[Greenears]

  According to http://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem it is mathematically impossible to reconstruct a continuous time signal from a discrete one without aliasing.
 
If what you mean by smoothness is that the output shouldn't contain frequencies above .5 Fs, maybe that's your preference, but not mine. I don't care if ultrasonic frequencies get to my ears, as long as the signal is at the proper resolution, and phase-coherent with the original.

"If the Nyquist criterion is not satisfied, adjacent copies overlap, and it is not possible in general to discern an unambiguous X(f). " Directly from the wikipedia article you quote.
 
If you read it carefully, it says "If".  As always on forums most people are not fully up to speed on the Nyquist criteria, they only focus on the Fs>=2B sampling rate, as I already stated above.   I have tried to highlight them above, but again, the signal being sampled needs to band-limited, usually written as f = -B to B.  It must have zero energy at f>B and f<-B.  If that is satisfied you will not have aliasing. The Wikipedia article is correct, they have the correct criteria in the preceding paragraph.  
 
You are also introducing questions about ultrasonics that have nothing at all to do with Nyquist.  If you want frequencies up to 100 kHz that is fine, just sample at 200 kHz.  But it must be bandlimited - ie no energy beyond 100 kHz otherwise you will have aliasing.

 

[22906]

 
but when did this become a contest of argumentative skill? it's about theory, application, and facts.
by filtering with a low pass filter we increase the fidelity of the signal compared to it's original analog counterpart. we get rid of some signals that shouldn't exist by cutting frequencies. keeping that signal would absolutely reduce the signal fidelity.
and if before that we oversampled or used any noise shaping trick to move some of the noise energy up in high frequencies, then when we cut the ultrasounds lose with the filter, we also get rid of that moved noise. that once again improve fidelity by lowering the noise inside the recorded range of frequencies.
they are tricks of sort, you may not like them, but their effectiveness is doubted only by you it seems. you're just being unreasonable here.

Science is about argumentation. Theories are facts are all logical constructs. It's the only way to reach a consensus on the matter that actually corresponds to reality. If you ignore the rules of logic and argumentation, you get hodge-podge results like delta-sigma ____. I'll let it slide that you're calling me unreasonable, when we all know what the truth is.

 

[22906]

  "If the Nyquist criterion is not satisfied, adjacent copies overlap, and it is not possible in general to discern an unambiguous X(f). " Directly from the wikipedia article you quote.
 
If you read it carefully, it says "If".  As always on forums most people are not fully up to speed on the Nyquist criteria, they only focus on the Fs>=2B sampling rate, as I already stated above.   I have tried to highlight them above, but again, the signal being sampled needs to band-limited, usually written as f = -B to B.  It must have zero energy at f>B and f<-B.  If that is satisfied you will not have aliasing. The Wikipedia article is correct, they have the correct criteria in the preceding paragraph.  
 
You are also introducing questions about ultrasonics that have nothing at all to do with Nyquist.  If you want frequencies up to 100 kHz that is fine, just sample at 200 kHz.  But it must be bandlimited - ie no energy beyond 100 kHz otherwise you will have aliasing.

Yes I think probably the only kind of barely justifiable filter in the chain would be a low-pass before the ADC. That's if the mic response goes past .5 Fs. And yeah, higher sampling frequency would be great.

 

[22906]

Haha guys... actually it's all a joke... I'm just preparing everyone for the launch of my new laser-trimmed R2R DAC chip, the RTO4665, which I designed on my own computer with CAD drawings, and which is manufactured on .18um equipment in Taiwan. PM me for pre-order details. Introductory pricing of $5000 per chip for the first 500 customers.

 

[22906]

Jokes aside, after doing some more independent research, I've realized that the parameter I am looking for is called "static linearity." I predict that the static linearity test will show the R2R coming out on top. Thanks to all for playing along for so long.

 

[cjl]

  So I should back down because some guy with a degree is emotional about a flawed paper?

OK, I give up. I'm done here.

