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Topic: Quantization in DSD (Read 26583 times) previous topic - next topic
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Quantization in DSD

Hey folks, I am new to the board here, and I had a question regarding DSD for anyone out there with the chops.

Basically I have gone through as many previous posts on all the issues from filtering, downsampling, to sigma-delta; however I still am curious about two particular things:

1-Both DSD and 24-Bit audio supposedly have approximately the same amount of dynamic range at around 120 dB; however, is there a difference in the quantization levels within the two systems.  Obviously how it is done is slightly different, but I am talking about how large these levels are that the signal most be approximated to.  (basically a micro-decibel type figure). 

2-While we all know the Nyquist Theorem guides our bandwidth in typical PCM, what guides the bandwidth of a DSD system.  Obviously it filters out high frequencies (or higher frequencies for that matter), but what is really the ratio used to figure out the bandwidth of a DSD system with such a strange sampling method.

I hope some folks out there know more than I do, cause this has been bugging the hell out of me and I just can't seem to find any info relating directly to these two issues.

Thanks,
Schex

Quantization in DSD

Reply #1 –
To find the dynamic range at a particular frequency for either format (using dithering in PCM), take the number of bits used to represent a quarter of the wavelength, then take 20*log(2^number of bits). For the nyquist frequency at 24 bits PCM, that's 20*log(2^24) ~= 144 dB. Lower frequencies have a higher dynamic range thanks to dithering, since the greater number of samples per wavelength tend to "average out," allowing the perception of sample values in between the actual sample values.

PCM is quantized to the nearest sample value, which is 1/2^bits per sample of full scale. Because dB isn't linear, each sample does not have the same difference in dB. The difference between two samples near silence can be 6 dB, while the difference between samples near full scale is .000001 dB.

DSD is a bit more complicated, you can't really call what it does "quantization," since technically everything is quantized to either positive or negative full scale. All you can really say is that it has a certain dynamic range at a certain frequency.

Quantization in DSD

Reply #2 –
I guess quantization may not be the best term; however, if understand it correctly that is, there is a finite amount of dynamics in each of those positive or negative values.  Since these values each represent a change, the system has to have some way of knowing how large of a change that is going to be, right?

I guess what I am searching for there is some type of way to compare this value of how much resolution DSD can produce within it's own dynamic range, as to how much resolution (1/2 quantization level size) PCM is able to.

Maybe this is off the mark, I am not sure.  But then again that's why I am the kid asking the question, and you guys that actually understand it are helping explain it 

Quantization in DSD

Reply #3 –
The possible resolution is exactly the same for the same bitrate (i.e. number of bits used to represent the same amount of time). If you can encode a quarter of a 96 khz sine wave using 24 bits, there will be 16,777,216 different possible amplitudes for that sine wave, regardless of the format you use.

EDIT: This is, of course, assuming you're not using any form of compression on the data.

Quantization in DSD

Reply #4 –
Hi,

See DSD Spectrum for more info regarding the Dynamic Range. Please note that the electronics after such a DAC are worse than this. The performance is thus dominated by the electronics after the DAC!

Quote
the bandwidth of a DSD system
That would be 1.4 MHz, one half of the sample frequency.

Regards,
Jacco
Logical reasoning brings you from a to b, imagination brings you everywhere.

Quantization in DSD

Reply #5 –
Wouldn't a signal at half the sampling frequency in DSD actually represent a DC signal?

Quantization in DSD

Reply #6 –
Yes and no. Remember it is just a sigma-delta modulator with two level output. The "yes" means that the value is a DC value, of coarse but that is always the case. In conventional multi-bit sigma-delta's the output is also DC value, but they chance every sample time. The more frequent they change in value as function of time, the higher the frequency is sampled.

Regards,
Jacco
Logical reasoning brings you from a to b, imagination brings you everywhere.

Quantization in DSD

Reply #7 –
Quote
Hey folks, I am new to the board here, and I had a question regarding DSD for anyone out there with the chops.

Basically I have gone through as many previous posts on all the issues from filtering, downsampling, to sigma-delta; however I still am curious about two particular things:

1-Both DSD and 24-Bit audio supposedly have approximately the same amount of dynamic range at around 120 dB; however, is there a difference in the quantization levels within the two systems.  Obviously how it is done is slightly different, but I am talking about how large these levels are that the signal most be approximated to.  (basically a micro-decibel type figure). 

2-While we all know the Nyquist Theorem guides our bandwidth in typical PCM, what guides the bandwidth of a DSD system.  Obviously it filters out high frequencies (or higher frequencies for that matter), but what is really the ratio used to figure out the bandwidth of a DSD system with such a strange sampling method.

I hope some folks out there know more than I do, cause this has been bugging the hell out of me and I just can't seem to find any info relating directly to these two issues.

