.

 

Absolutely. Analogue Domain modulators have severe stability issues, are prone to creating idle tones. As that is what is used as ADC it is what should be matter of debate.

 

I'm fine debating that, but I also expect then some real world realizations too from the people debating. So far I've put my efforts only on DAC side, but maybe I'll focus on the ADC side next. I have some idea for that area too... ;)

 

If we are debating PCM to DSD conversion, this process must be lossy, UNLESS we employ a theoretically perfect modulator with a noise-free bandwidth greater than the noise-free bandwidth than the source. As for 32/44.1 this bandwidth is 22.05kHz at the minimum 128 FS Sigma Delta would have to be used.

 

64x DSD is enough for practically flat noise floor in 22.05 kHz band. But I don't have any problem running 512 fs SDM in my software.

 

Considering that you have a tendency to measure at several MHz, rather than in the audio band I would have to question the point of your measurements. Even dogs do not hear past 100kHz. Now if you instead actually showed audio band measurements scaled to be comparable to the tests JA does at Stereophile (you can still at several MHz for addition) there may be some use tour measurements. Currently I fail to see any value to humans who have very limited HF hearing.

 

The figures I posted in my earlier mail are from Prism dScope III. Just because I thought that you would bring up the same topic again.

 

I'm still waiting to see a Sigma Delta DAC that has -144 dB THD+N with 24-bit input or 1-Bit input. At 2V 0dBFS level this is the same as the noise of a 50 Ohm resistor.

 

So far, the performance I've seen from delta-sigma DACs is much closer, especially in THD+N of low level signals below -100 dBFS. Equivalent resistance of 50 ohm is easy to achieve for example with my DSC1 DAC by using 1.6 kOhm resistors in the array.

 

There is a clear technical reason mes ami. Your measurements compare a system that is in effect 4 times oversampled (DSD256) to one that is not, or one might say apples to oranges. One would expect around 6dB improvement from that, I'd say your test results are within experimental error limits. You should have used 176.4k/32 not 44.1k/32 to compare to DSD256, or DSD64 to compare to 44.1k/32.

 

Wrong, the DAC IS internally oversampled by 8x plus additional SAH oversampling using the "Standard" digital filter built into the DAC chip. Using it in DSD mode bypasses oversampling and the internal modulator.

 

In the DSD case, source data is exactly same 44100/32 input file, but oversampled and modulated in my player.

 

Due to low order built-in modulator of the DSD1793 chip, the noise floor goes up early with PCM inputs.

 

This is incorrect. Every doubling of sample rate lower noise by 3dB (1/2 Bit) not 6dB (1 Bit). Please look up any basic text that deals with oversampling for confirmation.

 

 

For example: Understanding Delta-Sigma Modulators | Analog content from Electronic Design

 

The difference is because they incorrectly use 10*log10() in their calculation, while if they use 20*log10() you get 6 dB. The difference is only depending if you consider power or amplitude. Depending on particular subject, ½ is 3 dB or 6 dB.

10*log10(2) = 3.0103

20*log10(2) = 6.0206

 

And the formula doesn't take into account filtering out the noise from the oversampling.

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A couple of decades ago, when sigma-delta chips replaced R2R chips in DACs, did the distortion and noise specs of DACs suddenly become horrible?

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The difference is because they incorrectly use 10*log10() in their calculation, while if they use 20*log10() you get 6 dB. The difference is only depending if you consider power or amplitude. Depending on particular subject, ½ is 3 dB or 6 dB.

10*log10(2) = 3.0103

20*log10(2) = 6.0206

 

And the formula doesn't take into account filtering out the noise from the oversampling.

 

Little example:

 

For 2 times upsampled band, power noise in band equal half old (low) sample rate has 2 time less power (-3 dB).

 

 

 

Before upsampling:

 

1. Old sample rate F1

 

2. Energy noise in band F1/2 is E1

 

After upsampling:

 

1. New sample rate F2=F1*2

 

2. Now energy noise in old band F1/2 is E1/2 (i.e. 3 dB [by power] lesser than before upsampling).

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