Is the dynamic range of CD sufficient?

[DonH50]

Thanks jiannone. I have 30'ish years' experience designing various full-custom data converters and related circuits (including delta-sigma designs and digital filters) at the transistor level, but the vast majority were lower resolution and at very high speeds (100's MHz to 10 GHz+) for things like radar, lidar, sonar, telcom, datacom and such. A long time ago I designed a 16-bit, 100 MS/s DAC but that's about as close to audio as my day job has gone (though response to DC was critical in all these systems). Most of my audio experience is hobbyist, albeit with a bit more technical background than many audiophiles.

All that pompous babbling to explain that I understand sampling theory, but want to be clear about (and perhaps help others understand) the terminology being tossed about in this thread. Whilst I have definitions, I have found they do not always match those of others, and like to know what I'm talking about.

Which is why it's time for me to shut up.

 

[j_j]

Again they are keeping PCM to the classical definition that I have mentioned earlier, due to the fact 1-bit must switch to PDM/PWM type of encoding rather than explicit defined binary code values for amplitude.
Cheers
Orb

There is no switch. You can oversample multibit PCM the same way, if you want. In fact that's what DSD is, multibit delta-sigma.

So what's your gripe? You're giving a special name to an example of a continuum.

 

[j_j]

I am losing the terminology here, want to interject a few questions to j_j & julf about my assumptions and for clarity (mine and others):

1. A conventional DAC's output (pre-filtered) - or S/H output, not the same as a T/H (real circuit) - to me is a "stairstep" represented mathematically as an impulse and ZOH, true?
2. Are you saying the stairsteps are removed by the image filter, and that is why there is no stairstep visible in the final output?
3. In the practical (circuit) world, impulses are hard to come by, so the output of a delta-sigma DAC is still a pulse (not impulse) train, yes?
4. I am not used to seeing a delta-sigma converter referred to as "linear PCM" (implied in post 467) but rather still a non-linear system due to the quantization. You can make a linear D-S loop, is that the implication? Or do you consider a D-S converter a linear system (which would confuse the heck out of me)? I think you are referring to the model as a linear loop plus (quantization) noise, yes?
5. Perhaps it would be worthwhile to define PCM, PWM, and PDM explicitly for everyone else trying to follow this debate. (I would provide mine but rather it came from the principals.)

Sorry if this is too far off, can take to PM. Perhaps a new thread should be opened to discuss sampling methodologies and architectures.

Curious, thanks - Don

1), "pre-filtered" is meaningless, it's not PCM until the filter is used. So you're contradicting yourself in the question.
2) yes, the stairsteps are removed by the filtering. the stairsteps are caused, entirely, by the out-of-band images of the signal. You can see it in very clearly. What is going on in that plot is starting with a sinewave, and then adding the images via calculation. As you note, the more images added, all of them out of the passband, the closer you get to a 'stairstep'. This illustration has been shown to many here already, and frankly, is conclusive. Stairsteps are due to out-of-band images. Period. End of discussion.
3) the output of a PCM system has to do some sort of processing in order to have an output. This CAN consist of a FILTERED stairstep. No filter, no system. It's not PCM without the filter.
4) A delta-sigma convertor is exactly *PCM according to Jayant and Noll, or delta-sigma, or sigma-delta, depending on which initial author you as. Executed properly, it is a linear system (the noise at high frequencies is filtered out), in that it consists of a fixed noise floor plus a signal. I've said "llinear system plus noise" repeatedly here. It does not change gain, create signal-correlated distortion, what-have-you, unlike a PWM system, which has a distortion characteristic that depends very much on output level.
5) PWM is pulse-width modulation. It's well known, and well understood to have different distortion characteristics (i.e. signal related distortions) at different levels. PCM is a system defined by Pulse Code Modulation. Yes, that's circular, but that's what DSD and SACD are, systems that use modulated pulses to transmit information. In modern usage, a PCM system is a linear system (as always, with a fixed level of added noise). Now, things like muLaw and aLaw are called PCM systems, but their noise floor varies with signal, the key being that it is a noise floor that varies, rather than a distortion level. PDM is more or less a made-up term, really. Somebody needed a term so they invented it.

 

[DonH50]

I was not speaking of PCM specifically just DAC's in general but thanks very much for the clarifications.