 

[jcx]

so this is what we get with modern ed theory, schools pushing "self discovery", "self esteem" above teaching?
 
most of us aren't Newton, Einstein and Hawking all rolled up into one, able to use "pure reason" to understand the world - in fact they didn't either- they studied, learned from predecessors, books, schooling, university classes, professors...
 
 
no one I know wants to play adversarial rhetorical debating games with their students at every point - students are supposed to be willing partners in their own education

 

[22906]

I want to pre-empt some of the responses that have yet to be posted; and this will NOT be my last post on the topic.
 
Delta-sigma manufacturers have used various statistical linearity measurements to cover up the lack of resolution of the converters. There is no substitute for static linearity (linearity under DC conditions) because static linearity is the accuracy of how amplitude is quantified. That's why I have been saying delta-sigma is extremely accurate at timing, but not very accurate in amplitude (except over many many samples). Delta sigma simulates static linearity by using filters to "predict" what the amplitude of the sample will be; but without a discrete, independent reference for each possible amplitude of the sample, these predictions will result in a kind of "average" linearity that depends on the movement of the signal, and not on the original sample amplitude.
 
Linearity is important for audibility (even though audibility is not a valid standard by which to judge DACs or ADCs), because the Shannon-Nyquist sampling theorem states that a bandlimited continuous time signal may be reconstructed by a set of samples (Dirac impulses) in discrete time, and the accuracy of the reconstruction of the signal (as long as it is bandlimited and Fs is twice the bandwidth) depends on ONLY two factors: the accuracy of the amplitude, and the accuracy of the timing of each sample.
 
It is unethical for delta-sigma manufacturers to claim certain # of bits of resolution when the static linearity for their converters does not match that of a perfect PCM converter with the specified number of bits, with an acceptable error. And I want to say, it may be that modern sigma-delta is somehow different from what I have read, and that I am bringing up an old problem; forgive me if I am making an unfair accusation. However, for the benefit of everyone who takes part in hi-fi audio, static linearity measurements should be just as important, if not more so, than THD, SNR, etc when deciding on what architecture of converter to purchase for your audio system.

EDIT: Check the bottom of pg 5.12 in this document for support of my claims http://www.analog.com/library/analogDialogue/archives/39-06/Chapter%205%20Testing%20Converters%20F.pdf

 

[jcx]

 it may be that modern sigma-delta is somehow different from what I have read, and that I am bringing up an old problem; forgive me if I am making an unfair accusation 

it really is the case - one of the basics of how to learn about something is to look at current practice, why is accepted by the industry
 
read the white papers, seminar and app notes of Analog Devices, Texas instrument, other manufacturers on their delta sigma products, the datasheets, demo circuit's performance
 
it should tell you your conception has problems and you need to learn more
 
coming here with half baked ideas and denouncing an entire technical field, challenging people willing to point you in useful directions to a debate on your terms is unlikely to get far

 

[ubecko]

Hi, this is my first post here

I am absolutely not an audio expert, just an enthusiast... so I and the thread proposer are even
 
Due to biological limitations, the "real" (physical) audio signal can never be heard, a lot of the audio perception is inferred as the result  of postprocess carried out by brain processes; even the limited frecuency response of microphones in the lower part of the audio spectrum, impedes a proper capture.
 
The Nyquist-Shannon theorem states the minimal bandwidth needed by an IDEAL sampling device*, to encode all the features of a finite bandwidth signal; it shows us how to avoid spectral aliasing; this "minimal sampling frecuency" theorem never deals with information lost or corrupted due to quantization errors, non-linear phase shifts, or noise unintendedly added; all of them detrimental to signal fidelity.
 
So, I came here to state that: "nor a high resolution translate directly into better fidelity, neither a minimal noise spectrum power at the audible range". And, although both efforts can push toward our target, improving the later one is way more efficient than the first (also it's even better than oversampling).
Anyhow an audio system with linear phase delay should always be the top concern.
 
Conlcusion: Yes, a very cumbersome to build R2R stair SAR ADC could provide a de facto higher resolution; but with all the modern techniques developed for SigmaDelta ADC devices, digital audio system developers can offer an equivalent resolution (or perceived equivalent by our easy-to-fool hearing perception).
---
* wich got to sample an audio signal, already degraded by the pressure to voltage transceptor.
 
