Talk:Delta-sigma modulation/Archive 1

Archive 1

Technicality

Hello 129.173.105.28, I know that this is a difficult topic as it is too technical, and I've still to finish it, when I have time; I'll try to simplify if it I can. Regards --Katanzag 08:22, 28 November 2005 (UTC)

"The quantization noise spectrum is the same as in Nyquist (not oversampling) converter (in yellow), but it is distributed in a larger spectrum (blue), "

The spectum is the same but it is distributed over a larger spectrum... Is it a technical slang? I do not understand. I assume that the root of the confusion the article brings lies in the incompetence of the authors in what they write rather than in the low technical level of the public. See how Feynman states the quantum electrodynamics. Only masters dare for simplifications. --Javalenok 11:33, 1 May 2006 (UTC)

OK, it's nor a slang, neither incompetence, there was only a spectrum word more, now is fixed. I'm not Feynman, I will never be... Thank you for showing me this mistake so I was able to correct. --Katanzag 08:46, 3 May 2006 (UTC)

comparison between sigma delta ADC and Succesive approximation ADC

How would one compare the performance of a Sigma-Delta ADC to that of a Successive approximation ADC? Is there an advantage of each of these technologies in any particular field? How do i decide whether I need a sigma-delta or successive approx ADC in my application?

It depends on the application and on the frequency of the signal to be converted: ΔΣ are efficient, precise and with good noise rejection: they can efficacely convert few tenths of microvolt with high precision, but they need that the signal is slow compared with its clock; the ratio should be at least 1:100 in order to achieve good resolution. --Katanzag 13:55, 9 August 2006 (UTC)

Variance of in-band quantization noise for first order and second order sigma delta modulator

I would think that the following text might be useful under the subheading OverSampling :

---start text----

For a first order delta sigma modulator, the noise is shaped by a filter with transfer function $H_{n}(z)=\left[1-z^{-1}\right]$. Assuming that the sampling frequency $f_{s}$ is much greater than the signal bandwidth $f_{o}$, the quantization noise contained in the desired signal bandwidth can be approximated as $\mathrm {n_{0}} \,=\,{\frac {e_{rms}\pi }{\sqrt {3}}}\,(2f_{0}\tau )^{({\frac {3}{2}})}$ .

Similarly for a second order delta sigma modulator, the noise is shaped by a filter with transfer function $H_{n}(z)=\left[1-z^{-1}\right]^{2}$. The in-band quantization noise can be approximated as, $\mathrm {n_{0}} \,=\,{\frac {e_{rms}\pi ^{2}}{\sqrt {5}}}\,(2f_{0}\tau )^{({\frac {5}{2}})}$.

---stoptext----

Please let know if you find this acceptable. Beetelbug 16:11, 9 April 2007 (UTC)

According to the references cited in main article, rms noise power in signal band formula are correct, you can add them in the main article on your own, maybe connect them to a n-th order ΔΣ modulator formula, that is

$\mathrm {n_{0}} \,=\,e_{rms}{\frac {\pi ^{n}}{\sqrt {2n+1}}}\,(2f_{0}\tau )^{({\frac {2n+1}{2}})}$

(maybe it is too much technical?) regards Katanzag 07:07, 10 April 2007 (UTC)

MASH Article

An external link to my article "MASH (Multi-stAge noise SHaping) structure" was deleted as spam. Would anyone object if I re-included it? The article is uniquely targetted at a wider audience than most (all?) other papers on this subject. I've had gratifying messages of support from industry and academia. Recently, an employee of a well-known consumer electronics firm thanked me for helping him finally understand why overflowing accumulators are first-order sigma-delta modulators. Also, I've seen statements elsewhere on the web, but no derivation, of the Pascal's triangle coefficient weightings; and I only know one other paper presenting the same main result. Mine goes at a far gentler pace. Of course I hope visitors will find other items of interest on my hobby electronics site; I'm not selling anything; and yes I know I should submit an article to Wikipedia.

I don't know why your link was removed, you can check WP:EL and Spam blacklist for more information on external links, or contact directly the author of the rm (writing in the Talk page). I read your site, it's nice and interesting, and, as you correctly wrote, you can submit a new article in wikipedia (BTW, why don't you register?, it' better to track changes, etc.) regards Katanzag 07:59, 10 April 2007 (UTC)

OK, sorry, in this moment I read the message left in the Talk page of your IP, which says substantially the same as I wrote before. For me it's OK to reintroduce the link, as I wrote before, I found it interesting, though I'm not absolutely an expert in Wikipedia policies Katanzag 09:33, 10 April 2007 (UTC)

On the subject of this Wiki page, I have a comment on the MASH paragraph: the MASH is not exactly a type of sigma-delta modulator, it actually contains a chain of two or more first-order sigma-delta modulators in the forward path. --80.177.105.226 10:11, 7 April 2007 (UTC)

Your comment seems to me correct, MASH is something like cascading, why don't you fix the main article? Katanzag 07:59, 10 April 2007 (UTC)

OK, thanks. I have edited the main article; but I did not include my link because, although the person who removed it is now content for it to be replaced, a WP:COI would exist if I re-instated myself, and another spam fighter would most likely come along and delete it! Would you mind doing it for me? Thanks. --80.177.105.226 15:48, 12 April 2007 (UTC)

No problems. Done it. regards Katanzag 06:34, 13 April 2007 (UTC)

Charectoristics

What are the charectoristics of the output? Ill write some thing on this.

the mathematical properties of the bitstream are quite complex, maybe referenced articles can help you better than me.Katanzag 07:36, 18 April 2007 (UTC)

Stepper motor controler

I have a design for a steper motor controler using a delta sigma, Ill try to write something up.

nice application, I know it, a new page about it could be a good explanation of ΔΣ usage Katanzag 07:36, 18 April 2007 (UTC)

Plagiarizing from Wikipedia

The following note was added by another author (puffingbilly) to help those who simply needed a brief overview of the mode of operation of the sigma-delta modulator and now appears without attribution on the main page. Is this courteous? is this plaigiarism? is this policy?

1. In this context, yes
2. No
3. Yes

Yes, it is fairly common to present material in the talk page before deciding whether it's good enough to expose in the article itself. I have done it several times, including in articles EWSD and telephone. In these particular cases I was the one who later copied it into the article, but in other cases the final decision was someone else's. Talk pages are not at all private, secret, hidden or proprietary. They are merely exposed to fewer millions of viewers and search engines than article pages are.

