Talk:Quantization (signal processing)

Several comments on page

I am not an expert with Wiki markup, so I do not plan to edit the page directly. However, I have some brief comments/opinions that may be of interest to the next person who decides to edit this page:

1. I think the basic description of "quantization" could use a little bit of tweaking. The current definition is: "quantization is the process of approximating a continuous range of values (or a very large set of possible discrete values) by a relatively-small set of discrete symbols or integer values." I believe that the definition could be made more precise: "quantization is the non-reversible process of approximating a value to one of a countable set of values." Then, specify that the original value can be from a continuous and uncountable domain, and can be multi-dimensional (i.e. vector vs. scalar quantization). The problem with the current definition is that the set that is mapped to by the quantizer does not necessarily have to be "small". In fact, the set being mapped to could have infinite cardinality. The only restriction that is placed on a quantizer is that the range of values being mapped must be countable.. i.e. mappable to the set of integers in some way.

2. I disagree with the floor in the scalar quantization function. It is not correct to say that scalar quantizers perform a floor.

3. Some examples will be useful for non-technical readers. I would recommend the classical "round to the nearest integer" example, as well as an example with non-uniform scalar quantization. The non-uniform quantizer doesn't have to be useful in practice, but it is to open the mind of many readers who might think a quantizer must always "round" in some regular fashion.

4. Demonstrate that quantization is non-reversible by stating a simple example: For the "rounding to the nearest integer quantizer", demonstrate that the quantizer would round 2.6, 2.8, 2.95, 3.3 all to the value of 3. But given (only) the quantized value of 3, there is no way of recovering what the original value was. This is an important issue for lossy compression.

5. There is an error within the image that has the caption of "3-bit resolution with eight levels.". You will notice that the upper-most two levels are both currently labelled with '110'. The correct label for the upper-most level should be '111'. — Preceding unsigned comment added by KorgBoy (talk • contribs) 21:28, 10 July 2014 (UTC)

—Preceding unsigned comment added by 70.187.205.90 (talk • contribs) 02:37, 30 January 2006

1/ The lead has been rewritten since these comments.

5/ The image was corrected at some point. ~Kvng (talk) 19:40, 20 February 2022 (UTC)

Page is Mature Enough?

I did my best to bring the premature page of Quantization(Signal Processing) to an acceptable state. Now it has all the necessary definitions and mathematical explanations. It still lacks alot though. For example : - good graphs for quantizer I/O maps ( I cannot add, since I am not a member) - graphs for companding functions - a few numerical examples - adaptive quantization details - further decoration of the topics - application examples

I might add as much in the future, NEVERTHELESS, this page is acceptable now. we may get rid of the banner on top. —Preceding unsigned comment added by 88.226.92.114 (talk) 19:49, 6 April 2011 (UTC)

Maybe there is a new banner, but right now it says the article needs additional citations, and I think that is true.Constant314 (talk) 22:25, 6 April 2011 (UTC)

This article has substantial problems. I am not even convinced that the edits over the last month or so have been improvements.

• The article says it is a summary of what is in some book (Introduction to Data Compression, K. Sayood, M.Kaufmann). That does not seem proper for Wikipedia and I don't think that is actually true, based on the edit history (although I don't have a copy of that book to be able to say for sure).
• It has a substantial number of grammatical and formatting problems and spelling errors.
• It should be about quantization in general, but it now seems to be exclusively about scalar quantization.
• It isn't quite correct in various places.
• It no longer even contains a definition of what quantization is.

—SudoMonas (talk) 17:03, 8 April 2011 (UTC)

So you mean according to your standards the previous stage was better, then I will revert back my edits.

=> I tried but it is too tiring to revert back, you should do it to the date "15 February 2011" that was the prior date I began my edits. —Preceding unsigned comment added by 88.224.91.218 (talk) 21:33, 8 April 2011 (UTC)

Looking back, I don't really think that the shortcomings that I see in the article are your fault, and you made your edits in good faith, so I will not revert them. I think the article wasn't very good back in February either. I guess I should stop complaining and just try to help contribute to make the article better. —SudoMonas (talk) 01:17, 9 April 2011 (UTC)

I like what you have done with the introduction.Constant314 (talk) 22:57, 9 April 2011 (UTC)

