DSD vs PCM resolution

[magnum innominandum]

Bonjour,

 

That's my thesis. Would love to see some math about it.

 

It is very simple.

 

PCM gives a precise (within wordlength) absolute value at a specific point in time (not valid for PCM derived from Sigma Delta ADC). Then anything is ignored until the next sample. In principle PCM can traverse the full signal range within two samples. Neither previous nor following sample have any impact on the value of the current sample. This means there is a clear granularity in both amplitude and time domain. But each value is precise and absolute. Quantization noise exists at a predictable level that is linked directly to the number of bits involved.

 

At true PCM (multibit ADC and DAC, no digital filter) > 96kHz and > 18 Bit it will be hard to argue that this granularity matters (think 4k HDTV or Retina Display on your Mac vs Standard TV), at 44.1kHz and 16 Bit there is much room for debate.

 

Now Sigma Delta tells you at a precise moment in time if since the last sample the signal has moved up or down. There are no absolute values. Signals must be integrated over a very long time window (relative to the sampling frequency) to make any sense. Given that most audio testing is nowadays done using FFT (which integrates over very long time windows) it favours Sigma Delta systems. Using the plain old 5MHz heathkit tube oscilloscope of course shows a waveform that would make any analogue amplifier designer worth his salt swear the device under test was broken, severely so, but a 'scope is not an AP2. Actually, on the same 'scope a high grade PCM DAC looks fine. Additionally, to traverse the full signal range needs a large number of samples, so there is a severe implied slew rate limit, much lower in frequency than the Nyquist frequency of sample rate/2. The final point is that if we require more than 7.77dB dynamic range from a single bit DAC we must apply both high rate oversampling AND noise shaping. See Lipshitz/Vanderkoy on the challenges of that sort of thing. Again, we have a granularity, but unlike the PCM "regular blockiness" (which needs high sample rates and wordlength to disappear below analogue noise) it is a more random, irregular thing but at MUCH higher levels, kind of more like JPEG artefacts vs regular blockyness of lower resolution (and which needs very high sample rates or a combination of multibit and sigma delta at high rates to disappear below the noisefloor).

 

For a Delta Sigma modulated system if we used (say) 8 Bits of multibit and 5.6MHz sample rate with a 4th order modulator and a noise rise at > 50kHz, clearly the implied granularity is far enough outside anything that matters. At 2.8MHz and 1 Bit there is much room for debate.

 

Bottom line, both Sigma Delta and PCM have well defined and understandable limits.

 

For music both 44.1kHz / 16 Bit and 2.8MHz / 1 Bit are probably not good enough to be reliably transparent, if we pursue top end quality. And where there are differences there are preferences and audiofools love hearing differences more than they care if the difference makes them enjoy listening to music more or less and form preferences generally based on who tells a better story.

 

If we convert one format to another somewhere in the chain, any such conversion can only loose information and add noise/distortion. More differences audiofools can get giddy over...

 

So what do we actually hear?

 

Many early CD's are done with a Sony 1630, meaning non-oversampled 44.1/16 and early CD Players played like that (no oversampling).

 

Later Sigma Delta ADC's came in, then Sigma Delta DAC's placing Sigma Delta at both conversion stages but converting to/from Sigma Delta. HDCD's of course were recorded with a Multibit ADC, what the playback is - differs.

 

So, most of the time when people talk about comparing PCM and DSD, they actually compare the various conversion algorithms at different stages in the chain, not formats.

 

Moi!? I prefer PCM playback, even of DSD. Foobar does a good job in converting.

 

Using a Nelson Pass designed DAC with PCM63 true 20 Bit Multibit DAC, zero negative feedback FET output stage and a sound you just do not get from anything Sigma Delta, zip, zilch, nada. Mine has a 192k cirrus logic receiver fitted and bypasses the digital filter. I managed to keep Nelson's brilliant jitter killer SAW Clock working in this. Totally brilliant design, I see nowadays people turn to SAW clocks over Femto clocks for low jitter. Nelson was there 15 Years ago!