Nothing I put in Wikipedia belongs to me anymore. Talk page, article, or something else, it belongs to the encyclopedia and may be quoted, copied, distributed and whatever, with no further permission from me or attribution to me. None of this is stealing or impolite or contrary to custom or otherwise unconventional. It's only stealing if I stole it before giving it away in Wikipedia. If you wish to communicate information privately, E-mail it.

If you don't want your words exposed in the encyclopedia article, we can delete them. This will not destroy the material, since it will still be in the archives, but fewer millions of people will see it. Same for this talk page. Articles are not signed by any particular author, since each may have hundreds or thousands of authors. Sections, subsection, paragraphs, etc ditto. Your self attribution, however, will be removed from the article even if you'd rather keep it, since signed material in articles is not Wikipedia custom. Jim.henderson 04:51, 17 August 2007 (UTC)

Opinions can vary about this set of answers, another might be no, yes, don't know. The article appears to be identifiable as the work of apparently one man, Katanzag, from the discussion page, if nowhere else, because he answers all the questions. Without the distinction made it might be concluded by the reader that the work was all that of that one man. My insertion is distinctly different in style and substance limited as it is to a brief, non-mathematical overview which may be all the casual reader or user needs to know. Because of this I think it reasonable to highlight it as an interpolated note.Incidently the implication of your remarks that I am on some sort of ego trip, in the light of the fact that I am using a psuedonym, is insulting and absurd, the remainder of your remarks are merely patronising. Kindly moderate your tone. Puffingbilly 17:56, 17 August 2007 (UTC)puffingbilly

Having given the matter further thought, I would like to expand my comments as follows:-

There already exists in Wikipedia a page on the topic - Quantization (signal processing) - which at a quick glance seems excellent.

The article under consideration here - Delta-sigma modulation - is nothing more than an application of the theory of quatizization to the description of Delta- Sigma analogue to digital converters. Without my intervention it singularly fails to describe what such a converter is in terms the casual visitor is likely to understand. Witness the distress of AMackenzie on this page. Much of that difficult is caused by the use of block diagrams where the exact functioning of each block is unspecified, deeply unclear, and unstable. These may may acceptable to those familiar with the jargon but convey nothing to the casual visitor. The extensive treatment of quantizization noise in this article to the exclusion of all else gives the strong impression to the innocent oberserver that the actual reason for using a Delt-Sigma is to combat noise. It is not, the reason for its use is that it is a cheap and cheerful but nonetheless accurate way of achieving analogue to digital conversion. This is mentioned in the introduction to the article but the emphasis is lost in everything that follows.

In a practical world, the fact that the Delta-Sigma ADC has some of the characteristics of a low pass filter is interesting but irrelevant. An engineer plagued with out of band noise might take advantage of this characteristic but would most likely kill the noise with an analogue low pass filter, this would have none of the lumpiness of a digital equivalent. An engineer wishing to take advantage of the low pass filter equivalent of a digital filter would refer to the page - Quantization (signal processing) - for a full account of all the possibilities.

In my opinion the proper place, if it is not already duplicated there, for this article, as it stood before my intervention, is under the heading - Quantization (signal processing) - its acceptability there being a matter for the judgement of that page. This page - Delta-sigma modulation - need only carry a reference to the - Quantization (signal processing) - page for those with sufficient interest to need it.

It may be that my intervention will be found to say most, if not all, that is needed by the casual visitor, but I leave that judgement to others. An engineer worth his salt may find sufficient from that to go away and design his own version.81.131.49.202 18:13, 18 August 2007 (UTC)puffingbilly

Because silence may be taken as assent and frequently is, I take leave to correct an impression given above that Wikipedia owns my contribution. I own the copyright and always will because I am the author and will not transfer it. What Wikipedia may have, in common with the rest of the world, is a license under the GFDL terms because that was an automatic condition for acceptance of any contribution imposed by Wikipedia. It is questionable whether that will stand up because it does not allow my setting conditions in return. ie. It is unfair. The introduction to the GFDL contains the following clause:-

The purpose of this License is to make a manual, textbook, or other functional and useful document "free" in the sense of freedom: to assure everyone the effective freedom to copy and redistribute it, with or without modifying it, either commercially or noncommercially. Secondarily, this License preserves for the author and publisher a way to get credit for their work, while not being considered responsible for modifications made by others.

I see it contains a provision to preserve for the author and publisher a way to get credit for their work. Perhaps you would like to explain how Wikipedia complies with that provision. Puffingbilly 04:02, 19 August 2007 (UTC)puffingbilly

In my understanding, the credit is given by way of the revision history. (Also, you mentioned above that the article seems to be the work of Katanzag, because of his talk page presence. Again, the revision history of the page in question shows that it is the work of many authors, and you can see which authors contributed what changes.) I realize this is something of an old discussion, but it seemed you might be unaware of the revision history, so I'm pointing it out. 66.249.228.202 (talk) 14:00, 11 January 2008 (UTC)

You are correct that the original author owns the copyright, even after that author "contributes" that text to Wikipedia. How does Wikipedia comply with "credit" clause of the GFDL? A good question -- however, I think you will have more success asking that question at WP:COPYRIGHT or a related talk page such as Wikipedia_talk:Copyrights or Wikipedia talk:Text of the GNU Free Documentation License. --68.0.124.33 (talk) 03:09, 6 January 2008 (UTC)

Meaning of Delta

This article claims that the "delta" in delta-sigma comes from the Dirac delta function, in a way that's not entirely clear to me. I learned in undergraduate (EE) that the delta refers to the difference, as in Delta modulation. A brief check online turned up this, which agrees with my recollection. I'm not sure the definition in the article is right; I'm not spotting any support for it in the references. Think this should be changed? Is the article I linked above a suitable reference if the definition is to be changed? 66.249.228.202 (talk) 03:29, 11 January 2008 (UTC)

I agree. Delta does not refer to Dirac delta. If it did, then any type of pulse modulation would be a candidate to be called a "Delta modulation." --TedPavlic | talk 14:53, 18 February 2008 (UTC)

I have visited your reference and for what follows I ask you to refer to it again, at least for the circuit diagram. The operation of the circuit in your reference may be analysed to be an equivalent of that shown in figure 1. The duration of the impulse is determined by the clock, its amplitude by I_s and its strength by the product. The sum of the impulse and the input voltage V_in is made at the input to the integrator, sigma is accumulated in C2 and buffered in D whilst the summing interval is determined by the clock and counter C1.