While you are at it, you may want to eliminate the use of first person plural in favor of third person. Example: "After defining these two performance metrics for the quantizer, we can express a typical Rate–Distortion formulation for a quantizer design problem in one of two ways: " could be rewritten as "After defining these two performance metrics for the quantizer, a typical Rate–Distortion formulation for a quantizer design problem can be expressed in one of two ways: "Constant314 (talk) 13:43, 12 April 2011 (UTC)

There are no longer any occurrences of "we" in the article. ~Kvng (talk) 19:40, 20 February 2022 (UTC)

Mid rise, Mid tread, mu-law, A-law

I cannot find a reference right now, but my recollection is the mu-law was mid rise and A-law was mid tread which means the slightest noise causes the mu-law device to toggle between two states while the A-law does not. Thus, a mu-law circuit transmits noise where an A-law would not. This got to be a marketing issue over who had the quietest network. Manfacturers started adding a half a bit bias to the mu-law encoders to get a circuit so quiet that "you could hear a pin drop". Anyway, you may want to work mid-rise, mid tread into the section on mu-law and A-law or maybe work the A-law, mu-law into the mid-rise, mid-tread section.Constant314 (talk) 16:14, 23 April 2011 (UTC)

mu-law and A-law are no longer discussed in the article. Perhaps this difference could be mentioned in in μ-law algorithm or A-law algorithm. ~Kvng (talk) 19:40, 20 February 2022 (UTC)

Clipping

BarrelProof asserts that Clipping (signal processing) needs to mentioned as a source of quantization. Hopefully he'll explain why here. ~KvnG 19:11, 3 December 2013 (UTC)

To be more precise, I assert that clipping should be mentioned as a source of quantization error, not as a source of quantization itself. The sentence in question concerns the sources of error in analog-to-digital conversion (in the lead section of the article). In practice, there can be several sources of error in practical analog-to-digital converters, including such sources as analog circuitry nonlinearity, analog noise, etc., but we can neglect most of those in an idealized model. The term "analog-to-digital conversion" generally refers to the application of uniform quantization with a finite number of levels (e.g., using a 10 bit or 12 bit a/d converter, thus having 1024 or 4096 distinct representable values). In such an operation, there are basically two sources of error – granular distortion and clipping distortion (where clipping distortion is also known as "overload distortion"). Both kinds of distortion are discussed in sections in the article, and I don't understand why neglecting one of them in the lead section would be desirable. See, for example, Quantization (signal processing)#Granular distortion and overload distortion. Clipping is something that definitely does occur in practice. If clipping distortion was not a concern, one could just amplify the gain at the input and thus drive the granular distortion to zero and there would be no distortion. Clipping/overload can be a major source of the error introduced by a quantizer. —BarrelProof (talk) 20:14, 3 December 2013 (UTC)

The statement we're discussing is, "The difference between the actual analog value and quantized digital value is called quantization error or quantization distortion. This error is either due to rounding, truncation or clipping." The section you link to talks about overload distortion being caused by clipping. I can go along with that. Your proposed edit makes the claim that clipping causes quantization error or quantization distortion. I can't go along with that. ~KvnG 21:11, 3 December 2013 (UTC)

Actually, that wasn't the exact wording, but I suppose that doesn't matter for purposes of this discussion. My definition of "quantization error" is that it is any error introduced by a quantizer – i.e., any error introduced by conversion of a continuous-domain input signal (or an uncountable input domain or a countable input domain with a larger set of countable values) to a countable output representation. Do you disagree with that definition? —BarrelProof (talk) 21:26, 3 December 2013 (UTC)

Sorry if I misquoted your proposal. I did include the link to the diffs for those who want to go to the horse's mouth.

I believe quantization error, distortion or noise refers only to the error between steps. Here are some refs which corroborate. None of these discuss an overload element and I didn't find any that did (I looked): [1], [2], [3], [4], [5], [6], [7], [8]

Do you have a citation for a definition which includes overload? ~KvnG 21:53, 3 December 2013 (UTC)

Here is a classic one that is already cited in the article: The paper by Joel Max, "Quantizing for Minimum Distortion" (1960). It says "The difference between input and output signals, assuming errorless transmission of the digits, is the quantization error. ... one has to use a quantizer which sorts the input into a finite number of ranges, N." He then computes the mean-square quantization error by performing an integration of the pdf over the full range of the input signal from minus infinity to infinity (just above equation 1), while keeping the number of reconstruction values N as a finite constant. Since N is constant and finite, the (infinite-extent) integration range includes the error introduced both by granularity and overload. Does that suffice?