 

Converting DSD to 176.4k PCM in Foobar and playing it on that machine (using modified HiFace as SPDIF source) kills DSD on any Sabre Chip and Cirrus Logic Chip I had the chance to try. PCM does the same.

 

I guess the problem today is that all we have are Sigma Delta based DAC's (or read a large hammer) so all problems start looking like Sigma Delta being required to solve (or read a railway pin needing pounding in with said hammer).

 

Salud M.I.

[magnum innominandum]

Bonjour,

 

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.

 

Ok, lets take this easy.

 

We take (for arguments sake) 176.4kHz 24 Bit PCM strictly in the digital domain.

 

The smallest amplitude step possible scaled to 5.6V PP full scale is 5.6/16777216 or 333nV and the time for this step is 1/176400 or 5.66uS. So the smallest step is 333nV/5.66uS. The maximum step is 5600mV/5.66uS.

 

Compare 2.822MHz DSD. This gets difficult, as resolution varies with frequency, at DC DSD has "infinite" resolution, at 2.822MHz non (due to noiseshaping). But we know the actual noisefloor is -120dBFS integrated (or -156dBFS including the common FFT gain looking at a FFT plot).

 

Lets start at the min. If we take a 1kHz signal we have 2822 Samples available. The cycle time is 354nS and scaled to a 5.6V PP Level the minimum signal step is 5.6/2822 or 1.98mV/354nS. The maximum signal level requires essentially an 0.707/2 duty cycle, or 2822/2*0.707 or 997 "on" cycles in 2822 cycles. So the largest step is (5.6/2822*997)/1mS or 2V/mS.

 

Lets normalise to 5.66uS and 5.6V PP.

 

2.822MHz/1Bit has a minimum deflection 125uV over a 5.66uS interval

2.822MHz/1Bit has a maximum deflection of 11mV over a 5.66uS interval

176.4kHz/24Bit has a minimum deflection of 0.33uV over a 5.66uS interval

176.4kHz/24Bit has a maximum deflection of 5600mV over a 5.66uS interval

 

Now if we open up the window, things change.

 

But on the time and amplitude micro level 176.4/24 beats the proverbial out of DSD at all funloving levels, except for time resolution (which matters jack without matching amplitude resolution). PCM has 378 times the low level resolution and 509 times the high level resolution of DSD.

 

Of course, if we change our standard to 44.1kHz and 16 Bit things change substantially, the excercise of calculating this case is left to the reader.

 

Salud M.I.

[magnum innominandum]

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.

[magnum innominandum]

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...

 

 

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

 

 

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:

 

 

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]

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]

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]

Mes Ami Paul,

 

Perhaps you should re-read a few articles - PCM to DSD conversion is perfectly lossless. No audio or timing information whatsoever is lost. It is a conversion, -> not <- a compression algorithm.

 

If this was the case you could do the following:

 

1) Start with any music file in 16Bit/44.1kHz extracted from CD.

2) Convert to DSD64 using any conversion software you care to use.

3) Convert back from DSD64 to 16Bit/44.1kHz.

4) Run the original source file and the result of the double conversion through Audio DiffMaker:

Audio DiffMaker

 

If the conversion is completely lossless the two files will be identical.

 

If they are not, you will able to analyse (Listen, FFT, virtual oscilloscope etc. et all) precisely what the differences are.

 

If you find the results identical - please post the results here, including the source file and what converter you used with which settings. If you find them different, you may also wish to post the results and a retraction.

 

Salud M.I.

[magnum innominandum]

Bonsoir,

 

But at the end of the day - you gotta listen to music. You can't enjoy music by looking at bits and graphs. And the reason I listen to DSD is simple. I can listen to DSD without a DAC. And I do. Regardless of the technical merits of FSD vs PCM, I reckon that the physical implementation of the DAC is the biggest determinant of sound quality. And I find that DSD, played through a simple LPF, is better than any DAC. The sound has a holographic (analog) character that i don't experience from any DAC.

 

[ATTACH=CONFIG]20170[/ATTACH]

 

I did try a very similar "no-chip" DAC (DIYINHK USB Board with isolator and external clock) after it was talked up so much in some babillards. I used 3rd order passive filter at 100kHz.