It is not made explicit in your reference that the input to the integrator is forming the analog sum of the input voltage and a series of well defined impulses of strength I_s and duration determined by the clock. Without this it is left to the reader to discover by doing his own analysis. A Wikipedia reader is not necessarily equipped or inclined to perform such an analysis but he may be expected to follow a set of illustrative waveforms linked to explicit references to each functional element as is provided here. The differences mentioned in your reference possibly tally with delta modulation but they do not sit well the operation of the converter as described here. What difference are we referring to? Possibly to the difference between the integral of the input voltage and the integral of the impulse stream, if so it would be most helpful if it were made explicit but by this time we have introduced the integral of an impulse stream. The difference in operation between that described in your reference and that described here is that in your reference the impulses are constrained to occur at the next clock boundary following the integral crossing the threshold whereas in the circuit described here the impulse occurs immediately the threashold is crossed. However the integration continues after the threshold is crossed so that the integral of the summation of impulses with input voltage continues without error. The effect of the clocking delay is for the impulses to jitter about their ideal position with a maximum error in the count of 1 due to this cause. For a numerical example consider an input which produces impulses at an interval of 2.5 clock counts in the circuit described here then, in your example impulses will be produced at clock counts of 3,5,8,10,13,15 etc.Puffingbilly (talk) 01:17, 26 January 2008 (UTC)

So far as the use of the Dirac delta function to describe the integral of impulses is concerned, that is exactly what the function was invented for. The fact that it will describe impulses without knowledge of their actual shape in no way prevents its use when the shape is known. For more information please see the Wikipedia article. I have now included examples of how properties of the Dirac delta function can be used in the construction of the integrator waveforms.

If you accept that the waveforms and discussion for figure 1 of this (Wikipedia) article is essentially correct although simplified so that the essential elements are illustrated separately then the description of the impulse as equivalent to the Dirac delta function is also correct. To understand the operation of your reference to the point where waveforms may be drawn as is done here will require that it be similarly separated. The introduction of the term 1-bit DAC masks the fact that we are dealing with the integral of a series of impulses matched to the integral of the input voltage. The innocent might be forgiven for wondering how a 1-bit DAC can produce anything other than 2 states, 0 and 1, say. At which point he will be forgiven for retiring, confused. Delta-Sigma Converter is sufficient of itself to identify the function and 1-bit DAC simply obfuscates this. I have seen the Inose et. al. paper who are credited with coining the name and can find no rationale for the choice of name presented there. We are left to second guess their thinking on the matter. The later paper by Inose and Yasuda has the title "A UNITY BIT CODING METHOD BY NEGATIVE FEEDBACK", PROCEEDINGS OF THE IEEE, Vol 51, November 1963, pp1524-1535 may be the point at which the 1-bit crept into the jargon. At that time it may have been thought necessary to emphasise the economy of the method. A good idea at the time but must we be tied to it 45 years later. I have found one web page which is quite specific about delta, http://www.cs.berkeley.edu/~kfall/EE122/lec05/sld019.htm which, in part, states, "Important parameters: delta: size of step change at each bit". Whether we identify delta with the step or the impulse that produces it we are certainly not talking of a difference. My preference is for the impulse to be called delta because of the association with the Dirac function.Puffingbilly (talk) 16:14, 25 January 2008 (UTC)

Wrong to derive SDM from DM

The section that "drives" SDM from DM seems to be based on a poorly written Motorola paper by Sangil Park, Ph. D., from the DSP section of their "Strategic Applications" group.

The analysis you take exception to was published in two highly respected and refereed journals, namely:- H. Inose, Y. Yasuda, J. Murakami, "A Telemetering System by Code Manipulation -- ΔΣ Modulation," IRE Trans on Space Electronics and Telemetry, Sep. 1962, pp. 204-209. and Inose and Yasuda "A UNITY BIT CODING METHOD BY NEGATIVE FEEDBACK", PROCEEDINGS OF THE IEEE, Vol 51, November 1963, pp1524-1535 You are mistaken, the analysis in terms of delta as the impulse function is correct. In this instance the impulse is the quantum v.dt and quantization is the conversion of an analog waveform into its equivalent pulse stream, the short term frequency of which is an analog of the short term voltage at the input. The operation of the converter is fully explained in the main article with block and circuit diagrams and associated waveforms. Examination of these shows that the circuit operates to hold the integral of the linear difference between the analog input and the impulse stream within well defined limits.Puffingbilly (talk) 22:08, 5 April 2008 (UTC)

[The derivation of the ideas for the method from earlier DM is discussed in the Inose et. al. papers, referred to elsewhere, who are credited with originating the term SDM, where the treatment of the summation of the impulses with the input is linear. I suggest you consult those papers. As has ben explained at great length in the main article, when considering the impulse, it is only its integral which is important in the analysis, in essence the impulse could be of infinite amplitude and zero duration and still the analysis remains applicable. As explained above, in the special case where the amplitude is constant during the impulse, then the strength of the impulse is determined by the product of its amplitude and duration, but the analysis is aplicable for any arbitary impulse shape determined by any arbitary process such as, for instance, differentiation of a known step. In the case of the communication channel it is the frequency proportional to input voltage of the pulse train that is transmitted, it is perfectly possible to regenerate the pulses on reception to a standard form before further processing them with a low pass filter and in this regeneration it is possible to introduce a scaling factor. You miss the point of the assertion that DSM was developed out of concepts already in use in DM, if you read the Inose papers you will see that they fully explain that the system is entirely different in outcome but their thinking was influenced by the prior art. I suggest you reconsider your edits in the light of their probable value to ordinary readers]Puffingbilly (talk) 23:51, 20 February 2008 (UTC)

SDM is not simply a refactoring of DM! It's ENTIRELY DIFFERENT. The "derivation" implicitly depends on the quantizer being linear. However, quantizers are not linear (actually, we don't even need linearity). That is:

$A\operatorname {Quantize} (b+c)\neq \operatorname {Quantize} (Ab+Ac)\,$

It is possible to refactor the DM block diagram, but the result *FLIPS* the order of the quantizer and the integrator. In other words, an ANALOG signal gets sent across the channel and that analog signal INTEGRATES the noise. In fact, this is the reason why DM and SDM have different noise performance.

I'm sure Dr. Park meant well when he described SDM in terms of DM, but the derivation is flat wrong. It must be omitted or included with strong caveats. It's simply WRONG to even MENTION the linearity of integration. Doing so gives the impression that the derivation can be made rigorous, but it CANNOT. --TedPavlic | talk 15:00, 18 February 2008 (UTC)

Additionally, the quantizer output levels are completely different for DM and SDM. In DM, they're small with respect to the input signal because they represent steps up and down an approximation of the signal. In SDM, the quantizer outputs must be OUTSIDE of the range of the signal (e.g., at the supply rails). Otherwise, the LPF could not possibly extract the right signal. --TedPavlic | talk 16:34, 18 February 2008 (UTC)

Equivalent bit-depth performance

Hi, I feel this article is missing a comparison of delta-sigma with standard quantizing (i.e. bit depth/time resolution tradeoff). I'm keen to put this graph and an explanation in somewhere for this article.

