Talk:Root mean square

Formula changes
Can someone please check and verify the change I just made, and the change of another editor that I reverted? Dicklyon (talk) 15:39, 15 October 2011 (UTC)

RMS for modified square wave and rectangular wave
I add now a new section.

First, Dicklyon said he reverted my change. He didn't, he changed it to something else.

Second, I made a change in talk page, but didn't add a new section, sorry for that.

Third, I calculated the integrals. Did any of you?

So I would say that rectangular wave should be $$D a$$.

And modified square wave should be $$\frac{a}{2}$$.

There is no basis for any square roots in PWM case. Roots in sine waves come from sine^2 integrals. This can be seen quite clearly when simplifying and just calculating discrete sum with eg. 10 steps per cycle.

If you want to keep the page incorrect, fine with me. But as I already spent some time, I am not going to spend any more my time with arguing with you, thank you. — Preceding unsigned comment added by Sinihappo (talk • contribs) 19:58, 15 October 2011 (UTC)

P.S.

I checked how rectangular wave was added to the article. Well, it was added without any discussion. And it is clearly wrong. When I niw try do correct it, you try to revert it, but change it to someting else than originally, after I have made an addition to the discussion page.

Could you, Dicklyon, explain, why you feel that both versions are wrong? — Preceding unsigned comment added by Sinihappo (talk • contribs) 20:14, 15 October 2011 (UTC)

P.P.S.

Sorry for not adding signature. I am a little new with this. Sinihappo (talk) 20:33, 15 October 2011 (UTC)
 * Thanks very much for drawing the problem to our attention, and sorry, but stuff ups happen on Wikipedia as elsewhere. I saw your change (before Dicklyon's edits) and checked it (rather quickly, on quite a small piece of paper, so I'm not guaranteeing the results), and I believe your edit was precisely correct. It's rather unexpected that some equations that have been prominently in an article like this for some time are plainly wrong, so when we see changes like yours there is a tendency to be skeptical. I see that Dicklyon posted on your talk page after my welcome, and I don't have time now to think, so I won't change the article, but will invite Dicklyon to do the simple math which I thought confirmed the accuracy of . Johnuniq (talk) 07:41, 16 October 2011 (UTC)
 * Eerk, scratch what I said. My quick calculation must have blundered because after some thought it is clear that the article is correct. Next step would be to find a source that contradicts the article. Johnuniq (talk) 09:53, 16 October 2011 (UTC)

Sinihappo, if you look at the article's edit history, you'll see my revert of your edit, followed by what I believe is a correct correction of one formula that was wrong (I left the other as before your edit). The "modified square wave" has half the power of the square wave, and the duty cycle D wave has 1/D the power of the square wave, and the half and D need to be rooted to get the effect on the rms, yes? I did it without pencil, paper, sliderule, or matlab, so asked for someone to verify. A good source for these examples would be even better. Sinihappo, thanks for trying; your version would have been correct for the mean absolute voltage, but rms is a bit different. Dicklyon (talk) 18:46, 16 October 2011 (UTC)

Sorry, I was wrong all the time. And sorry for my arrogance, too. Sinihappo (talk) 06:42, 4 November 2011 (UTC)


 * Just to clarify here is the working for the "modified sinewave" case
 * Let T1=0 T2=1 and f=1 (integrating over a single cycle)
 * $$RMS = \sqrt{\frac{1}{1-0}\int\limits_{0}^{1}y^2\, dt}$$
 * $$RMS = \sqrt{\int\limits_{0}^{1}y^2\, dt}$$
 * $$RMS = \sqrt{\int\limits_{0}^{0.25}y^2\, dt+\int\limits_{0.25}^{0.5}y^2\, dt+\int\limits_{0.5}^{0.75}y^2\, dt+\int\limits_{0.75}^{1}y^2\, dt}$$
 * $$RMS = \sqrt{\int\limits_{0}^{0.25}0^2\, dt+\int\limits_{0.25}^{0.5}a^2\, dt+\int\limits_{0.5}^{0.75}0^2\, dt+\int\limits_{0.75}^{1}(-a)^2\, dt}$$
 * $$RMS = \sqrt{\int\limits_{0.25}^{0.5}a^2\, dt+\int\limits_{0.75}^{1}a^2\, dt}$$
 * $$RMS = \sqrt{[ta^2]_{0.25}^{0.5}+[ta^2]_{0.75}^1}$$
 * $$RMS = \sqrt{(0.5-0.25)a^2+(1-0.75)a^2}$$
 * $$RMS = \sqrt{(0.25)a^2+(0.25)a^2}$$
 * $$RMS = \sqrt{\frac{1}{2}a^2}$$
 * $$RMS = \frac{\sqrt{1}}{\sqrt{2}}\sqrt{a^2}$$
 * $$RMS = \frac{1}{\sqrt{2}}a$$
 * -- Plugwash (talk) 14:29, 4 November 2011 (UTC)
 * Thanks for verifying. Dicklyon (talk) 15:43, 4 November 2011 (UTC)

error in formula (section "RMS in frequency domain")?
there is something wrong with the last formula in this paragraph: if the n (for the freq. domain equations) is pushed below the square root, it has to become n squared [ or vice versa ...] Herbst (talk) 21:47, 18 October 2011 (UTC)


 * Good point. I fixed. Dicklyon (talk) 15:42, 4 November 2011 (UTC)
 * Except I fixed it wrong. Should be better now.  Dicklyon (talk) 04:40, 11 November 2011 (UTC)