PD: Sorry for my bad english!

 

[22906]

  Hi, this is my first post here

I am absolutely not an audio expert, just an enthusiast... so I and the thread proposer are even
 
Due to biological limitations, the "real" (physical) audio signal can never be heard, a lot of the audio perception is inferred as the result  of postprocess carried out by brain processes; even the limited frecuency response of microphones in the lower part of the audio spectrum, impedes a proper capture.
 
The Nyquist-Shannon theorem states the minimal bandwidth needed by an IDEAL sampling device*, to encode all the features of a finite bandwidth signal; it shows us how to avoid spectral aliasing; this "minimal sampling frecuency" theorem never deals with information lost or corrupted due to quantization errors, non-linear phase shifts, or noise unintendedly added; all of them detrimental to signal fidelity.
 
So, I came here to state that: "nor a high resolution translate directly into better fidelity, neither a minimal noise spectrum power at the audible range". And, although both efforts can push toward our target, improving the later one is way more efficient than the first (also it's even better than oversampling).
Anyhow an audio system with linear phase delay should always be the top concern.
 
Conlcusion: Yes, a very cumbersome to build R2R stair SAR ADC could provide a de facto higher resolution; but with all the modern techniques developed for SigmaDelta ADC devices, digital audio system developers can offer an equivalent resolution (or perceived equivalent by our easy-to-fool hearing perception).
---
* wich got to sample an audio signal, already degraded by the pressure to voltage transceptor.
 
PD: Sorry for my bad english!

 
I hold a BSEE from UCLA. You can make fun of my degree all you want.
 
Your claims about hearing processes are not relevant to creating a hi-fi signal chain. Whether we can hear non-linearities in the system is irrelevant to the fact that they are there; if digital audio was based on the "science" of hearing processes, then we would all be listening to VBR MP3s. Sounds the same, doesn't it?
 
Noise is something added to the signal; if the signal isn't accurate to begin with, no amount of noise reduction can add that accuracy back in.
 
To clarify: a successive approximation register (SAR) is a type of analog to digital converter (ADC); and R-2R ladder is a type of digital to analog converter (DAC).
 
Sigma-delta devices, in their current state, are not suitable for discerning hi-fi enthusiasts only because of their non-linearity at DC, and possibly phase non-linearity in the low-pass filters employed. As I have stated before, their noise and frequency domain characteristics are great, but that is not enough for a truly high-fidelity signal.
 
And, the Shannon-Nyquist sampling theorem is the basis of almost all modern digital electronics. It is much more than a debate about sampling frequency. Quantization error directly affects the signal integrity, and it is as important as static linearity, but on the ADC side of the signal chain.

 

[ubecko]

Hi m3_Arun, thank you very much for your clarification, and for the thread.

By reading all converstions in thread, I have manage to clarify a lot of concepts, I have read a llitle about audio tech before (The Art of Digital Audio), and all along the way sigma delta ADCs looked suspicius, it is not an easy topic. The argumentative approach made reading the thread very useful.

Edit: mainly orthographic corrections

 

[22906]

ubecko,
 
I applaud your attempt to understand what's going on; keep up the good work.

Your new friend at Head-fi,
m3_arun

 

[jcx]

definitely the expected problem with the thread - newbies, those without tech background use debate rhetoric scoring as a proxy for deciding technical correctness
 
m3_arun appears to have just scratched the surface of the engineering, technical description of signal representation, "digital" representation of analog signals and converter technologies
 
the projecting too far with "logic" from too narrow a base of domain knowledge is well known - called "Sophomoric" for good reason http://www.geocities.ws/lclane2/soph.html
 
one way to check yourself for "knowledge gaps" is to look to examples in the real world, accepted practice by professional engineers - if your "logical reasoning" contradicts the actual practice you should be trying to learn what you are missing, not going public with "you all are wrong, and can't fault my logic"
 
 
delta-sigma conversion is usually described at 1st  introduction in the 1st order, "slope converter/modulator" form - used >1/2 a century ago in digital Voltmeters built with tubes and relays
 