This graph shows the equivalent number of bits resolution at the original sampling rate that a delta-sigma at some higher rate but lower resolution achieves (in terms of quantizing error standard deviation). It was generated by simulation which was run several times (that's why there is more than 1 trace).

I want to confirm with someone that I haven't made any errors. The scilab script used is in the summary of the image.

I also intend on doing a frequency performance comparison too. Thanks! Darrell.barrell (talk) 11:03, 7 June 2008 (UTC)

This graph looks excellent.

May I suggest one minor tweak: extend the range of the graph so it includes 256x oversampling.

I've been told that that many 1-bit sigma-delta DACs are designed to play CD-quality audio with, I guess, 256x oversampling.

(Although the audio DACs I've looked at so far are 4-bit with 128x oversampling).

--68.0.124.33 (talk) 04:23, 2 July 2008 (UTC)

Merging Sigma Delta with Delta-Sigma Modulation

Hello folks,

IMO the merging should be done here because the suggested name is DeltaSigma (and not vice versa). Of course I'm open to any comment Regards --Katanzag 12:45, 10 November 2005 (UTC)

They should definitely be merged as they are simply different names for the same thing, the most popular being delta-sigma modulation

IMO, ΔΣ looks logically unnatural. It is like we are taking delta of sigma; whereas, the meaning is quite different - accumulating errors (ΣΔ). --Javalenok 15:04, 1 May 2006 (UTC)

Unfortunately, ΔΣ is the name that their fathers gave to this kind of conversion and that now is mostly used; your consideration is however correct, please check references which better than my two-line explanation show the reason of this name. Regards --Katanzag 08:46, 3 May 2006 (UTC)

I have realized something: the math and english are two different languages with two different word orders! The correct math notation would be ΣΔ. In English, the modifiers precede the noun turning "sum of changes" into "change sum"! That is how we get the ambiguating opposite spellings! May I put this my discovery into the article? :) --Javalenok (talk) 11:37, 17 December 2008 (UTC)

I agree.

Regarding the improvement of the main DS-mod page....The first step should be to explain how DS differs from straight Delta mod, and then go on from there.

Correctness

Diagrams: The delta section has a sigma sign, while correct it is confusing. The Sigma section is shown as an integrator, this is also confusing.

Δ section is for (algebrical) sum, that is the summation sign; Σ section is the integration section. It could be a bit confusing, I know; please read some of the referenced documents, which can help you better than me in understanding the whole process.

The 2nd order filter seems to me to be just a filter followed by a delta sigma. The first stage is not part of the delta sigma.

Please consider that there it is a feedback loop, it would be a filter if it was in a direct path. As before, check references for a detail explanation.

I do not understand what the digital filter does, as a follower. Though an optional digital filter before the delta sigma does make sence (e.g. the extra order of the 2nd order system.

ΔΣ modulates noise at high frequences (out of the band of interest) so a low pass (digital) filter can get rid of them; besides, it acts as a decimator to reduce frequency (see example.

There is a lock of arrows on feedback loop.

See answer 1

What is the 1 bit dac on the feedback? It is only needed for an analoge input device.

Yes, the input is analog: DAC converts the 1 or 0 output of ΔΣ in a such way that can be summed (in an analog way) with the new input.Katanzag 07:36, 18 April 2007 (UTC)

In the 100 sample example, isn't the red line supposed to be -cos(x) instead of sin(x)? That is, shouldn't 1 0 1 0 1 0 align with the section of the wave where the wave's derivative is 0? —Preceding unsigned comment added by 80.203.238.44 (talk) 08:45, 18 November 2010 (UTC)

What's missing from this article (IMHO)

I came to this article because I'm interested in the SACD format. I followed this chain of articles: Super_Audio_CD -> Direct_Stream_Digital -> Delta-sigma_Modulation -> Delta_Modulation, and gave up in frustration at that point.

I can't find an explanation of what Delta-sigma modulation _IS_. The article describes electronics to do the modulation (I think), and a mathematical algorithm to do it. I would like to see a higher level description: what is the mathematical principle? What would simple waveforms (say, a sine wave at 440 Hz) look like after being modulated into digital by this process? How would the digital form change if it was raised an octave to 880 Hz? What if its amplitude was doubled? Is it a linear process? (By which I mean, could you do it on the components of a waveform's Fourier transform and straightforwardly combine the results?)

Would a knowledgeable expert please consider adding this level of explanation to the article?

Thanks in advance! AMackenzie 18:42, 15 August 2007 (UTC)

THIS REQUEST LACKS PRECISION - WILL WHOMEVER RAISED IT PLEASE BE MORE SPECIFIC ABOUT WHICH SECTIONS NEED WORK - THANK YOU

In part 1 Description the operation description is almost reduced to words of one syllable. If the general reader understands the description he probably has as much as he needs to know and he should quit while he is ahead.Puffingbilly (talk) 22:52, 4 June 2011 (UTC)

The following note was added by another author (puffingbilly) to help those who simply needed a brief overview of the mode of operation of the sigma-delta modulator and now appears without attribution on the main page. Is this courteous? is this plaigiarism? is this policy?

The method can be thought of as a voltage controlled oscillator, where the controlling voltage is the voltage to be measured and where linearity and proportionality is determined by a negative feedback loop. The output of the oscillator is a pulse stream, each pulse of which is a known, constant, amplitude and duration but variable separating interval. The interval between pulses is determined by the feedback loop so that a low input voltage produces a long interval between pulses and a high input voltage produces a short interval between pulses. Counting the pulses produced in the way described above in a fixed summing interval produces a count proportional to the input voltage to be measured. Variations in scaling can be produced by either varying the fixed summing interval or by counting down the pulses by a fixed ratio or both methods can be used. The output count finally produced is the digitization of the input voltage.Puffingbilly 15:32, 16 August 2007 (UTC)puffingbilly

The pulse described above is the delta and the count is the sigma of the delta sigma analogue to digital converter.

There are several ways to generate a voltage impulse other that given above but that is the simplest to communicate.

