Talk:Decibel/Archive 8

Non-negative and non-complex input
I think some words are necessary about the assumption of non-negative and non-complex input. Unless one disputes decibels being real-valued? For power quantities this follows from the definition of power. But for root-power quantities, the modulus operation must be involved, either inside the decibel formula or outside, in the presumed input preparation. Otherwise, the equivalence between power and root-power decibel formulations doesn't hold mathematically: 10*log10(F^2)=20*log10(|F|)<>20*log10(F). I suspect this was part of the motivation for ISO 80000 introducing the "root-power" terminology, F=sqrt(√(FF^*)), i.e., by implying that a square root must be invoked after taking the squared norm absolute square. fgnievinski (talk) 02:30, 17 May 2020 (UTC)
 * While not disagreeing, I think we would need a source to back up such a statement. Do you have one? Dondervogel 2 (talk) 05:57, 17 May 2020 (UTC)
 * I agree with you both. It's important that the "input" be nonnegative real, but if it goes unsaid in sources it might as well go unsaid here. Dicklyon (talk) 06:57, 17 May 2020 (UTC)
 * According to IEC 60027-3:2002 "Complex levels are not customary. Therefore, levels are generally given in decibels." It's not exactly what we're looking for, but it hints at it. Dondervogel 2 (talk) 10:47, 17 May 2020 (UTC)
 * Here are some sources:
 * "The use of |V|^2 instead of just V^2 allows for the possibility that the voltage V is complex. Note that converting from decibels back to the linear scale can recover only the magnitude of V. The phase of a complex voltage is lost in the conversion to decibels, as is the sign of a real-valued voltage."
 * "Note that although {x\tilde}_n is non-negative by construction, we here emphasize that the expression for converting from linear scale to decibel is only valid for positive values, so when this expression is used on signals, such as x_n, their absolute value, |x_n|, should be used".
 * "Voltages must first be squared to convert to power; that is, 10*log(V_2/V_1)^2 or, equivalently, 20*log(V_2/V_1)"
 * "Recall that an amplitude is always non-negative. (...) Let a denote the amplitude for a signal (peak or RMS). Then this amplitude's decibel (dB) level d is defined as d=20*log_10(a/a_0)"
 * "Representing the squared signal amplitude by |c_k|^2 for a single Fourier series component, which would have units of squared normalized voltage in the case of a signal from a microphone, the decibel value of this amplitude is calculated relative to the reference level p_ref^2 using the following definition: A_dB=10*log_10(|c_k|^2/p_ref^2)."
 * In all cases, the input to the decibel formula is either implied or explicitly converted to the real domain. fgnievinski (talk) 20:56, 17 May 2020 (UTC)
 * The issue of complex valued input is specially common when decibels are used for visualizing the power spectral density given the output of FTT, even when the original signal is real. fgnievinski (talk) 21:08, 17 May 2020 (UTC)
 * Good sources. We should be able to say something that's well enough supported by those.  As for this coming up commonly in FFT output, I don't see that; people just take the magnitude or its square, without it being an "issue". Dicklyon (talk) 21:51, 17 May 2020 (UTC)
 * Thanks, glad to find some convergence of ideas. About the FFT, my point is that if one naively uses the complex FFT coefficients as input to a field-to-decibel formula, then the decibel is actually only the real part of the result. But I agree that the modulus is used more often to avoid that complication. fgnievinski (talk) 22:19, 17 May 2020 (UTC)


 * I'm not sure it would be naive to carry out the operation you suggest, as doing so would retain the phase information that would otherwise be lost. I do agree that between them these references provide the sources we need to support your original statement, or one similar to it. Such a shame none of them says it outright. Dondervogel 2 (talk) 06:18, 18 May 2020 (UTC)

Withdrawal of ISO 80000-3:2006 and its impact on the definition of "decibel"
ISO 80000-3:2006 used to define the decibel. However, this standard has been superseded by ISO 80000-3:2019, which does not define the decibel. In other words the ISO definition of the dB is no more. I added an explanation to this effect, but this leaves a bit of a vacuum that deserves filling. I'm sure there are lots of alternative definitions out there, but probably none with the consensus and authority implied by ISO 80000. Thoughts? Dondervogel 2 (talk) 05:48, 16 July 2020 (UTC)