I may be confusing myself again, but if I output a 10 Hz tone from a conventional DAC, the steps will be very small but some will still remain after an image filter at 20 kHz (or whatever) though of course the edges are filtered. That is where quantization noise comes from. A conventional (Nyquist) DAC, not a delta-sigma type. Very small, yes (the noise floor goes as 9N for an N-bit conventional DAC). I think I mistakenly stepped in the middle of this and must apologize. I first thought of a conventional DAC, not a PCM system.

I was told ages ago by a reliable source (Gabor Temes) that the original paper was mis-translated and that is why "sigma-delta" is so widespread. He said they (Japanese authors, forget whom after all this time) said the differencer (delta) comes before the summer (sigma) in the loop.

"Executing properly" a delta-sigma converter so as to remove all signal-correlated distortion is a trick I have never actually performed or read in JSSC or CAS, at least at the circuit level. Always seem to be high-order (and some low-order) effects that affect the circuits. But, I do not claim to be an expert in DS designs, only done a few and not working on them currently.

I shall bow out of this, seem to be excelling at confusion and contributing no real meat to any of these discussions lately. - Don

 

[j_j]

I may be confusing myself again, but if I output a 10 Hz tone from a conventional DAC, the steps will be very small but some will still remain after an image filter at 20 kHz (or whatever) though of course the edges are filtered.

Nope, but you will see a NOISE added to the tone, no matter what the frequency.

The "steps" in a 10Hz signal are actually very easy to filter out, because they are very close to the sync zeros that you get with a rectangular window of one sample period from a DAC. So they have very little energy to start with.

The usual argument about "beating" in DAC's comes from looking at waveforms before filtering. There it's more important in terms of what you SEE, although the same in terms of what comes out of the filter. That's why this is a high frequency signal, it shows how the beating comes about strictly due to a lack of filtering.

Candy and Condon (look up their patent on Delta-Sigma) called it delta-sigma if I recall correctly. You'd be surprised just how far back that paper and patent go. And the noise is 6.02dB per bit in a baseband DAC, by the way, not sure what the 9N means.

 

[Mark (Basspig) Weiss]

That is not how it works. A properly functioning DAC does not produce "steps" in the output. It will produce a continuous wave that can represent any arbitrary voltage level in the output range. That is why a DAC includes a reconstruction filter.

The 8-bit DACs I built in 1982 used integrator filters, however, it could be demonstrated that continuous DC voltage levels could be fed to the inputs of the ADC and out of the DAC would come only so many discreet voltage steps. With dynamically changing signals, the integrator filter would create 'infinite' voltage levels between these discreet steps, but that is settling time of the filter and I don't see that as real resolution. It's phantom information.

 

[Mark (Basspig) Weiss]

Let's test your assertion which says that something with only 2 steps must be bad. Ok.

For instance, SACD home systems use a 1-bit playback DAC. Yes, they oversample, but in that revelation lies your failure to understand how it all works. SACD uses oversampled, noise-shaped PCM. Yes, boys and women, that's all SACD is, an inefficient form of PCM.

When you have no oversampling, it is still entirely possible to switch that 1 bit (2 level) system so that the resulting sound is pure white noise. That's what dither is supposed to do, and what it does perfectly well when it's done properly.

As to your illusion of steps, don't forget that there is a reconstruction filter in any DAC, so you don't actually see the steps in any case.

You are operating from a point of view that has been intentionally propagated by some completely irresponsible authors and bloggers, which I am not blaming you for, HOWEVER, I must advise you that you are flat-out wrong in your assertion that you MUST have granularity at low levels in PCM.

SACD is a perfect example of how that has to be wrong, since it's a 1-bit system that is oversampled, yet lacks granularity. And, yes, it's oversampled PCM with quantization noise shaping, nothing whatsoever more or less, despite all of the hype and claims about it.

Your first assertion conflicts with my experiments done with 8-bit ADC/DACs I built in 1982. Your assertion only holds true of dynamically changing signals. But the same two levels still exist in a conventional ladder type DAC. If you have, for example, four possible voltage levels on the output of a crude, simplified DAC, then the only way you could get in between voltages is via a changing level, smoothed by an integrator filter downstream, and those in between levels are only for a fleeting moment as the R-C circuit charge fades. With DC levels, the discreet number of steps in the DAC becomes clear. There are no in between levels.