To answer AMackenzie more directly the bandwidth of a typical commercially available sigma-delta analogue to digital converter is extremely limited because of the necessity to make the summation(sigma) over a relatively long interval. It seems to me most unlikely that a converter able to render 880Hz would be available, (a search on Google may show otherwise) but if one were available it would output a stream of digitized samples at the constant sample rate of the converter, each sample would be the digital representation of the mean of the input waveform over the sampling period. Thus the difference between a 440Hz signal and an 880Hz signal would be that the data stream would still emerge at the constant sampling rate but the data emerging would vary at either 440Hz or 880Hz.Puffingbilly 15:58, 16 August 2007 (UTC)puffingbilly

Converters into 10's of kHz, at least, are used in audio work. One benefit of the d-s system is the simplicity of the circuit; this allows clocking it at 10's or even 100's of MHz. 66.249.228.202 (talk) 13:16, 11 January 2008 (UTC)

Technical

I've added a technical tag to the article. The Description would be improved if concepts were described in English rather than algebra. Plenty of time for algebra later. This is a start. There are other problems. --Kvng (talk) 13:15, 21 June 2011 (UTC)

Cleanup

I've added a cleanup tag to the article. The Motivation section is written in non encyclopedic style. The Description section is a collection of one-sentence paragraphs. This is a start. There are other problems. --Kvng (talk) 13:15, 21 June 2011 (UTC)

Introduction

Kvng, I'd like to revert the changes you made. Here is my reasoning. DSM applies to both analog to digital conversion and digital to analog conversion, and even digital to digital transcoding. The most popular application, at least in the sense a non-engineer will run into, is probably an audio application of D/A. And in this case, I don't know of any big cases where more than two levels of analog output are used. (The power efficiency for consumer electronics comes precisely because only the on/off states are used.) For these reasons I respectfully submit that the original wording is more helpful as an introduction. Perhaps a second example describing A/D should be added instead.Serrano24 (talk) 15:28, 14 July 2011 (UTC)

I have reverted. 1 bit DACs do dominate. I note however that the low power claims made here are not supported by anything in the article or by any citations. --Kvng (talk) 00:03, 15 July 2011 (UTC)

You're right on the power claims. I'd like to work this explanation into the D/A section, where I'll refer to the Wiki entry on class D amplifiers. Alas, power circuitry isn't my area of expertise. Serrano24 (talk) 16:58, 15 July 2011 (UTC)

Note for laymen

Laymen are mystified by entirely accurate descriptions which contain no how or why information. Although much of what they may be seeking is presented, often by implication, at length, herein, this note attempts to extract and elucidate the information a layman most needs.

Firstly why convert an analog signal into a stream of pulses?

In brief, because it is very easy to regenerate pulses at the receiver into the ideal form transmitted. The only part of the transmitted waveform required at the receiver is the time at which the pulse occurred. Given the timing information the transmitted waveform can be reconstructed electronically with great precision. In contrast, without conversion to a pulse stream but simply transmitting the analog signal directly, all noise in the system is added to the wanted analog signal quickly rendering it useless.

Each pulse is made up of a step up followed after a short interval by a step down. It is possible, even in the presence of electronic noise, to recover the timing of these steps and from that regenerate the transmitted pulse stream almost noiselessly. Then the accuracy of the transmission process reduces to the accuracy with which the transmitted pulse stream represents the input waveform.

There are several methods available to the specialist for quantifying the distortions introduced, all of which are technical, mathematical and are assumed to be of no great interest or value to the layman. All the layman needs to know is that the specialists have determined that the distortions are within acceptable limits and may even have a value in reducing unwanted aspects of the original signal.

Secondly, why Delta-sigma modulation?

Delta-sigma modulation converts the analog voltage into a pulse frequency and is alternative known as Pulse Density modulation or Pulse Frequency modulation. In general frequency may vary smoothly in infinitesimal steps as may voltage and both may serve as an analog of an infinitesimally varying physical variable such as acoustic pressure, light intensity etc. so the substitution of frequency for voltage is entirely natural and carries in its train the transmission advantages of a pulse stream. The different names for the modulation method are the result of pulse frequency modulation by different electronic implementations which all produce similar transmitted waveforms.

Thirdly, why use Delta-sigma modulation on a CD?

A CD works by optically reading pits formed on the CD. This reading process does not necessarily produce well formed pulses but the pulses may be electronically reformed so that only the presence or absence of a pit need be detected and all the analog information is present in the analog frequency of the detected pits.This frequency is determined by the pit density along the replayed track and the velocity of the track under the optical pit detector.

This isn't a very good description. First, delta-sigma modulation for digital discs is a digital-to-analog conversion method, not analog-to-digital. Second, how the data is physically recorded on a CD/DVD/Blu-ray is irrelevant. On CDs and DVDs the sound must be decoded first from the bits on the disc, then turned from a digital record to an analog waveform. The sound data is encoded digitally as a PCM waveform, and can be converted to analog using either multi-bit DACs or with Delta-Sigma modulation. On SACD (which is physically a DVD), the data is encoded to simplify the A/D process so that a single bit A/D can be used, but a full delta-sigma modulator is not required. Whether the underlying data is recorded as PCM or not, delta-sigma modulation is preferred today because for an audio application it delivers high quality at low cost.Serrano24 (talk) 16:22, 12 July 2011 (UTC)

I put the paragraph on CD's in to help readers like AMackenzie who complains within.

You have deleted it in its entirety.

You clearly have knowledge that could help him.

Why don't you edit it to your own satisfaction and replace it. — Preceding unsigned comment added by Puffingbilly (talk • contribs) 21:05, 30 July 2011 (UTC)

I deleted the section because I feel it is misleading and factually incorrect. I described why in the comments above. A layperson reading it will think that delta-sigma modulation has something to do with CDs, when in fact it really does not. Therefore I think deleting the section is more helpful then describing in the text why the section shouldn't be in the text. The application of delta-sigma modulation to audio signals is described elsewhere in the article, and there is already an article on SACD.Serrano24 (talk) 20:25, 4 August 2011 (UTC)

Fourthly, why the sigma-delta analog to digital conversion?

The ADC accurately converts the mean of an analog voltage into the mean of an analogue pulse frequency and counts the pulses in an accurately known interval so that the pulse count divided by the interval gives an accurate digital representation of the mean analog voltage during the interval. ΣΔ is the mathematical symbol for the summation of delta pulses and is read sigma-delta.