1st order delta-sigma seems to be the topology m3_arun is "reasoning" about ultimate technology limitations from
 
but the technology used today in commercial delta-sigma ADC/DAC is quite a bit beyond that - higher order converters use more than just one integration stage, effectively the "bit stream" controls or represents higher derivatives of the signal rather than just whether it is sloping up or down at a constant rate in the 1st order converter
 
the SACD version of DSD, while the internals are not public has technical performance consistent with 5th order delta-sigma modulation
 
the math is complicated, the operation isn't "intuitive" so descriptions of higher order modulators don't usually make it into the introductory articles on delta-sigma conversion
 
delta-sigma converters are used in the most demanding "static linearity" applications - delivering 20 bit linearity, precision in weigh scales, electronic "balances" in really cheap single chips or even integrated in single chip microcontrollers
 
I know this directly having spent decades designing Industrial/Scientific Instrumentation electronics - I have used pretty much every type class of monolithic ADC/DAC made and had to have product performance pass independent lab verification testing - its not just an opinion
 
 
Audio however doesn't require "static linearity" down to DC - differential linearity is much more important to perceptible distortion - and delta-sigma excel there - outperforming Successive Approximation/R2R converters
 
and Audio ADC/DAC today is dominated by Multi-bit high order delta-sigma converters that offer some advantages over "single bit" DSD
 

 

 
 
table from: http://web.archive.org/web/20070118012711/http://www.iet.ntnu.no/~ivarlo/files/School/PhD/Report_audiodac.pdf
 
a 2005 graduate level report on audio DAC internals - if you really want to know more about multi-bit delta-sigma

 

 

[22906]

  definitely the expected problem with the thread - newbies, those without tech background use debate rhetoric scoring as a proxy for deciding technical correctness
 
m3_arun appears to have just scratched the surface of the engineering, technical description of signal representation, "digital" representation of analog signals and converter technologies
 
the projecting too far with "logic" from too narrow a base of domain knowledge is well known - called "Sophomoric" for good reason http://www.geocities.ws/lclane2/soph.html
 
one way to check yourself for "knowledge gaps" is to look to examples in the real world, accepted practice by professional engineers - if your "logical reasoning" contradicts the actual practice you should be trying to learn what you are missing, not going public with "you all are wrong, and can't fault my logic"
 
 
delta-sigma conversion is usually described at 1st  introduction in the 1st order, "slope converter/modulator" form - used >1/2 a century ago in digital Voltmeters built with tubes
 
but the technology used today in commercial delta-sigma ADC/DAC is quite a bit beyond that - higher order converters use more than just one integration stage, effectively the "bit stream" controls or represents higher derivatives of the signal rather than just whether it is sloping up or down at a constant rate in the 1st order converter
 
the SACD version of DSD, while the internals are not public has technical performance consistent with 5th order delta-sigma modulation
 
the math is complicated, the operation isn't "intuitive" so descriptions of higher order modulators don't usually make it into the introductory articles on delta-sigma conversion
 
delta-sigma converters are used in the most demanding "static linearity" applications - delivering 20 bit linearity, precision in weigh scales, electronic "balances" in really cheap single chips or even integrated in single chip microcontrollers
 
 
Audio however doesn't require "static linearity" down to DC - differential linearity is much more important to perceptible distortion - and delta-sigma excel there - outperforming Successive Approximation/R2R converters
 
and Audio ADC/DAC today is dominated by Multi-bit high order delta-sigma converters that offer some advantages over "single bit" DSD

jcx:

While I can't say I appreciate the cynicism and utter lack of evidence in your post, I do appreciate your attempt to discredit my ideas.

Hi-fi audio does require static linearity, and "perceptible distortion" is not a valid criterion for judging the fidelity of an audio signal.
 
- m3_arun

EDIT: The paper you linked to doesn't provide any static linearity measurements