Cryptic paragraph I tried to remove
I still say this is uninterpretable. I don't disagree that "Since the human ear is not equally sensitive to all sound frequencies, noise levels at maximum human sensitivity, somewhere between 2 and 4 kHz, are factored more heavily into some measurements using frequency weighting such as Psophometric weighting", aside from the abuse of the term "levels" therein. Yet this pretends to have something to do with decibels. And the added source seems broken. And while I'm a fan of Stevens's power law, I can't see how the see-also there makes any sense. What exactly is the intent of this paragraph? Can we turn it into something sensible, or shall I just delete it again as uninterpretable? Dicklyon (talk) 04:10, 21 August 2020 (UTC)
 * There is something wrong with the source. Give me a few minutes to troubleshoot it. Constant314 (talk) 04:13, 21 August 2020 (UTC)
 * I was just in the middle of an edit and somehow lost it all. Anyway, the source has been fixed.  I made a slight change to the wording.  Is it less uninterpretable?Constant314 (talk) 04:31, 21 August 2020 (UTC)
 * You made sentence fragments of it. And it's still unclear what the relevance is supposed to be.  The "annoyance" angle is weird.  Does the source mention decibels?  Certainly, frequency weighting is an important issue in noise measurement.  But this paragraph remains uninterpretable w.r.t. decibels. Dicklyon (talk) 05:06, 21 August 2020 (UTC)
 * The source does mention annoyance and it compares the readings using a c-message filter, in dB and shows a graph of weighting in dB vs frequency. Constant314 (talk) 05:13, 21 August 2020 (UTC)
 * I notice that the article already has "dBrnC" which is how measurements made with a c-message filter are usually stated. Also, the sentence fragments have been fixed. Constant314 (talk) 05:30, 21 August 2020 (UTC)
 * I'm not saying weightings don't exist, just that the role of those statements in relation to decibels is unclear. I'm fixing that a bit... In truth, though, the psophometric stuff is about electrical, not acoustic, noise.  Dicklyon (talk) 19:57, 21 August 2020 (UTC)
 * I don't know about the particulars of every way the psophometric weighting is used, but for c-message it is the electrical measurement of electrical noise that will be perceived as audio noise by the telephone subscriber. Constant314 (talk) 20:35, 21 August 2020 (UTC)
 * Right; it's a weighted noise voltage measurement; not ideal in a section on acoustics, where the reference is usually a pressure, not a voltage. Dicklyon (talk) 05:33, 22 August 2020 (UTC)
 * I agree with that this is confusing as currently written. It would fit better under audio or electrical engineering. Dondervogel 2 (talk) 08:16, 22 August 2020 (UTC)
 * If you want to take it out because it is too peripheral to the topic, I don't have a counter argument. But I don't see how it could be confusing.Constant314 (talk) 12:31, 22 August 2020 (UTC)
 * I'm not arguing for removing it. I just find it confusing under 'Acoustics' when it's about electricity, not sound. Why not start a new 'Use' entitled 'Audio-engineering', 'Telephony' or similar and put it there? Dondervogel 2 (talk) 13:21, 22 August 2020 (UTC)
 * I think telephony is appropriate. I made a stub for your consideration. Dondervogel 2 (talk) 13:25, 22 August 2020 (UTC)
 * Thanks for clarifying the cause of confusion. It is true that the source I added is talking about electrical measurements of the noise before it hits the telephone earpiece where it becomes auditable noise. I guess it is one step removed from acoustics.  However, frequency weighting is also used for direct acoustic measurements.  I do not have a ready source, but it easy to find advertisements for acoustic noise measuring sets that use A-weighting. Constant314 (talk) 20:47, 22 August 2020 (UTC)
 * Yes, that was part of the problem. I had added a source already for the acoustic A weighting.  The c-message weighting and electrical stuff should be moved to another place such as this telephony stub. Dicklyon (talk) 05:56, 23 August 2020 (UTC)