NB. I think laymen might find it helpful to find the above note at the start of the article. The mechanics of placing the note at the start of the article without disturbing the contents numbering elude me and require more effort and time than I have available so if anyone with the wiki expertise likes to do this it might be helpful but it might also break the wiki rules.Who knows? If this is implemented it would be helpful to remove the duplication that will then exist in the Remarks section Puffingbilly (talk) 22:55, 7 June 2011 (UTC)

I don't think it's very scientific/encyclopedic to state this kind of "why use this-and-that", so I think this part is not suited to be on Wikipedia, at least not in this form. I agree that there should be a "shorthand, low-tech explanation" for laymen, but this isn't really it, is it? Also, it looks a bit awkward when you use headers like that (Firstly,...Secondly, etc.)... Lord Le Brand (talk) 13:18, 21 June 2011 (UTC)

-- This added section should be edited for accuracy. Some of the things said above are false. — Preceding unsigned comment added by 204.9.221.70 (talk) 15:23, 12 July 2011 (UTC)

Usage in compression

Delta-sigma modulation can be used when compressing signals, because it significantly reduces range of values in stream, thus allowing more aggressive quantization. Right? --91.213.255.7 (talk) 22:00, 27 December 2011 (UTC)

Deletion of "Why use Delta-sigma modulation on a CD?"

SDM is not used on CDs. This is not the place for a general discussion of all modulation methods so it is difficult to justify the inclusion of this paragraph.Puffingbilly (talk) 09:42, 22 December 2012 (UTC)

I agree that the modulation article is the place for a general discussion of all modulation methods, not this article. However, the Wikipedia compact disc, Super Audio CD, and Direct Stream Digital articles all seem to agree that delta-sigma modulation is, in fact, used on Super Audio CDs. --DavidCary (talk) 13:05, 6 August 2014 (UTC)

1st Person Writing

How about someone rewriting all this “Lets do...” “We can...” stuff. Its amateurish and reads dreadfully. Kevin Aylward 12:00, 11 August 2013 (UTC)

— Preceding unsigned comment added by Kevin aylward (talk • contribs)  

What's stopping you? Puffingbilly (talk) 22:20, 20 February 2014 (UTC)

It's a matter of taste. Maybe "let's do" is a bit OTT (awful expression, but possibly appropriate here). However, in my day, "we can" was extensively used in mathematics up to the highest levels - and with good reason (maybe this persists?). I find that the present fashion for using the passive form makes the sentences longer; in some contexts it also removes content. I personally find that papers from Lord Rayleigh's peroiod where actions are attributed are easier to read than currently accepted styles. It may of course be that the education of the time resulted in scientists being better schooled in writing techniques, but I believe that freedom to use first person and other active language as appropriate is helpful.PhysicistQuery (talk) 18:18, 30 November 2015 (UTC)

Simplified summary?

Took me ages to figure out how it worked, until I re(a)d "Pulse density modulation", and it all started making sense.

Is this summary correct and/or easier to understand than the current mathematical gobbledygook?

"Keep a running sum of the inputs. Output a 1 every time the running sum exceeds a multiple of full scale. Therefore, the percentage of output 1 pulses equals the input value."

--67.170.240.95 (talk) 22:58, 14 February 2015 (UTC)

Actually I forgot to mention that every time the input exceeds, it's reset back down. Is it -= fullscale, or := 0? --67.170.240.95 (talk) 23:01, 14 February 2015 (UTC)

I'm not an audio expert, my field is industrial and scientific electronics, but perhaps an 'outsiders' viewpoint would make things more readable. It took me a long time reading this to understand what it was about and what it was good for. How about an introduction along the lines of the following. I'll leave it to the experts to correct my errors and to add such a paragraph if it is felt appropriate.

"Delta-sigma (sum of differences) is a method of encoding an analogue signal (e.g. audio) into a stream of digital pulses suitable for transmission over a non-linear medium (e.g. optical transmission or storage). It is a form of frequency modulation consisting of a stream of equal-length pulses separated by idle gaps proportional in length the the analogue signal (pulse density modulation). Unlike other analogue-to-digital (ADC) methods, it is only the signal level that is encoded, its timing remains analogue. Compared to other methods delta-sigma offers good linearity, low distortion and introduced noise, and invariant transmission delay. It's main advantage is that the encoding and especially the decoding circuitry are very cheap and simple. It's disadvantages are that it requires a very large bandwidth of the transmission medium, which makes it unsuitable for narrow-band media such as radio, and that it does not encode timing, so is unsuitable for digital circuits (e.g Internet)."

Puposet (talk) 11:11, 8 December 2015 (UTC)

I agree that the current lead is difficult to understand. Thanks for trying to untangle it a bit. Unfortunately I don't see this proposal as a significant improvement. Both are getting a bit lost in digital, analog, digital-to-analog converter and analog-to-digital converter topics. The lead needs to focus more on the specifics of delta-sigma modulation. I will come back in a bit and see if I can make some improvements here. ~Kvng (talk) 15:33, 11 December 2015 (UTC)

I think I see what you are driving at. I came here researching prior art for what I thought might be a novel ADC design, so that is my angle. I'll agree that delta-sigma is not truly a digital conversion, although some users describe it as such. However I do think it important that the lead describe what the point of it is (i.e. utilising a non-linear transmission medium for linear signals), to give some context to a reader lacking an optical-storage background.

Puposet (talk) 12:40, 17 December 2015 (UTC)

Confusing labelling in figure

The final waveform in the figure (6) is a bit confusing, because it looks like it should belong to some node in the figure, but it is only referenced in the text. It would be helpful if all signals (including the output of the counter, buffer) were included in the figure, and, and waveforms like (6) which are only referenced in the text could be shown in a separated section below. — Preceding unsigned comment added by 145.109.124.88 (talk) 08:13, 5 April 2017 (UTC)

External links modified

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Improper use of questions for subsections

The 3 parts that make the "Motivation" section should not be questions but titles like "Conversion analog signals to pulses" instead of "Why convert an analog signal into a stream of pulses?". Beside, it's just not a good writing style.

ICE77 (talk) 00:03, 7 August 2015 (UTC)

More than a year later and this unencyclopedic wording still hasn't been cleaned up. Robert K S (talk) 16:26, 11 October 2016 (UTC)

This whole section is uncited and lacks context and makes dubious or tangential assertions. I have reviewed it to make sure it is not obviously wrong and will review other content in the article before proposing a remedy. Please have patience or jump in an help. ~Kvng (talk) 23:09, 4 October 2017 (UTC)

This is the best Wikipedia article I've ever seen...

and I still don't understand. Kyle Cronan (talk) 06:31, 11 June 2016 (UTC) 😝

I think it would be helpful if Kyle were to tell us which part or parts he does not understand so that we may direct our efforts more effectively.Puffingbilly (talk) 03:08, 14 January 2019 (UTC)Puffingbilly

Too Technical?

