Talk:Delta-sigma modulation

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

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)

Note for laymen[edit]

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 (talkcontribs) 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 (talk) 15:23, 12 July 2011 (UTC)

What's missing from this article (IMHO)[edit]

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)


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. (talk) 13:16, 11 January 2008 (UTC)


Hello, 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)


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 (talk) 08:45, 18 November 2010 (UTC)


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[edit]

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)

Merging Sigma Delta with Delta-Sigma Modulation[edit]

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.

comparison between sigma delta ADC and Succesive approximation ADC[edit]

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)

MASH Article[edit]

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. -- 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. -- 15:48, 12 April 2007 (UTC)
No problems. Done it. regards Katanzag 06:34, 13 April 2007 (UTC)

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

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})} [1].

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})}[2].

  1. ^ Derivation of in-band quantization noise variance for first order delta sigma modulator [1]
  2. ^ Derivation of in-band quantization noise variance for second order delta sigma modulator [2]


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)

Plagiarizing from Wikipedia[edit]

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. 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. (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. -- (talk) 03:09, 6 January 2008 (UTC)

Meaning of Delta[edit]

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? (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 Is and its strength by the product. The sum of the impulse and the input voltage Vin 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 Is 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, 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[edit]

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}( A b + A c )\,

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[edit]

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. Delta sigma dithering 1st order results.svg

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


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)


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)


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)

Usage in compression[edit]

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

1st Person Writing[edit]

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 (talkcontribs)  

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

Simplified summary?[edit]

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."

-- (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? -- (talk) 23:01, 14 February 2015 (UTC)

Improper use of questions for subsections[edit]

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)