Sorted table
Previous discussion indicated that a sorted table might work well in. Here's a prototype. There are issues with this implementation so I'm not sure it is worth pursuing further. I do think we should continue to discuss ways to improve presentation of this list. ~Kvng (talk) 15:03, 31 October 2020 (UTC)
 * I agree something like this would improve the article, but my editing skills are not up to the challenge. Dondervogel 2 (talk) 23:05, 31 October 2020 (UTC)

Lead section has regressed
AFAIR, the lead section used to be relatively reader-friendly. Now it seems to have substantially deteriorated, not to mention the HORRIBLE layout whereby a large technical lookup table, that we don't anyway need to see at this point, forces the lead text into a tiny column. Not good. 2A00:23C8:7B08:6A00:6450:3519:2A88:94C2 (talk) 23:39, 6 November 2020 (UTC)
 * I moved the table down, and did a few copyedits that might help. Fix it better if you like. Dicklyon (talk) 00:21, 7 November 2020 (UTC)

Amplitude and power ...
... are related in a simple way for harmonic signals, but not in general. For this reason the wording "(usually equivalently)" is incorrect. Dondervogel 2 (talk) 07:31, 12 November 2020 (UTC)
 * I shall wait until a week has passed and then implement this change. Dondervogel 2 (talk) 08:16, 17 November 2020 (UTC)
 * Sorry, I missed your first ping. Please explain; I don't see how "harmonic" is relevant here (what it means, even). Dicklyon (talk) 17:08, 17 November 2020 (UTC)
 * I don't think it needs to be harmonic, but it does need to be a non-reactive (resistive) load. If current is proportional to voltage, then either squared is proportional power. Gah4 (talk) 20:52, 17 November 2020 (UTC)
 * It has to be a root-power quantity, but not necessarily a non-reactive load. E.g the voltage across a parallel RC circuit is OK, even though the proportionality of current to voltage is frequency dependent. Dicklyon (talk) 22:09, 17 November 2020 (UTC)
 * Hello. I would like to hear what exactly is meant by harmonic.  In one textbook I have, it just means the the time variation is sinusoidal. Constant314 (talk) 22:12, 17 November 2020 (UTC)
 * What I object to is the use of “usually equivalently” in “Two signals whose levels differ by one decibel have a power ratio of 101/10 … or (usually equivalently) an amplitude … ratio of 101/20”. It would be more accurate to say “usually inequivalently” but I am not suggesting that because I find it unhelpful. The wording I suggested was “sometimes equivalently”, the accuracy of which surely cannot be disputed, but my edit was reverted. I was using the word “harmonic” in the sense of a harmonic oscillator (Constant314 is correct), but let me spell out my concern more precisely.
 * First consider two harmonic signals, both of the form y = A sin(wt – p), where A is the amplitude, w is the angular frequency, t is time and p is the phase, and let postfixes 1 and 2 denote each of the two signals. Thus y1 = A1 sin(wt – p) and y2 = A2 sin(wt – p), where for simplicity I am assuming the two signals have the same frequency and phase, as any change in these do not affect my main point. Now imagine that y represents current, such that the power is 0.5 A2/r, where r is resistance. If r is the same in both cases we can write P1/P2 = A12/A22 and the statement I am objecting to is therefore correct for a harmonic signal if the resistance is unchanged.
 * Now consider a situation with some other form of current fluctuation. The two currents could be random noise but they could be anything (in real life, most fluctuations are not sinusoidal). One can measure the current fluctuations and from these compute the ratio of their powers P1/P2, but in general there is no amplitude here. One can address the absence of a clearly identifiable current amplitude by replacing it instead with a root-power quantity (R) proportional to the square-root of the power, such that R = constant * sqrt(P). In this situation the statement I am objecting to is incorrect (because there is no amplitude) but becomes correct if one replaces either "usually equivalent" with "sometimes equivalent" or “amplitude ratio” with “root-power ratio”.
 * Dondervogel 2 (talk) 09:28, 18 November 2020 (UTC)
 * Now consider a situation with some other form of current fluctuation. The two currents could be random noise but they could be anything (in real life, most fluctuations are not sinusoidal). One can measure the current fluctuations and from these compute the ratio of their powers P1/P2, but in general there is no amplitude here. One can address the absence of a clearly identifiable current amplitude by replacing it instead with a root-power quantity (R) proportional to the square-root of the power, such that R = constant * sqrt(P). In this situation the statement I am objecting to is incorrect (because there is no amplitude) but becomes correct if one replaces either "usually equivalent" with "sometimes equivalent" or “amplitude ratio” with “root-power ratio”.
 * Dondervogel 2 (talk) 09:28, 18 November 2020 (UTC)