Thanks,
Schex
[{POST_SNAPBACK}][/a]


This paper is always a good read:

[a href="http://sjeng.org/ftp/SACD.pdf]Why 1-bit Sigma-Delta conversion is unsuitable for high-quality applications[/url]

Quantization in DSD

Reply #9 –
Nooooooo!!!
Over thinking, over analyzing separates the body from the mind.

Quantization in DSD

Reply #10 –
Oh, good, another religious flame war is building.

Quantization in DSD

Reply #11 –
I've yet to be able to ABX one of my multichannel/dual channel SACD's from the remastered CD version (there's a few titles that overlap my CD's), so I (personally) doubt that there is much difference between DSD and PCM in real life. Which means that unless you are interested in picking up a couple of surround recordings (as I've done), stick to CD 

Quantization in DSD

Reply #12 –
Quote
stick to CD
Yes, CD can be very good. The problem is that we still don't know how to do it in practise. After all these years we are still learning.
Logical reasoning brings you from a to b, imagination brings you everywhere.

Quantization in DSD

Reply #13 –
Quote
I've yet to be able to ABX one of my multichannel/dual channel SACD's from the remastered CD version (there's a few titles that overlap my CD's), so I (personally) doubt that there is much difference between DSD and PCM in real life. Which means that unless you are interested in picking up a couple of surround recordings (as I've done), stick to CD 
[a href="index.php?act=findpost&pid=244823"][{POST_SNAPBACK}][/a]


I have to agree with you there, Cygnus X1.
I cannot hear the difference between the SACD and CD layers on any of my SACD's.

I have been sampling SACD output into 2496 wave files and comparing it with 44.1k CD-layer rips, and my ABX scores are appalling. Here is an example:

-------------------------------------
WinABX v0.42 test report
09/26/2004 20:00:30

A file: M:\audio_experiments\01_Quality_of_silence_track1.wav
B file: M:\audio_experiments\01_quality_of_silence_track1_16_96.wav

20:02:18    1/1  p=50.0%
20:02:36    2/2  p=25.0%
20:02:51    2/3  p=50.0%
20:03:08    2/4  p=68.8%
20:03:29    3/5  p=50.0%
20:03:51    3/6  p=65.6%
20:04:05    4/7  p=50.0%
20:04:19    4/8  p=63.7%
20:05:07    4/9  p=74.6%
20:05:36  4/10  p=82.8%
20:05:55  4/11  p=88.7%
20:16:56  4/12  p=92.7%
20:17:23  reset

Note: I can't seem to get WinABX to play 24-bit 96khz files on my system, so I dithered the 2496 SACD sample down to 16 bits for my ABX test.

When doing FFT's of sampled SACDs, I have noticed that some SACDs (NOT all) still have the same 20khz lowpass cutoff as CDs- LOL. I guess I really wasted my money on those disks. The characteristic "rising noise floor" of SACD is also clearly visible in the FFTs, but it is still only about -70dB at 45khz.

Quantization in DSD

Reply #14 –
Quote
Quote
stick to CD
Yes, CD can be very good. The problem is that we still don't know how to do it in practise. After all these years we are still learning.
[a href="index.php?act=findpost&pid=244827"][{POST_SNAPBACK}][/a]


I'm not sure what you mean by this statement; there's a wealth of excellent, properly mastered CD titles on the market. The problem is that recent recordings are poorly mastered, which is the fault of the industry and recording engineers, not the CDDA format itself. CD's are capable of over 100dB with dithering, and a frequency response of 22KHz. I've yet to see real, conclusive research that a) a greater bit depth makes a big difference over properly dithered 16-bit audio, and b) that the presence of ultrasonics in music is detectable in a blind test.

And if we indeed are still learning how to coax the best sound out of a CD (with things like dither, etc), why is that a compelling reason to abandon the format for something new and (yet) unproven? Smells like marketing to me....I'm sure that the recording industry is drooling over the prosepct of making people dish out $18 for new albums that aren't rippable and don't cost them anything more to produce.

Quantization in DSD

Reply #15 –
Hi,

Quote
I cannot hear the difference between the SACD and CD layers on any of my SACD's.
Well, I can and especially in our listening room where there is much better equipment than I have.

Quote
a) a greater bit depth makes a big difference over properly dithered 16-bit audio
This is indeed a good question. Properly dithered is also misleading since the time domain itself is not better than before dithering, but the mean of several sine waves will resemble closely the original. I am not interested in sinewaves that continue forever. However, I think 24 bits is preferable.

Quote
b) that the presence of ultrasonics in music is detectable in a blind test
I did some experiments and there is nothing to hear. At least I didn't, may be my ears are not good enough. Perhaps correlated ultrasonic sounds can be heard, I am not sure yet. But the effect of low-pass filtering can be heard, ie. musicians were able to hear the effect of 50 kHz low-pass filtering. So 96 kHz is not the way to go in my humble opinion. 192 kHz is ok.
Logical reasoning brings you from a to b, imagination brings you everywhere.