 

Using Foobar2k's DSD converter I tried this at the different supported DSD rates. Even at DSD256 I felt the original Pass converter with PCM63 DAC Chip's did a much better job of sounding "analogue" or "like the best of vinyl minus clicks, pops, noise and tracking distortion". At slower speed the advantage of the Pass converter increased, I felt CD->DSD64 by comparison produced a hilarious dummy sound, caricature de la musique de merde.

 

But the killer was listening to actual DSD downloads. I found that many DSD files I played via this kind of "chipless DSD DAC" had very audible distortion and background sounds I would call "birdies" (based on my Ham radio days). Merde de merde.

 

Funny thing, DSD converted to 88.2kHz PCM and played via Pass D-1 sounds okay, but not as a good CD.

 

Salud M.I.

[magnum innominandum]

Bonjur,

 

At megahertz, layout is critical. The noise is gone with a proper layout.

- I use a flip flop with complementary outputs for a balanced signal. Perhaps this helps with noise. My motivation was simply that I have a balanced system, and I wanted to keep this new source balanced as well. But I think that noise rejection may be another benefit.

 

I build this fully balanced using Potato Semi PO74G74A Flip Flop with complementary outputs and fully balanced signal path (my whole system is) and with a super-reg kit for the supply. PCB made from solid copper plane FR4 for groundplane and SMD Cap's etc. in very tight "dead bug" style. You can prototype GHz stuff like that, we did that back when I worked as EE for that Texan Semi maker...

 

Birdies did not happen for any PCM material converted with Foobar2k DSD upsampler even to DSD64. They only happened with real DSD recordings (SACD Rips more precisely).

 

As said, compared to a good multibit DAC I found the sound quality lacking, though compared to some contemporary DAC's I would say this little "Flip-Flop" DAC did quite well, if the sample rate was high enough... But I already own a better DAC.

 

- Forget Foobar. I used foobar for years, but I found HQPlayer a few months ago and there is no going back.

 

I use J-River. I only use the PCM-DSD conversion part of Foobar in this experiment.

 

I downloaded the Trial of HQ Player. Sorry, I have never encountered such an infuriatingly unusable piece of software before. Usability scores on one out of ten are minus infinity. I pass, thank you.

 

- I have a DIYINHK board, and as far as I can tell it only plays DSD as DoP. Therefore it is limited to DSD128 AFAIK. How did you get DSD256?

 

The problem is the XMOS USB Driver, not the hardware/xmos firmware which has support build into the code. Some unscrupulous people in a part of the world where copyright is mostly ignored have been modifying drivers to allow many cheap chinese devices to use ASIO DSD.

 

http://www.pchifi.cn/forum.php?mod=viewthread&tid=104816&extra=&page=1

 

Salud M.I.

[magnum innominandum]

Bonjour,

 

Yep to all the above, Hazard, and great thread over at diyaudio which became much better than my older one.

 

The so-called 'birdies' most probably had to do with the implementation since the down-conversion to 88 PCM was OK, but some people conclude the format isn't good...

 

I agree, the birdies result from implementation, but non of the DAC le FlipFlop, but of the ADC modulator during SACD recording.

 

Both Doede Douma (the creator of DDDAC who inspired me to bypass the digital filter) John Swenson have reported similar problems. It may be we hearing the problems predicted by Lipshitz/Vanderkoy in their paper criticising DSD.

 

JS observed that the Burr Brown style analogue FIR Filter (as also found in several DIY DSD DAC's) do a good job of scrambling these tones out of existence.

 

I thin purely digital modulator (e.g. the one in the DSD converter from Foobar2k) can perform near the theoretical limits and avoid creating these tones. Real modulators in analogue hardware seem to have problems though.

 

Anyway, birdies were only observed playing SACD Rips, not with (CD Standard) PCM converted to DSD.

 

A great way to justify not trying what is possibly the highest SQ player currently available...

 

There is an initial learning curve, but once you're past it, it's really easy to use.

 

Use PCM if you can't use DSD.

 

Note, I use PCM only, normally.