dBSPL
As much as I love all the technical stuff in this article, probably 90% of the people who find this are just looking for information about "how loud is x vs y" sound pressure levels, which are often reported for point sources in "dB" without any distance or reference level specified.

It might be good to have a simple explainer in the introduction that the "dB" people have heard of is only one of many types, that it's short for "dBSPL", and that the measurements they've heard of are largely meaningless because they don't include distance. — Omegatron (talk) 22:37, 3 December 2020 (UTC)
 * I think you need a space in "dB SPL". Dicklyon (talk) 04:24, 4 December 2020 (UTC)
 * Maybe improve the hatnote to include a link to dB SPL or sound pressure level? ~Kvng (talk) 15:13, 7 December 2020 (UTC)
 * I have improved the hatnote. ~Kvng (talk) 19:56, 14 December 2020 (UTC)

Improper use of attachments to dB
I am afraid this is a misinterpretation. As a unit, there is one decibel only, equal to the ratio 101/10:1 for a power quantity and 101/20:1 for a root-power quantity. All the attachments belong to the quantity name, not to the quantity unit name, see ISO standards: "Any attachment to a unit symbol as a means of giving information about the special nature of the quantity or context of measurement under consideration is not permitted." . Particularly for dB, see .JOb (talk) 10:52, 24 December 2020 (UTC)
 * Can you suggest a way to improve the article? Dondervogel 2 (talk) 12:06, 24 December 2020 (UTC)
 * OK, but it will take quite a time. I shall prepare something. JOb (talk) 12:58, 24 December 2020 (UTC)
 * Just I modified 3rd paragraph of "Suffixes and reference values". Do you agree so? JOb (talk) 15:26, 24 December 2020 (UTC)
 * Apart from a minor edit I just made it looks fine to me. Dondervogel 2 (talk) 15:41, 24 December 2020 (UTC)
 * Fine. Btw, in shortest time, a new "ISO/IEC 80000-15:2021 Quantities and units. Part 15 - Logarithmic quantities" will occur. When it appears officially, I shall reflect it here. JOb (talk) 16:02, 27 December 2020 (UTC)

Power and amplitude ratios in lead
I think the lead may be too technical or confusing for some people. I have a very rough idea of these topics but let's look at it from a layperson's perspective, to which I'm closer than to that of a knowledgeable person. It says:
 * The decibel (symbol: dB) is a relative unit of measurement corresponding to one tenth of a bel (B). It is used to express the ratio of one value of a power or root-power quantity to another, on a logarithmic scale. A logarithmic quantity in decibels is called a level. Two signals whose levels differ by one decibel have a power ratio of 101/10 (approximately $1.259$) or (sometimes equivalently) an amplitude (field quantity) ratio of 10$1/undefined$ (approximately $1.122$).