Quantization in DSD

Reply #16 –
Quote
Well, I can and especially in our listening room where there is much better equipment than I have.

Are they still using the Marantz SM-2 with (27 kHz) B&W 801? Hope they installed coupling caps after blowing 6 of them.
Quote
Properly dithered is also misleading since the time domain itself is not better than before dithering

You do realise that dithering is all there is to DSD?
Quote
But the effect of low-pass filtering can be heard, ie. musicians were able to hear the effect of 50 kHz low-pass filtering. So 96 kHz is not the way to go in my humble opinion. 192 kHz is ok.

Please accompany your statements with some proof.

I was in one of the tests you refer to, and did not hear the 50kHz difference until it was pointed out. After that it no longer was a blind ABX test. And even so, with a 27 kHz system, I wonder what portion of 'hearing' was tweeter distortion, instead of 'more information'. If there's really 'music' in supersonics, the system should be blameless to at least that bandwidth (with thanks to Douglas S for the adjective  ).

In later reports, a conclusion was drawn upon, amongst others, this test. The staggering number of 8 listeners was called upon as significant. The AES should have read Hydrogen's TOS...
Being one of the 8 and remembering my poor performance, I find yours an ambiguous statement.

Sorry about fueling the fire here, but I found it necessary to include some inside info about 'research'.

Quantization in DSD

Reply #17 –
Quote
Quote
I cannot hear the difference between the SACD and CD layers on any of my SACD's.
Well, I can and especially in our listening room where there is much better equipment than I have.

Most likely they are differently mastered. There was a thread around here recently, where an email from some official guy was posted who acknowledged the fact that the CD layer was mastered differently. In particular they aplied more dynamic compression to be "competitive" in the CD changer.

Quote
This is indeed a good question. Properly dithered is also misleading since the time domain itself is not better than before dithering, but the mean of several sine waves will resemble closely the original. I am not interested in sinewaves that continue forever. However, I think 24 bits is preferable.

Dithering improves the perceived dynamic range, not less, not more. Whoever claimed anything else? A PCM sampled signal can be perfectly reproduced within the limits of bandwidth and dynamic range. If you have a signal with infinite precision then you can deconstruct that into an infinite number of sine waves without loosing any information at all. It's just a different represantation of the same thing.

Quote
But the effect of low-pass filtering can be heard, ie. musicians were able to hear the effect of 50 kHz low-pass filtering. So 96 kHz is not the way to go in my humble opinion. 192 kHz is ok.

The effect of the lowpass may be that the intermodulation within the speaker is changed. Speakers are nonlinear. Input 40kHz and you may get an output of 40kHz. Input 60kHz and if you are lucky you will also get 60kHz output. But play them both at the same time and a signal of perhaps 8kHz will be output which is audible. In this case a lowpass which removes content above 50kHz would also remove the 8kHz tone.

I would go so far as to recommend band limiting the signal fed into the speakers to reduce the effects of intermodulation distortion, resulting in a more faithful reproduction.

Quantization in DSD

Reply #18 –
Quote
1-Both DSD and 24-Bit audio supposedly have approximately the same amount of dynamic range at around 120 dB; however, is there a difference in the quantization levels within the two systems.  Obviously how it is done is slightly different, but I am talking about how large these levels are that the signal most be approximated to.  (basically a micro-decibel type figure). 
[a href="index.php?act=findpost&pid=244689"][{POST_SNAPBACK}][/a]


What is your question ? (Sorry, I did not understand. But hopefully my comments below are of help for you)

Quote
2-While we all know the Nyquist Theorem guides our bandwidth in typical PCM, what guides the bandwidth of a DSD system.  Obviously it filters out high frequencies (or higher frequencies for that matter), but what is really the ratio used to figure out the bandwidth of a DSD system with such a strange sampling method.
[a href="index.php?act=findpost&pid=244689"][{POST_SNAPBACK}][/a]


DSD is not that different to PCM. just with a very high sampling rate but only one bit per sample. In both systems you make a per-sample quantization error. Since DSD has one-bit samples the power of the quantization noise is very high but it's possible (more or less) to shift most of the power into the ultrasonic range and out of the audible range because of the very high sampling rate. So you've about 120 dB within 0-20 kHz and much less above.

Theoretically the quality of a PCM/DSD stream mostly depends on the bitrate since you can compensate for fewer quantization levels by using high sampling rates and noise-shaping techniques to some extend - so DSD may seem like a logical choice to eliminate complicated circuits for upsampling/filtering in a player. An SACD player only sends the "bittrain" to a 1BIT DAC and applies an analogue lowpass filter to remove the ultrasonic quantization noise (pretty damn simple compared to DAC circuits which accept PCM data)

On the other hand there are currently some problems with DSD:
- You can't apply full dithering which leads to non-linearities and possibly percible limit-cycles (birdies) in some situations
- It's hard do design good and stable noise shaping filters for 1BIT quantizers.