In my opinion sections 6 and 7 are too technical for the average reader. They are abstruse, highly technical and convey information the average reader neither wants or needs but they are required reading for specialists. Since these sections merely mimic the technical literature available from the various manufacturers would it not be better delete these sections, mention the content and refer the reader to that literature. This has the advantage that it will track current practice as it varies with time. I'm confident the average reader won't bother and won't miss much. If it is determined that this information is necessary for the average reader then in my opinion these sections demand expansion to give the kind of detail available in earlier sections.Puffingbilly (talk) 15:11, 14 January 2019 (UTC)Puffingbilly

I agree that section 6 (Principle) does not offer much. There is a single reference in this section and it does not appear to support much of the content in this section.

I do think that section 7 (Variations) is valuable, I don't find it particularly difficult to follow but I will be reviewing this in the coming weeks and will try and make improvements. ~Kvng (talk) 15:20, 20 January 2019 (UTC)

I think that, in the sections using advanced mathematics mostly without mentioning it or giving the results of such analysis without even detailing the analysis, the ordinary reader needs to be told explicitly the mathematical techniques in use, e.g. Laplace Transforms, and given references to suitable tutorial material so that he can determine for himself whether to plough on or know that he has reached his limits.Puffingbilly (talk) 21:24, 20 January 2019 (UTC)Puffingbilly

Detailed summary from Digital-to-analog converter

I am trimming down the summary of the oversampled delta-sigma DAC in Digital-to-analog converter. I think this material is already covered in this article but in case it is useful here I am reproducing it below. ~Kvng (talk) 16:17, 19 December 2018 (UTC)

Oversampling DACs or interpolating DACs such as the delta-sigma DAC, use a pulse density conversion technique. The oversampling technique allows for the use of a lower resolution DAC internally. A simple 1-bit DAC is often chosen because the oversampled result is inherently linear. The DAC is driven with a pulse-density modulated signal, created with the use of a low-pass filter, step nonlinearity (the actual 1-bit DAC), and negative feedback loop, in a technique called delta-sigma modulation. This results in an effective high-pass filter acting on the quantization noise, thus steering this noise out of the low frequencies of interest into the megahertz frequencies of little interest, in a process called noise shaping. The quantization noise at these high frequencies is removed or greatly attenuated by use of an analog low-pass filter at the output (sometimes a simple RC low-pass circuit is sufficient). Most very high resolution DACs (greater than 16 bits) are of this type due to its high linearity and low cost. Higher oversampling rates can relax the specifications of the output low-pass filter and enable further suppression of quantization noise. Speeds of greater than 100 thousand samples per second (for example, 192 kHz) and resolutions of 24 bits are attainable with delta-sigma DACs. A short comparison with pulse-width modulation shows that a 1-bit DAC with a simple first-order integrator would have to run at 3 THz (which is physically unrealizable) to achieve 24 meaningful bits of resolution, requiring a higher-order low-pass filter in the noise-shaping loop. A single integrator is a low-pass filter with a frequency response inversely proportional to frequency and using one such integrator in the noise-shaping loop is a first order delta-sigma modulator. Multiple higher order topologies (such as MASH) are used to achieve higher degrees of noise-shaping with a stable topology.

Re quantizer: The term is not well defined and leaves people confused. In some contexts it can mean a circuit that produces an accurately defined impulse, often in such contexts a clock is involved. Where a clock is not involved it can be as simple as the output of the comparator or a so called 1 bit DAC which follows the comparator. Without accurate definition of what is meant in the particular context the reader is left guessing. In the case of the first order implementation, Fig. 2 - 3) where no clock is involved, all that can be said of the quantizer is that the integral of the output is equal to the integral of the input but the frequency is not proportional to the input voltage. The waveform is pulse width modulated but not pulse width modulation as commonly understood in which the pulses are generated at fixed frequency but variable width. In fact during high positive input voltage the positive pulses are long and the intervening interval short. Conversely during high negative input values the positive pulses are short and the intervening negative intervals are long.It would also be helpful if the mechanism of oversampling were discussed. eg. increasing the frequency by reducing the time constant of the integrator or reducing the level interval of the 1 bit DAC. Puffingbilly (talk) 06:30, 13 January 2019 (UTC)Puffingbilly

The problem is not so much the quantizer as the omission of an explicit sampling, I think. Even first-order delta-sigma would normally have a clocked sampler. Dicklyon (talk) 06:44, 13 January 2019 (UTC)

I have gone to some length to show the meaning of Σδ as the summation of impulses and described the general principle with a block diagram.It does not necessarily follow any particular implementation. It illustrates a principle. It attempts to answer the question - " What is Delta Sigma modulation"? in the abstract sense not the question "What are particular instances of practical implementations"? I dare say very important practical implementations can be found labelled Delta Sigma which include a clocked sampler, that does not necessarily mean that the label is accurate. The conflict comes with the sloppy use of the label. I do describe a particular implementation, which, at the time of first writing was mentioned in the talk page and so must have been familiar to the then editors. It is clocked but hardly meets the description "clocked sampler" but it does produce a countstream with frequency proportional to analogue input. It is not practical or possible to describe every instance described as Delta Sigma and the reader is better served if he is referred to the manufacturers literature.Puffingbilly (talk) 13:11, 13 February 2019 (UTC)

Are you saying there are delta-sigma converters without a clocked sampler? I don't think that's conceivable, but show me if you find one. Dicklyon (talk) 18:27, 16 February 2019 (UTC)

It depends what you mean by sampler, I think of sample and hold as an example of sampler, I do not see the circuit I describe as a sampler. — Preceding unsigned comment added by Puffingbilly (talk • contribs) 07:59, 17 February 2019 (UTC)

I'm referring specifically to a clocked quanitizing sampler, or clocked comparator. There is no bit stream without clocking, and do delta-sigma without a bit stream, as far as I'm aware. The original Inose paper of 1962, for example, shows a "sampling pulse generator" in its block diagram, and sampling pulses (clocks pulses) at the top of its waveform diagram. The 1963 Inose paper shows it as "clock pulse generator". If you don't have that, you don't have delta-sigma -- unless you show me otherwise in a source. Dicklyon (talk) 18:47, 17 February 2019 (UTC)

Check the edits I did to reflect this stricter definition of what a delta-sigma converter is. Also, I made some comments on your schematic at [3]. Do you get notified automatically? Can you do the suggested simplifications? Dicklyon (talk) 19:18, 17 February 2019 (UTC)

I refer to the diagram on page 16 of "The Evolution of Oversampling Analog-to-Digital Converters" Bruce A. Wooley. It can be seen that it has exactly the same structure as Fig. 1. The difference is that the impulse for the Wooley figure is clocked and fig. 1 is not. The essential character of both figures is that the integral of the output stream matches the integral of the input analogue voltage by using negative feedback. It is a convenience rather than a necessity to clock the system in that clocking keeps the system synchronised with others; e.g. in a time division multiplex environment. Puffingbilly (talk) 20:44, 17 February 2019 (UTC)