 

My Pass D1 DAC handles up to 96kHz/24Bit, I use M2Tech Hi-Face to drive SPDIF from a spare Lenovo Thinkpad.

 

I have been keeping some DSD/SACD images around as they seem to have better overall mastering and dynamic range than CD copies in circulation. For these I use the Foobar2k DSD-PCM converter to 88.2kHz/24Bit. It sounds no worse than any notional DSD DAC I had around to play with.

 

I found no sound difference between J-River and HQ Player, non.

 

If it actually sounded better I might be willing to put up with the interface (read lack thereof), lack of usability and learning curve and all if it did anything for sound.

 

Salud M.I.

[magnum innominandum]

Bonsoir mes Amis,

 

Wasn't that paper thoroughly debunked by another paper?

 

Debunked? L & V presented a further paper in replay on the same day that thoroughly "debunked" the papers of Philips and Angus criticising theirs, not just making claims (like the papers criticising theirs), but showing the full math.

 

There are excellent modulators and filters in HQ Player.

 

I only play PCM without digital filter, I fail to see relevance.

 

Knowledge of the exact provenance could be helpful here: if the SACD was made from PCM tracks, this is going to give you vastly different results than if the SACD was made from pure DSD recordings as any conversion is lossy.

 

I think the SACD's I like are made from analogue master tape.

 

It's important here to note which DAC and how they work internally (any internal conversion and how).

 

I had the iffy stuff here, both model (so-so sound, not much resolved, plus not balanced out which is a pain), several China made "Sabre" DAC's, a Weiss Sabre DAC (they all sounded rather similar - not bad not good) and a DIY Unit with discrete DSD DAC from Japan. They all did little to convince me of the merits of DSD or PCM -> DSD conversion. For the japan DAC I needed to add my old Tube Preamp back as well, no volume.

 

There are people with vastly better equipment than me who would agree to strongly disagree with you about what they perceive, but so long as you're happy, go with what you like.

 

My equipment is very modest. I follow the ideas of Arthur Salvatore in the system setup, due to trying his advise I removed my Tube Preamplif and got my speakers.

 

I use Thinkpad plus M2TECh hiface, Win8, Fidelizer and J-River (tried J-play, no difference). This replace CEC TL1 Beltdrive CD Transport.

 

DAC is Pass D1, refurbished in 2011 (nichicon Muse capacitors replacing old tired caps) and modified with no digital filter (on idea of Mr. Doede Douma - I much like the result) and J-Fets in the I/V-Converter which is said lowers distortion.

 

The DAC directly drive Amplif Pass Aleph 2, these I refurbished in 2011 with upgrades in Capacitors (Nichicon Muse KG Super Through and other Nichicon Muse and SCR Fast Cap) and Mosfets from Fairchild (more linear).

 

The speaker is A.R.S. Acoustique System Max, think Wilson Watt/Puppy but with good sound.

 

Cables are Kimber Argent for signal and Shunyata for mains.

 

Room treatment is Acoustic Sciences.

 

The Pass D1 DAC may accept 24bit/96kHz PCM, but its nonlinear distortions (THD) are at 74dB...

 

So? Speakers distort a lot more (I measured my ones while treating room).

 

Pass uses sans-contre reaction design, so distortion at maximum level is a little high. Lower level, distortion much lower. Music is most well below maximum (more like -20dB).

 

At diyaudio publish modification with J-Fet 2SK170 for lower HD, I have applied it, sound is better I think, distortion is lower.

 

If I follow M.I's fallacious logic here, he seems to be suggesting that CD (PCM) files converted to DSD with a Sigma Delta Modulator weren't exhibiting any issues, only those made originally with a modulator of the same resolution did.

 

Observation:

 

1) Play CD-File converted to DSD64/128/256 via Le DAC FlipFlop, no birdies, okay sound, but not as good as Pass D1

2) Play SACD Rip file directly via Le DAC FlipFlop, birdies, strange sounds

 

Theory after observation:

 

Digital conversion PCM->DSD is different to using DSD ADC. DSD ADC seems less perfect than digital conversion.

 

The logic is not fallacious, but other theories are possible.

 

Salud M.I.