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DSD vs PCM resolution


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I was just thinking... To get a large signal in DSD format you need to have a bunch of 1's together, then a bunch of 0's to go back down a lot. In PCM you just encode the signal size in one sample.

 

I get the feeling that this means that in DSD loud signals have lower resolution, quieter higher. In PCM it is the opposite given the logarithmic nature if hearing.

 

Could this be the reason for the difference in the sound signatures of these two methods of encoding?

 

Or maybe I have it all wrong...

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It's a fun domain of thought the differences between these two.

 

My POV is that DSD is really like the analogue sound pressure when sound travels in air. Case in point, if you output it on a pin, then you need only add a low-pass filter after it to hear sound.

 

Which means, you can suppose the D/A occurs on the pin output. It's a format defined in the Limbo between digital and analogue or it's analogue within a digital format since the density of 1s make for the high signal.

 

Now, another thing you could take into account is the totally ming-boggling amount of information in attack transients and try to see which format captures those better. I think the filtering at ADC with PCM is audible and probably detrimental. No such filtering on capture with DSD.

 

Additionally, when most PCM is output, there's a few more steps before output as SDM ultimately compared to native DSD output, so maybe with PCM we get more 'digititis' or more of the digital circuits' signature.

 

We can take into account the more gentle filtering with DSD on output as well.

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[My POV is that DSD is really like the analogue sound pressure when sound travels in air. Case in point, if you output it on a pin, then you need only add a low-pass filter after it to hear sound./QUOTE]

 

An early DAC design for RB CD by Sir Clive Sinclair only needed output cable capacitance for filtering.

 

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Look for a Mark Mallinson RMAF video. Best discussion I've seen of the way "resolution" works for PCM compared to DSD.

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An early DAC design for RB CD by Sir Clive Sinclair only needed output cable capacitance for filtering.

 

Interesting even though at the time of the Sinclair computers, I was using Oric and Commodore.

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I get the feeling that this means that in DSD loud signals have lower resolution, quieter higher. In PCM it is the opposite given the logarithmic nature if hearing.

 

Voltage matrix PCM DAC and ADC faster, of course, than DSD.

 

PCM use half band (sample rate).

 

But DSD has huge reserv in band: 20 kHz used in 2.8 MHz sample rate.

 

 

 

From mathematical poing of view spectrum of transferred useful signal don't depend on bit resolution.

 

Only noise of quantization higher for lower bit resolution.

 

Main feature of DSD (sigma delta modulation) is displacement quantization noise out of audible range.

 

Reserve of band in place for quantization noise.

 

But it is not influence to useful audio signal restored after DAC.

 

Sound quality depend on used electronic components, scheme and tuning of scheme.

 

In scientific applications where need, as example, "right" steepest front, need more wide band (than 20 kHz) and used PCM DAC.

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It's a fun domain of thought the differences between these two.

 

My POV is that DSD is really like the analogue sound pressure when sound travels in air. Case in point, if you output it on a pin, then you need only add a low-pass filter after it to hear sound.

 

Which means, you can suppose the D/A occurs on the pin output. It's a format defined in the Limbo between digital and analogue or it's analogue within a digital format since the density of 1s make for the high signal.

 

Now, another thing you could take into account is the totally ming-boggling amount of information in attack transients and try to see which format captures those better. I think the filtering at ADC with PCM is audible and probably detrimental. No such filtering on capture with DSD.

 

Additionally, when most PCM is output, there's a few more steps before output as SDM ultimately compared to native DSD output, so maybe with PCM we get more 'digititis' or more of the digital circuits' signature.

 

We can take into account the more gentle filtering with DSD on output as well.

Understood. Yes, the simplicity is incredible.

 

However, my point is one of actual resolution, meaning there's a mathematical way to describe resolution in each case, and they look to be different (bw DSD and PCM that is) for different output levels. It might be the case that DSD has inherently more resolution with low level signals, less with high level signals. This would make a meaningful diff compared to a system that has linear resolution such as PCM.

 

I will check Jud's reference.

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From mathematical poing of view spectrum of transferred useful signal don't depend on bit resolution

Exactly. If I sample at 44KHz and I have 1 bit resolution I could in principle reproduce a 22KHz square wave. But that would not sound great... :)

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Look for a Mark Mallinson RMAF video. Best discussion I've seen of the way "resolution" works for PCM compared to DSD.

Jud: Do you have a link? Can't find it on the google.

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I think you are viewing dsd as pcm. It just doesn't directly equate. If I understand it, the dsd bit is signalling either an increase or decrease in amplitude in the MHz range.