I feel very strongly that many people will be totally confused by this little paragraph. If they wanna know things such as "what's the loudness difference from one decibel to another?" (I know perceived loudness is measured differently, but bear with me, since again, we're looking at it from a layperson's perspective). Unlike centimeters or inches, which many people can visualize, I don't think the bel is a familiar unit of measurement. I know experts will cringe at the suggestion, but maybe we could add some plainer explanation, with some visual analogies, somewhere in the lead? I would attempt to do it myself, but I don't know much about the topic beyond what one picks up producing and compressing music at home for fun. By the way, if you look up "power ratio" on Google the first result is from Investopedia (finance-related website) and the next seem to be references for engineers or physicists. --Paper wobbling sound (talk) 06:15, 13 March 2021 (UTC)

You are right (I agree to your position). Bel or db is not a "class" of it´s own. First "comes" a Ratio (r)of Power P, for example r = P2/P1. In many cases it may be of advantage, to say:  x = log P2/P1 where x is said to be x Bel or xB. Where is the trouble for nontechnicians? Here it is: Bel oder decibel (dB) is not a unit! You should not recognize  xB as a mathematical product like   x multiplied by B. B is not a factor like all (!) other Units. It`s an How To Do, nothing else. Edgar Wollenweber (Germany) --79.204.169.180 (talk) 17:42, 16 April 2021 (UTC)
 * I have made an incremental simplification reducing the amount of different technical terminology used in the opening paragraph. Readers don't really need to know what a bel is in the first paragraph. The key point to get across in the first paragraph is that it's a relative unit of measurement using a logarithmic scale. ~Kvng (talk) 15:05, 19 April 2021 (UTC)
 * I suppose so. It might be worth saying that "root" means "square root" in case people don't know that. It might be nice to say somewhere why everyone uses decibel instead of bel, when all the other log units use the log10 version.  (pH, optical density, for two). Gah4 (talk) 16:02, 19 April 2021 (UTC)
 * , I have imporved Power, root-power, and field quantities to explain where root comes from.
 * Why is it that other log units don't use 10log10? ~Kvng (talk) 14:08, 22 April 2021 (UTC)
 * Why would they? Dondervogel 2 (talk) 15:44, 22 April 2021 (UTC)
 * Why do it here? It is a little easier to work with whole numbers. Easier to pronounce, easier to think about. Optical absorption is commonly log10, but the filters used in color printing are numbered with two digits after the decimal point, and then forgetting the decimal point. That would be centibels if one wanted a unit for them. But they are commonly unitless. For pH, often enough whole steps are fine, but in real experiments often 0.1 steps. Gah4 (talk) 06:45, 23 April 2021 (UTC)
 * Why is it that other log units don't use 10log10? ~Kvng (talk) 14:08, 22 April 2021 (UTC)
 * Why would they? Dondervogel 2 (talk) 15:44, 22 April 2021 (UTC)
 * Why do it here? It is a little easier to work with whole numbers. Easier to pronounce, easier to think about. Optical absorption is commonly log10, but the filters used in color printing are numbered with two digits after the decimal point, and then forgetting the decimal point. That would be centibels if one wanted a unit for them. But they are commonly unitless. For pH, often enough whole steps are fine, but in real experiments often 0.1 steps. Gah4 (talk) 06:45, 23 April 2021 (UTC)
 * Why do it here? It is a little easier to work with whole numbers. Easier to pronounce, easier to think about. Optical absorption is commonly log10, but the filters used in color printing are numbered with two digits after the decimal point, and then forgetting the decimal point. That would be centibels if one wanted a unit for them. But they are commonly unitless. For pH, often enough whole steps are fine, but in real experiments often 0.1 steps. Gah4 (talk) 06:45, 23 April 2021 (UTC)

New page for logarithmic units
I believe that Wikipedia should feature a conversion table of units that express ratio. This is not only decibel, but also neper, decade, music intervals from semitone to octave and cents as well... Shall I make a new page and cross-link? --FDominec (talk) 08:40, 8 June 2021 (UTC)
 * We already have Logarithmic_scale. I suggest expanding that before creating a new page. Dondervogel 2 (talk) 08:56, 8 June 2021 (UTC)

Acoustics: intensity, pressure, or what?
The part about uses in acoustics is confusing. First it talks about pressures, for which a factor 20 must be used. Then it apparently mixes between pressures and intensities, and it's not clear what happens with the formulae (see italic):