Now this 1-bit DAC is a bit different. If I recall correctly, it uses a PWM-like technology to switch the bit on or off and the duty cycle corresponds to the wave shape. Totally different animal. I was referring to the more conventional ladder DACs used in conventional audio players of modest cost.

 

[Mark (Basspig) Weiss]

Mark,
I suggest you find 25 uninterrupted minutes and watch this video:
http://www.youtube.com/watch?v=cIQ9IXSUzuM

Some people disagree with the presenter's opinions on the use of dither in some cases, but the technical content is correct.

That was a well produced presentation and very clear. I think the point made at 6:30 into the video, that sample points in time are UNDEFINED explains a lot of this confusion. My thinking stems from my work with early DAC technology, which was what the presenter referred to as 'zero order hold'. I think this explains a lot of the confusion.

What I was hearing on my Ultimate Fireworks Blu-ray, as played on a Sony BDP-S301, versus an Oppo BDP-83, I don't doubt, was the result of the DAC quality on the players. The Sony produced a sound like that of switching through a few steps, while the Oppo sounded close to the original recording master, while playing the 16-bit Dolby AC3 audio.

So based on this presentation, an infinite number of possible levels in between MSB and LSB are possible, due to the undefined nature of where that sample occurred in time. I get that. Quite different from the stuff I worked on in 1982. Fascinating demonstration in just 25 minutes.

 

[j_j]

If you have, for example, four possible voltage levels on the output of a crude, simplified DAC, then the only way you could get in between voltages is via a changing level, smoothed by an integrator filter downstream, and those in between levels are only for a fleeting moment as the R-C circuit charge fades.

What you just said is that the anti-imaging filter (which you refer to as an integrator) is not a sufficient filter. Look at the plot I put up a few articles above, where you will see the squareness disappear as the bandwidth gets closer to the proper FS/2. It doesn't matter if you have 2 levels or 200,000,000 levels.

And, if you've dithered properly, don't forget the output of your low-res DAC is likely to be changing at each clock tick.

 

[Julf]

That was a well produced presentation and very clear. I think the point made at 6:30 into the video, that sample points in time are UNDEFINED explains a lot of this confusion.

No, the sample points are not undefined. The sampled signal is a function that is discrete, and only defined at the discrete, well defined sample points. It is undefined *between* the sample points.

My thinking stems from my work with early DAC technology, which was what the presenter referred to as 'zero order hold'. I think this explains a lot of the confusion.

Yes, the old "zero order hold" model is one that a lot of people have in their head - it just illustrates how dangerous it is to rely on "intuitively sensible" models instead of doing the math. In the beginning I made exactly the same mistake.

 

[Orb]

I was not speaking of PCM specifically just DAC's in general but thanks very much for the clarifications.

I may be confusing myself again, but if I output a 10 Hz tone from a conventional DAC, the steps will be very small but some will still remain after an image filter at 20 kHz (or whatever) though of course the edges are filtered. That is where quantization noise comes from. A conventional (Nyquist) DAC, not a delta-sigma type. Very small, yes (the noise floor goes as 9N for an N-bit conventional DAC). I think I mistakenly stepped in the middle of this and must apologize. I first thought of a conventional DAC, not a PCM system.

I was told ages ago by a reliable source (Gabor Temes) that the original paper was mis-translated and that is why "sigma-delta" is so widespread. He said they (Japanese authors, forget whom after all this time) said the differencer (delta) comes before the summer (sigma) in the loop.

"Executing properly" a delta-sigma converter so as to remove all signal-correlated distortion is a trick I have never actually performed or read in JSSC or CAS, at least at the circuit level. Always seem to be high-order (and some low-order) effects that affect the circuits. But, I do not claim to be an expert in DS designs, only done a few and not working on them currently.

I shall bow out of this, seem to be excelling at confusion and contributing no real meat to any of these discussions lately. - Don

Well part of the problem Don is the definition of a PCM system and PDM-PWM, they are different as you are probably thinking and why every engineer document I have linked clearly shows PCM system (its encoding) cannot be seen as the same as PDM encoding, the difference is very fundamental as the last Philips document (summary basic paper by Philips DSD engineer) tries to show.