Exactly. If I sample at 44KHz and I have 1 bit resolution I could in principle reproduce a 22KHz square wave. But that would not sound great... :)

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This would make a meaningful diff compared to a system that has linear resolution such as PCM.

 

PCM has inherently more resolution with high level signals and less resolution with low level signals. DSD has at high and low levels the same resolution.

 

KR Matt

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I think you are viewing dsd as pcm. It just doesn't directly equate. If I understand it, the dsd bit is signalling either an increase or decrease in amplitude in the MHz range.

 

The example was a pcm example meant to show that it's not just 'bandwidth' that matters (obviously).

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PCM has inherently more resolution with high level signals and less resolution with low level signals.

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

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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.

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Exactly. If I sample at 44KHz and I have 1 bit resolution I could in principle reproduce a 22KHz square wave. But that would not sound great... :)

 

Reproduce square is not task for audio applications.

 

First, real musical signal haven't pure square.

 

Second, thru ears we can't transmit pure square (according traditional theory about 20 kHz human perception limitation).

 

DSD able transmit wider band, but with worse signal / noise ratio.

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Jud: Do you have a link? Can't find it on the google.

 

Seems to've disappeared, drat! This "second, shorter" Mallinson presentation from the same RMAF may have some info about resolution, as he apparently gets into digital volume controls:

 

(Edit: And it would help if I got his first name right - Martin, not Mark.)

 

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It is very simple.

Ok I get what you're saying (not everything) but it doesn't answer my question I don't think:

 

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.

 

My thesis is that what people like from DSD is the low level resolution. I don't know this for a fact, I just stumbled upon the thought.

 

And to be clear: I have no agenda, I have heard magical and crappy sounding recordings in both formats and I have no particular preference for one or the other.

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Reproduce square is not task for audio applications.

 

First, real musical signal haven't pure square.

 

Second, thru ears we can't transmit pure square (according traditional theory about 20 kHz human perception limitation).

 

DSD able transmit wider band, but with worse signal / noise ratio.

It's meant to be an extreme example, not a suggestion!

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Your post is interesting reading, thanks.

 

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 have opposite experience ... I started with hiFace2 modded by feeding it with cleaner +5V power and found that for example Gustard U10 was much better USB to SPDIF transport than hiFace2. Then I compared PCM with DSD on my DAC and found that PCM converted to DSD by SW sounds more naturally on Sabre 9018. I got this conclusion with foo_input_sacd and foo_dsd_asio, but then I found HQPlayer does clearly better job in converting PCM to DSD.

 

My experience complies with opinions that well implemented SW conversion of PCM to DSD is better than interpolation and SDM implementations of current delta-sigma DAC chips. I don't have experience with other DACs than delta-sigma.

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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, signa stellarum nigrarum

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Bonjour,

 

 

 

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.

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

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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.

 

This is wrong, for 0 dB level signal for DSD64 you need about 24 values of '1'. So you can get 50+ kHz at full level out of DSD64.

 

Theoretical maximum SNR of DSD64 in 0 - 20 kHz band is 424.81 dB, if you can shovel all the noise to the band above 20 kHz.

 

 

(for 48k-base DSD512, maximum theoretical SNR for 0 - 100 kHz band is 739.81 dB)

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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.

 

Wrong, for correct reconstruction you need to run it through reconstruction (low-pass) filter with fs/2 cut-off, theoretically perfect filter being infinitely long sinc function.

 

If you don't do this, you get horrible timing distortion with any signal that is not in sync with the PCM sampling rate. You can nicely see this timing inconsistency for example with eye pattern of 7 kHz square wave reproduced by many PCM DACs. (you'll need a good DPO scope for the purpose)

 

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.

 

I don't think so, take a look here:

Squarewaves from DACs - Blogs - Computer Audiophile

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Seems to've disappeared, drat! This "second, shorter" Mallinson presentation from the same RMAF may have some info about resolution, as he apparently gets into digital volume controls:

 

(Edit: And it would help if I got his first name right - Martin, not Mark.)

 

 

 

Mark is his brother and the guy who runs Resonessence. Both very nice guys

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This is wrong, for 0 dB level signal for DSD64 you need about 24 values of '1'. So you can get 50+ kHz at full level out of DSD64.

 

Theoretical maximum SNR of DSD64 in 0 - 20 kHz band is 424.81 dB, if you can shovel all the noise to the band above 20 kHz.

 

 

(for 48k-base DSD512, maximum theoretical SNR for 0 - 100 kHz band is 739.81 dB)

 

Hi Miska,

 

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

 

Best regards,

Yuri

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