Relationship to 2-norm
It is easy enough to see, but for a beginner this article obscures the fact that the rms is just the 2-norm divided by root n (for an n-dimensional vector space), and thus is also a norm on the vector space. Add it as another section? 18.63.6.219 (talk) 14:22, 6 June 2012 (UTC)


 * True, but a varying quantity is most typically not viewed as a point in an n-dimensional vector space (though a sample of it is often handled that way). Do you have a source that talks of that relationship?  Dicklyon (talk) 01:25, 14 June 2012 (UTC)

Why is RMS usually not discussed in textbooks on statistics?
Could anyone talk a little bit about why RMS is usually not discussed in textbooks on statistics? --Roland 23:35, 13 June 2012 (UTC)


 * Because the mean square is so much easier to use in the statistical context, and its square root is not so important. Dicklyon (talk) 01:22, 14 June 2012 (UTC)

Mention electrical power distribution
I think electrical power distribution/transmission should be mentioned for 2 reasons.

First, because rms voltage is the default way to indicate the line voltage in AC power distribution (ie 120V in the US is an rms value).

Second, the rms voltage between any 2 phases of an ideal 3-phase distribution system (ideal meaning perfect sine waves and phase separation of exactly 1/3 period) is equal to sqrt(3) * Vrms of one phase (phase-to-ground). The most common example I've seen is the term "120/208 V", indicating 120 Vrms phase-to-ground and 208 Vrms phase-to-phase. This term shows up in the power requirements for commercial/medical appliances and motors. This example is for the US. I think it would be appropriate for this article to explain what terms like "120/208 V" mean, as the values are directly related to the root mean square.

Unfortunately I don't have sources for this info (which is why I didn't edit the article directly), however I am an electrical engineer in the power distribution field and it is common knowledge. I think this article could benefit from this real world example of rms in action. — Preceding unsigned comment added by 74.92.43.41 (talk) 19:51, 13 March 2014 (UTC)

mean-subtracted RMS
It might be worthwhile to point out the common (but incorrect) usage of RMS to refer only to the fluctuating part of a signal. Examples:


 * I have a "True RMS" electrical multimeter from a well regarded signal test company, which discards the DC level in calculating RMS voltage. For example the meter reads 0 V rms for a battery, when the actual voltage is 1.3 V.
 * The software package Gwyddion, for analyzing scanning probe microscopy data, calculates rms after subtracting mean.

--Nanite (talk) 11:40, 3 November 2015 (UTC)


 * Do you have source to say that this is common? Dicklyon (talk) 20:17, 6 November 2016 (UTC)

Mean Square redirects to Mean Square Error
These are not the same thing; Mean Square is something used by Mean Square Error, in much the same way Mean Square is used by Root Mean Square. There needs to be an article that explains what the Mean Square is. — Preceding unsigned comment added by 130.195.253.13 (talk) 00:42, 7 November 2016 (UTC)
 * Good idea from over 3 years ago. I just stubbed in an article at Mean square.  It could use work.  The definitions of these things vary across fields, and even within statistics to some extent.  There is a lot that could be said to make this into a useful article. Dicklyon (talk) 00:32, 6 January 2020 (UTC)

root-mean-square speed
"The generally accepted terminology for speed as compared to velocity is that the former is the scalar magnitude of the latter. Therefore, although the average speed is between zero and the RMS speed, the average velocity for a stationary gas is zero." These statements seem to be verbosely and vaguely saying: (1) "In physics, speed is defined as the scalar magnitude of velocity" - maybe that is useful here? (2) "For a stationary gas, the average speed of its molecules can be in the order of thousands of km/hr, even though the average velocity of its molecules is zero".

Also, could someone explain to me (or in wikipedia) why r-m-s is so often used in physics, in preference to mean, and what the conceptual and numerical differences are. Perhaps it is because, in physics, fundamental formulae often involve the use of squared values (such as Kinetic Energy). JohnjPerth (talk) 02:54, 6 January 2021 (UTC)JohnjPerth

In the "error" section
"The mean of the pairwise differences does not measure the variability of the difference, and the variability as indicated by the standard deviation is around the mean instead of 0. Therefore, the RMS of the differences is a meaningful measure of the error."

These statements seem to imply that RMS of differences is a meaningful measure BECAUSE some other measures are not. This does not seem to be valid logic.

A better commentary on measures of variability might be...

"Due to the effect of negative differences, the mean of the pairwise differences does not measure the variability of the difference. I would probably omit this trite observation - many other measures could also be listed as not useful

The mean of the absolute values of the pairwise differences could be a useful measure of the variability of the differences. However, the RMS of the differences is usually the prefered measure, probably due to mathematical convention and compatability with other formulae."

BTW: RMS seems to be always greater than or equal to the mean-of-absolute-values and is therefore often an exagerated measure of pairwise differences. My comment on why it is preferred could be expanded. JohnjPerth (talk) 04:32, 6 January 2021 (UTC)JohnjPerth


 * Make it so. Dicklyon (talk) 05:47, 6 January 2021 (UTC)

Thank you for those changes to 'speed'and 'error'. Please excuse my titivating your words in 'error'. JohnjPerth (talk) 22:56, 16 April 2021 (UTC)JohnjPerth

Grainy
The media is grainy, I think is about the establishment, for fine, I study (...) "root mean square", under means and root, square, all quadratic is area-averaging, so there are means, averages, ..., square.

So, when I put in (... for generalized distributions) then to do that freely is providing the rest of what exists.

The, ..., "graininess", then, is where essentially imaging is, ..., grainy, as that it gathers, ..., for grain, as for fine.

So, this way in terms, of, "root mean, square", is usual root mean square. 75.172.96.27 (talk) 08:45, 8 September 2022 (UTC)