"The human ear has a large dynamic range in sound reception. The ratio of the sound intensity that causes permanent damage during short exposure to that of the quietest sound that the ear can hear is equal to or greater than 1 trillion (1012).[39] Such large measurement ranges are conveniently expressed in logarithmic scale: the base-10 logarithm of 10^12 is 12, which is expressed as a sound pressure level of 120 dB re 20 μPa. "

However, 20 x log (10^12) = 20 x 12 = 240 ... I've corrected using only intensities for now, but I'm not sure how correct this is. Am I missing something? Can it be explained better and correctly? Kruiser (talk) 15:24, 14 December 2020 (UTC)


 * The statement is correct as quoted above, but I agree it's confusing (the 20*log10 is a red herring; better to think of SPL as being 10*log10(p^2/p_0^2) dB). One option might be to replace the sound pressure level of 120 dB re 1 uPa with a sound intensity level of 120 dB re 1 pW/m^2, but I'm not sure that really helps. The whole paragraph could do with a spring clean. Dondervogel 2 (talk) 15:42, 14 December 2020 (UTC)


 * You are probably seeing the word intensity being used differently between sound and electromagnetics. In E&M, intensity is a field quantity, such the magnetic field intensity, H or the electric field intensity, E.  The field quantities go as 120 x log10.  Power in E&M is represented by E X H; it goes as 10 x log10.  In sound, intensity is power.  It goes as 10 x log10. Constant314 (talk) 16:49, 14 December 2020 (UTC)


 * I'm not too confident with sound intensity, but I'm not really relating to electromagnetism or other fields. Is just that exchanging pressures and intensities is confusing for a reader, I believe. To answer Dondervogel 2, 10*log10(p^2/p_0^2) is exactly 20*log10(p/p_0), so I don't see how that helps. To me, the only explanation is that SPL is 10*log10(p/p_0) or 10*log10(I/I_0), which is the same for a constant velocity (I=pv). Kruiser (talk) 11:48, 16 December 2020 (UTC)
 * The equations for sound pressure level (SPL) and sound intensity level (SIL) are
 * SPL = 10*log10(p^2/p_0^2) dB
 * SIL = 10*log10(I/I_0) dB
 * Dondervogel 2 (talk) 13:03, 16 December 2020 (UTC)
 * @Dondervogel 2
 * I'll try to explain, why this formula is correct: dB SPL = 20*log10(p/p_0)
 * In Math, 20*log10(p/p_0) = 10*log10(p^2/p_0^2), but in the real world, the real sound pressure in Pascals will change for 1 000 000 times for 120 dB (for example), but Intensity will change 1 000 000 000 000 times with the same 120dB because Pressure is root-power quantity and Intensity is power quantity
 * These quantities are always confusing an I think it's better not use them in one sentence or even in one paragraph
 * English is not my native language so it's very difficult for me to explain math and physics. Hope you'll understand
 * Yes it's me who corrected trillion to million here
 * 37.214.77.175 (talk) 23:14, 4 December 2021 (UTC)
 * What you've written here is correct, but I don't understand how it relates to your proposed edits. Please suggest a change (here) and explain why you think it is an improvement. Dondervogel 2 (talk) 09:51, 5 December 2021 (UTC)

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Fourier transform or Fourier trnasform, and logarithms
There is a complication with Fourier transform that it works in linear space, but sometimes people want a spectrum in logarithmic space. As well as I know it, there is no easy trick to doing it, like there is with FFT. That is, no fast logarithmic transform. I don't know what means anything should go here, though, but it might be interesting to mention spectra with a logarithmic frequency axis. Gah4 (talk) 01:03, 10 February 2022 (UTC)
 * That's probably not really relevant for the decibel article, but you may want to check out the constant-Q transform, which sounds close to what you're talking about. Hqb (talk) 07:15, 10 February 2022 (UTC)
 * I think you are right, but I wanted it to get discussed to be sure. Gah4 (talk) 07:49, 10 February 2022 (UTC)
 * I think you are right, but I wanted it to get discussed to be sure. Gah4 (talk) 07:49, 10 February 2022 (UTC)
 * I think you are right, but I wanted it to get discussed to be sure. Gah4 (talk) 07:49, 10 February 2022 (UTC)