If they were the same manufacturers would not bother with the internal DSM (DSD)-to-PCM conversion process on modern audio DACs when both come out of the final DAC analogue output stage....
Some DACs allow native DSD to bypass the internal conversion to PCM, but importantly they both use the same final output; why bother doing this if they are identical in terms of system application and behaviour.
As an interesting sidenote the Philips enginners said in one of the papers, DSD does not necessarily need to rely on DSM.

Regarding the "a stair or step" function or looks like, well as you know there are 3 potential stages this happens; theory of transfer function due to not being ideal line, alias images especially when no reconstruction filter or very poor rejection, and low level low bit (16-bit or lower) signal without dither (which technically is an artifical added noise source to the original signal but resolves this problem).
I do wonder regarding debating the "stair or step" is due to difference between EE training-education and DSP training-education.
Appreciate you know all that I am stating and your background ties into the EE descriptions-papers I have been providing.
Cheers
Orb

 

[Julf]

Well part of the problem Don is the definition of a PCM system and PDM-PWM, they are different as you are probably thinking and why every engineer document I have linked clearly shows PCM system (its encoding) cannot be seen as the same as PDM encoding, the difference is very fundamental as the last Philips document (summary basic paper by Philips DSD engineer) tries to show.

If they were the same manufacturers would not bother with the internal DSM (DSD)-to-PCM conversion process on modern audio DACs when both come out of the final DAC analogue output stage....
Some DACs allow native DSD to bypass the internal conversion to PCM, but importantly they both use the same final output; why bother doing this if they are identical in terms of system application and behaviour.
As an interesting sidenote the Philips enginners said in one of the papers, DSD does not necessarily need to rely on DSM.

And round and round we go again. I suggest you read JJ's posting #485.

 

[Orb]

And round and round we go again. I suggest you read JJ's posting #485.

And I suggest you accept a Philips research engineer involved with DSD from one of the papers:

Instrumental in the conception of DSD is the Sigma Delta Modulator (SDM), of which the principle has been introduced by F. de Jager at Philips Research in 1952 [2].
This device applies the technique of noise shaping to obtain a high-resolution in a limited bandwidth, in spite of the mere use of 1-bit data words. Performing signal processing on these 1-bit signals, is radically different from performing signal processing on PCM signals.

Anyway I have provided enough links for others to try and mull this over and what the fundamental description-function difference is between PCM and DSD (PDM-PWM).
As I keep saying wanting PCM at 1-bit means you have to use PDM type encoding and not PCM, meaning it MUST be converted from PCM to DSD if staying with the audio analogy, which all the links or even quoting application notes I have provided show.
Orb

 

[Orb]

And round and round we go again. I suggest you read JJ's posting #485.

And I notice you ignore the fact modern audio DACs that are SDM still internally convert the signal to PCM (they even show that in their application notes) or bypass PCM and remain native DSD, however both instances use the same final output stage.
Now why bother providing this differentiation if PCM and DSD are identical in system application and behaviour, after all the final same stage is the signal to the preamp/integrated amp in analogue.
I am sure you will respond by saying it is a marketing ploy...
Orb

 

[Julf]

Now why bother providing this differentiation if PCM and DSD are identical in system application and behaviour, after all the final same stage is the signal to the preamp/integrated amp in analogue.

I am sure you understand the difference between 1-bit and multi-bit PCM.

 

[Julf]

And I suggest you accept a Philips research engineer involved with DSD from one of the papers

As I said, round and round we go again. Did you read (and understand) JJ's post?

Could you please stop quoting papers and actually answer my questions?

If we are saying something looks like a duck, swims like a duck and quacks like a duck, but that people often keep calling it a pigeon, it doesn't really help if you keep digging up more examples of people calling it a pigeon. What would help is you explaining in what way that something *isn't* like a duck.