To me, it seems rather self-evident that "quantization error" or "quantization distortion" should be interpreted as referring to (all of) the error/distortion introduced by quantization – which should include all sources of such error (both granularity and overload). While some authors may provide simplified presentations that neglect to discuss overload, and while there may not be any overload distortion in some applications (e.g., if the signal has a known finite input range and the quantizer gain is set to cover that entire range), when there is overload in the quantization operation, the error introduced by the overload is part of the quantization error/distortion. If you want to refer to only the granular element of the error, then the appropriate term is "granularity error", but the "quantization error" properly/generally should include all error induced by the quantization operation.

The sources that you cited seem to generally not even consider the topic of clipping/overload distortion. They seem to mostly be less scholarly, simplified discussions of the topic. Here's an alternative challenge: Can you find any sources that actually include a discussion of clipping/overload in any significant detail and do not include it within the scope of their definition of "quantization error" or "quantization distortion"?

—BarrelProof (talk) 22:17, 3 December 2013 (UTC)

I took a quick look at the sources at Clipping (signal processing) and Clipping (audio) and didn't find what you're looking for. I don't have access to the paper you cite above. Hopefully another editor will join the conversation and help get us unstuck. ~KvnG 23:19, 3 December 2013 (UTC)

The detailed scholarly survey paper "Quantization", by Gray and Neuhoff (1998), is the most extensively cited paper in the article (cited in eight <ref> tags). Its first paragraph defines "quantization error e = q(x) − x", where q(x) (which is defined in Equation #1) is the quantization function that maps input values to output representations. Figure #1 shows the input signal range of x covering from minus infinity to infinity. In the second paragraph they discuss the "granular region" of the quantizer and the "overload or saturation region" (italics in the source) and they say that this outer region is "where the quantizer error is unbounded". There is lots of further analysis of overload in the paper, but that much should be sufficient to make it very clear that their definition includes the distortion in the overload region as part of the quantization distortion (which is minimized in various ways by techniques described in the paper). When deriving the usual approximation $D=\Delta ^{2}/12$ for the mean-square quantization error associated with a uniform scalar quantizer with a step size of $\Delta$ (at the top of page 2344), they say that this approximation is for "when overload distortion can be ignored". —BarrelProof (talk) 00:29, 4 December 2013 (UTC)

I also just looked at another classic paper that's referenced in the article – "Quantization" by Gersho (1977). It is very similar to the other two in that regard. To save myself some time, I won't bother to quote exact text to prove that in detail, although it would be pretty easy. As one example, I refer to its Figure 4, which is a diagram of quantization error as a function of signal value. At the left and right extremes of the input signal range, it shows what is clearly clipping error effects. That paper also contains extensive discussion of granular error and overload error (and discussion of total quantization noise as being a combination of the two effects). —BarrelProof (talk) 01:47, 4 December 2013 (UTC)

There is a presentation of this at Quantization (signal processing)#Granular distortion and overload distortion. The question here is if and how this should be addressed in the lead. ~Kvng (talk) 19:40, 20 February 2022 (UTC)

Common correction methods

The page needs a list and references to methods for reduction of quantization noise. — Preceding unsigned comment added by 206.132.109.103 (talk) 13:39, 11 April 2018 (UTC)

Higher resolution is the way to reduce quantization noise. Dither makes it sound better and that's already mentioned in a couple of places. ~Kvng (talk) 19:40, 20 February 2022 (UTC)

First image misleading

The description of the image "Quantization error.png" implies that only quantization is shown, even though the signal is both sampled and quantized. Adding reconstruction to the mix furthers the confusion. I prefer the German wikipedia's image, but it's missing quantization noise. 141.23.221.10 (talk) 12:41, 23 November 2023 (UTC)

In the most common applications sampling, quantization and reconstruction are used together. If we plotted quantization error for the German Wikipedia's image (right) we'd get a nasty jagged thing which I don't think would help readers understand the issue as it exists in the context of reconstruction where it commonly occurs. The obvious fix is to improve the caption of the existing image but the caption is already long enough. It would be good if we could find a way to introduce the reader more gently but considering the case without sampling and reconstruction is probably a digression. ~Kvng (talk) 15:42, 26 November 2023 (UTC)

Fair point, i still think it's misleading how every picture in this article shows both quantization and sampling and it's not clarified prominently. 141.23.209.210 (talk) 11:59, 2 December 2023 (UTC)