Also - according to the paper disgustipated mentioned - DSD's quality per bit ratio is less effective compared to PCM. (The 2-level quantizer cannot fully be compensated by noiseshaping). It's quite interesting that 4*44.1=176.4 kHz at 8 bit/sample results in higher quality using half the bitrate compared to DSD, 64*44.1 kHz at 1 bit/sample.


HTH,
Sebastian

Quantization in DSD

Reply #19 –
DSD is a solution for the wrong problem. If the recording engineers and labels actually did their jobs, we would all be satisfied with Red Book digital for the rest of our mortal lives (for 2-channel audio at least).

Quantization in DSD

Reply #20 –
Quote
DSD is a solution for the wrong problem. If the recording engineers and labels actually did their jobs, we would all be satisfied with Red Book digital for the rest of our mortal lives (for 2-channel audio at least).
[a href="index.php?act=findpost&pid=244933"][{POST_SNAPBACK}][/a]


Amen.

Quantization in DSD

Reply #21 –
Quote
Perhaps correlated ultrasonic sounds can be heard, I am not sure yet. But the effect of low-pass filtering can be heard, ie. musicians were able to hear the effect of 50 kHz low-pass filtering. So 96 kHz is not the way to go in my humble opinion. 192 kHz is ok.
[a href="index.php?act=findpost&pid=244838"][{POST_SNAPBACK}][/a]


How?

1) Most recordings don't contain any musical information past 20kHz. Recordings from 1890-1945 probably only go up to 10kHz at best. Recordings done in the analog tape era (late 40's-80's) might have information past 20kHz, but not much. Digital recordings done in 44/16 or 48/16 will only have information up to the low 20's. It's only very recently that we've been able to capture higher frequencies in recordings, making the extra bandwidth a moot point for 95% of recordings out there. Moreover,

2) Most mics don't capture a ton of ultrasonic information past our hearing limits. Most speakers in people's homes don't go past 20kHz (if even that  ), and most amps don't either. So, the frequencies won't be there, even if the medium is capable of storing them.

So, even if we could hear a 50kHz tone in isolation, would it matter for music? Would people be able to reproduce it on most recordings, on the equipment usually found in homes? No. Therefore, 44.1 or 48kHz is probably all we'll ever need.

PS- I'm a classically trained musician and can't even detect a 17kHz lowpass on most music, let alone 50kHz. 

Quantization in DSD

Reply #22 –
Bringing this back to DSD....

I think the reason for DSD being interesting to audiophiles has more to do with marketing than technical superiority. Open any SACD and you'll find a little insert that explains how "DSD closely resembles an analog waveform," resulting in a warm, analog-like sound quality. It's the old "16/44 makes a waveform look like a pile of bricks" argument all over again. The problem is, has anybody ever proven the existence of a correlation between a "smooth" waveform and "warmth?" I've come to believe that what many people call "warmth' is a codename for distortion. And with DSD, there's lots of that to go around beyond 20kHz.

I guess I just don't see why using PCM is "wrong." 24/96 audio, which is overkill, results in a frequency response of 48kHz and a dynamic range of 144dB over the entire range, unlike DSD, which has to shove all the noise from its 1-bit process up in the ultrasonic bands, where the dynamic range falls off sharply. Multi-bit PCM just seems like a simpler way of accomplishing the same thing, without having to dither all that noise. Am I right in thinking this way?

Edit: typo

Quantization in DSD

Reply #23 –
If the optimal recording/processing/playback method really is 1-bit noise-shaped, then DSD would drastically reduce the complexity of the playback stage - basically a very simple decoder and a class D amplifier. But
  • it is definitely not the best recording format - everybody uses multi-bit DS nowadays, for what I understand are overwhelmingly good technical reasons, requiring a (drumroll) PCM to DSD conversion.
  • it is definitely not the best processing format - PCM is far, far, far easier to work with. Is there even a full-featured DAW which supports DSD natively? Pro Tools sure doesn't (its SACD plugin is a PCM to DSD converter. So to use most modern hardware for processing you need (drumroll) PCM to DSD conversion.
  • its economy for playback is made questionable by the rapidly shrinking cost of good 24/192 playback devices, as well as "universal" players that play SACD and DVD-A from a single chip, IIRC.

Quantization in DSD

Reply #24 –
This is an interesting article regarding >20kHz hearing.

The world above 20kHz

Basically it suggestes that response in the time domian determines the transparency/naturalness of a microphone or loudspeaker. Perhaps this relates to high resolution digital recording as well.

Also, as a recording engineer, I don't like to take the blame for all bad recordings. The issue is more complicted than one person or group of people not doing their job(s).