That diagram shows a Z-domain (discrete-time, clocked) integrator. Without the clocking it's not a delta-sigma thing. Without the clocking it doesn't produce a bit stream, or "code", just analog timing of a bi-level signal. I'm not disagreeing with the "essential character", just about what delta-sigma means. Dicklyon (talk) 21:08, 17 February 2019 (UTC)

What are you going to call an asynchronous converter where the integral of the output stream is matched by negative feedback to the integral of the input waveform? — Preceding unsigned comment added by Puffingbilly (talk • contribs) 10:50, 18 February 2019 (UTC)

My point is the modulator works perfectly well without a clock, the clock is needed for reasons external to the modulator.Puffingbilly (talk) 11:09, 18 February 2019 (UTC) This article is intended for the general public who probably only need to know the principle of operation. To introduce a clock is to muddy the issue. The average reader may well ask "Why is it clocked"? the answer to which is obvious to every insider but totally unknown to to the average reader.Puffingbilly (talk) 11:35, 18 February 2019 (UTC)

It is possible that applications exist or could be brought into existence for an asynchronous system eg. when generating a pulse stream for a D type amplifier, then the noise due to clocking is avoided.Puffingbilly (talk) 12:41, 18 February 2019 (UTC)

I refer to https://www.semanticscholar.org/paper/Class-D-Audio-Amplifier-Using-1-Bit-Fourth-Order-Kang-Roh/01b6e6e484ff27621b89245b9458cd2a7aa11a2f Class-D Audio Amplifier Using 1-Bit Fourth-Order Delta-Sigma Modulation

   Kyoungsik Kang, Jeongjin Roh, +3 authors Songjun LeePublished 2008 in IEEE Transactions on Circuits and Systems II…
   DOI:10.1109/TCSII.2008.922457

We present the design of a single-chip delta-sigma (DeltaSigma) modulation-based class-D amplifier for driving headphones in portable audio applications. The presented class-D amplifier generates output pulse signals using a single-bit fourth-order high-performance DeltaSigma modulator. To achieve a high signal-to-noise ratio and ensure system stability for a large input range, the locations of the modulator loop filter poles and zeros are optimized and thoroughly simulated. The test chip is fabricated using a standard 0.18-mum CMOS process. The active area of the chip is 1.6 mm2. It operates for the signal bandwidth from 20 Hz to 20 kHz. The measured total harmonic distortion plus noise at the 32-Omega load terminal is 0.022% from a single 3-V power supply.

Fig. 1 shows no clock.Puffingbilly (talk) 15:47, 18 February 2019 (UTC)

Right, Fig. 1 is ambiguous about that, but subsequent figures and the text make it clear that it's clocked; e.g. "The single-bit quantizer is realized using a regenerative comparator and an SR latch, shown in Fig. 5. The whole comparator is a purely dynamic circuit controlled by clocks..." That is, the output of the comparator, and therefore of the modulator, is a clocked bit stream. There are Class-D amplifiers that don't clock the comparator, but those are not delta-sigma. Dicklyon (talk) 17:07, 18 February 2019 (UTC)

If you look for continuous-time sigma-delta, you can find papers by Woolley's student Kulchycki, such as this one. But if you read, you find that the loop filters (integrators) are continuous-time, but there's still a clocked quantizer. Dicklyon (talk) 21:36, 18 February 2019 (UTC)

Yes I see that the chip layout shows a clock generator but I cannot find a clock shown on any of the circuit diagrams.The search continues. I think we should seek dispute resolution. Puffingbilly (talk) 21:46, 18 February 2019 (UTC)

Fig. 1 shows quantization noise which you wouldn't have without clocking. Fig. 2 show discrete-time integrators. Figs 3, 4, and 5 show clocked circuits. And it's oversampled: " The oversampling ratio (OSR) was set to 80 and the clock frequency to 3.2 MHz for the peak SNR of 103 dB in an ideal behavioral simulation." It's all clearly clocked; the clocks are labeled with the phi symbol for clock phase.

I've put a note at Wikipedia_talk:WikiProject_Electronics#Delta-sigma_modulation to seek more eyes on this. If nobody shows up, try WP:3O.

In the mean time I'll refs to note that the clockless one is sometimes called asynchonous delta-sigma modulation, but that it's analog, i.e. does not produce a symbol sequence. Dicklyon (talk) 01:13, 19 February 2019 (UTC)

I don't agree with your changes but life's too short. My original objective was to get something the ordinary reader could understand and I believe that object is achieved with or without the changes Puffingbilly (talk) 09:05, 19 February 2019 (UTC)

Incidently I believe any circuit that produces a series of pulses which, when integrated or low pass filtered, produces a waveform that reproduces the original analogue, falls within the meaning of the term "sigma delta modulation" The narrower meaning you assign to it no doubt reflects the dominant current practice but it is specialist and narrow. On the topic of the asynchronous delta sigma modulator, if as you say, it does not produce a symbol sequence then it does not meet even the broad definition of sigma delta modulation. Do you have a reference for such a circuit. In my original, many years ago description of Fig. 1 I remember saying words to the effect "for the modulator it is the delta pulses that are transmitted to form the signal stream" It may well have been edited out in the intervening years to make a nonsense of the description. I don't have the time or the inclination to permanently watch editing but it comes as no surprise if such an event occurred.Puffingbilly (talk) 09:59, 19 February 2019 (UTC) I think it a discourtesy that you have modified the text in my figure without mentioning it on the figure page. Puffingbilly (talk) 12:39, 19 February 2019 (UTC)

I refer to https://www.researchgate.net/publication/243767842_Asynchronous_Delta_Sigma_Modulation Kikkert, Cornelis & J. Miller, D. (1975). Asynchronous Delta Sigma Modulation. 36. The properties of asynchronous delta sigma modulation (ADSM) are discussed, and its performance compared with that of FM and pulse width modulation (PWM). ADSM is a modulation method whereby the information in an analog or binary input waveform is contained in an analog form in the transitions of a binary transmitted signal. The advantages of ADSM are discussed. None of the circuits discussed involve a clock.

Now kindly revert the article to the state it was before you made so many changes.Puffingbilly (talk) 15:11, 19 February 2019 (UTC)

Your theories about what our rules are are without merit and bear zero resemlence to our actual rules. Your repeated demands telling other editors what to do are denied with prejudice. And you sure seem to post a lot for someone who said "farewell". --Guy Macon (talk) 22:28, 20 February 2019 (UTC)