 

[Orb]

Right Julf,
you want me to stop quoting or posting links to DSD papers written by Philips Research engineers involved with the development of DSD that state why PCM and DSD-PDM are different (in fact they say that)
I am not ducking your question because it is meaningless as you are trying to create a specific scenario that is not applicable to PCM but to PDM-PWM.
Anyway if it helps you, I give up so post away until all those Philips Research DSD papers and other application notes I quoted are long forgotten
I guess Philips Research Labs and their definitions are not good enough even though they were also involved with the invention of Delta Sigma Modulation (F. de Jager ), along with DSD.
Orb

 

[Julf]

Right, Orb,

I don't mind you quoting or posting links to DSD papers written by Philips Research engineers (or anyone else) per se. It just that blind quoting won't get us anywhere.

It would help if you could explain why my question (and which of them) is meaningless. I am talking about the specific scenario we are discussing in this thread.

As Don pointed out,it is hard to make sense of the discussion if you don't define what you are talking about. What is *your* definition of PCM?

Mine is "a stream of fixed-interval, fixed-sample-rate, fixed-pulse-width N-bit data values (where N can be anything between 1 and as high as you want to go) that describe the input signal".

So, please, could you let us know if a) you agree with that definition (and if not, why not), and b) why you think DSD doesn't fit that definition?

 

[Orb]

Right, Orb,

I don't mind you quoting or posting links to DSD papers written by Philips Research engineers (or anyone else) per se. It just that blind quoting won't get us anywhere.

It would help if you could explain why my question (and which of them) is meaningless. I am talking about the specific scenario we are discussing in this thread.

As Don pointed out,it is hard to make sense of the discussion if you don't define what you are talking about. What is *your* definition of PCM?

Mine is "a stream of fixed-interval, fixed-sample-rate, fixed-pulse-width N-bit data values (where N can be anything between 1 and as high as you want to go) that describe the input signal".

So, please, could you let us know if a) you agree with that definition (and if not, why not), and b) why you think DSD doesn't fit that definition?

Good grief, look back the application note I quoted specifically described in summary PCM and PDM (this matches nearly every digital application note I have ever read although the others go into much more detail).
Then the Philips papers also go into detail describing both PCM and PDM, there is NOTHING vague about application quote nor how the papers differentiate between PCM and PDM when taken in full.
It is pretty obvious what the difference is but you and JJ keep confusing the issue by giving PCM encoding a definition-nature it simply is not...
THE papers and application notes DO NOT MATCH WHAT YOU AND JJ ARE ARGUING FOR THE POSITION OF PCM OR HOW YOU DECIDED TO CORRECT ME WHEN I POINTED OUT SACD IS ACTUALLY DSD-PDM AND NOT PCM at all.
Since then you have been arguing that PCM is same 1-bit as DSD, but it cannot be because it MUST USE DSD/PDM/etc; we have had 10 pages now with me quoting and providing engineer papers and still both of you saying but PCM is 1-bit (meaning it does NOT NEED CONVERSION TO DSD-PDM-ETC and that view is wrong as it does need conversion) and same as DSD-SACD.
Enough is enough.

Oh and if you really want to argue this then from a DSP rather than EE perspective, then take it up with one of the developers for HQPlayer - Miska on Computeraudiophile who spends plenty of time correcting those who keep saying DSD and PCM are the same...Or with DAW developers such as at Merging Technologies.
Seriously given up now.
Orb

 

[Orb]

As those other quotes/papers did not satisfy the description of PCM/DSD-PDM, then how about this one by Sharp who also develop DSD related products-components:

1-Bit Signals and PCM Multi-Bit Signals

While both 1-bit signals and PCM multi-bit signals are digital, there are great differences between the two.
Multi-bit signals record each quantized sample as an absolute value, while 1-bit signals just record the fluctuation of the sample from the previous one.
And unlike multi-bit signals, the information of 1-bit signals do not need any estimated decimation or complement.

A 1-bit system does not use PCM encoding techniques and does have a different behaviour-definition; hence why I keep on about saying PCM has to be converted IF you want it as 1-bit, which means using something like PDM/SDM/etc.

They also say (and again matches in technical context everything I have quoted or linked papers to so far):

Even in the multi-bit processing, delta-sigma modulation is used during the conversion between analogue signals and PCM.
An intermediate step in this interchange process generates a 1-bit signal which is closer to the original analogue signal than PCM.

But feel free to change the EE concept-encoding and behaviour of what PCM is to be that of SACD and DSD.
Orb