How Is RMS Measured?

[SouthSIDE Glen]

Flatfinger's thread on the "loudness war meter" resurrected a question in my head I have had for a long time, and for which I have yet to find a consensus answer. I didn't want to hijack that thread with this question, hence this thread ...

I know that RMS is a measurement of "average" (actually root-mean-square) energy output over time, but I have not (yet) found a standard for just how much time or how many samples this average is measured. Is there a standard? For example, when someone like Roger Nichols or Pleasurize Music puts out a real-time (dynamicly-reading) RMS meter, over how many samples is that real-time measurement taken? Also, are those look-ahead samples or elapsed samples?

And, at the extreme, is there a standard for RMS measurement of a full track? When one uses something like Sound Forge's tools to get the "RMS" of a whole track (which is kind of a useless measurement, but one we all seem to like using when this subject comes up), is it just an average of all fifteen million or so samples, an average of discreet sequential RMS measurements, a measurement of the peak RMS level within the song, or something else? Is there any such standard?

G.

 

[NL5]

I only have time for the short answer.

Audio is made up of sine waves. They "peak" power of the wave doesn't represent the average output of the wave. It a function of trig that gets you the RMS. If you have a pure sinusoidal wave of constant frequency and amplitude, with a peak of 1 volt, the RMS would be .707v. It gets a lot more complicated for audio waves, as they have to take frequent samples, sum them together, and then divide by the number of samples to figure the average output.

 

[SouthSIDE Glen]

It gets a lot more complicated for audio waves, as they have to take frequent samples, sum them together, and then divide by the number of samples to figure the average output.

That's exactly where my question lies; the length of time/number of samples over which the average is taken.

G.

 

[flatfinger]

Glen ,
most of the definitions I've seen are using analog methods (.775 X BLAH BLAH) and don't mention samples but a time period ( I know, the same really , just a conversion).

You might want to look up AES-17 as it is the latest attempt at standardizing.

I know that the algorythmix's crest meter mentios in the manual that a peak sine wave and rms are the same ; there used to be 3 db difference.
WL6 allows you to use either method ......I think this is something else that yanks and the euros don't agree on .


Sorry I can't be of more help , but It's a mathmatical formula and I'm alergic to them!!! ( there are 3 kinds of people who can do math ........those that can and those that can't !)

 

[NL5]

I know that the algorythmix's crest meter mentios in the manual that a peak sine wave and rms are the same

This is impossible.

You can't have an RMS and Peak value the same when dealing with a waveform of any kind. It would have to be a highly regulated DC signal.

 

[noisedude]

I guess one way to find out would be to use a couple of different measures of rms, from different developers, and see if the numbers are the same.

It's an interesting question though, the real-time ones can't be instantaneous because 0.707 of the peak at any point in time isn't a reading worth having. Somewhere in the manual for such a plugin must surely be a clue as to how many samples backward or forward its reading is taken from.

 

[NL5]

I guess one way to find out would be to use a couple of different measures of rms, from different developers, and see if the numbers are the same.

It's an interesting question though, the real-time ones can't be instantaneous because 0.707 of the peak at any point in time isn't a reading worth having. Somewhere in the manual for such a plugin must surely be a clue as to how many samples backward or forward its reading is taken from.

Yeah, .707 only works for a pure sine wave. And is the RMS of that wave. It's not the value at any point (well, it is twice per wave in each direction), but the "average" power output.

As far as a standard, I can't find one.

 

[flatfinger]

Ok , here is what the dr manual says then...pg 13

The idea behind the DR meter is a simplified way of determining thickness and NOT psycho-acoustically perfect loudness measurment tool. The RMS value is corrected by +3db so that sine waves have the same peak value and RMS value. This is the case with most meters

I know that the +3db is related to AES-17 and that it is a switchable option on my IXL meters and in WL6 . I've never quite understood what's going on with this . With any luck ( and if I know SS) we'll get it sorted by the time this thread peters out !!




http://audiofile-engineering.com/support/helpdesk/index.php?pg=kb.page&id=66

 

[SouthSIDE Glen]

I guess one way to find out would be to use a couple of different measures of rms, from different developers, and see if the numbers are the same.

This is how I have decided which ones to "trust" in the past; there are a handful of of them from some of the more reputable that give identical or similar numbers. For example, Sonic Foundry/Sony's tools and Voxengo's Span FFT tool match pretty well, along with some others that I don't remember right offhand, and it's their numbers that I personally use for my "standard". They are also the ones that just seem to look the most right by sight (for whatever that's worth...which is probably not a lot.)

But there are some tools and meters from otherwise decent developers that seem to be doing something different because their numbers don't come out quite the same.

Somewhere in the manual for such a plugin must surely be a clue as to how many samples backward or forward its reading is taken from.

While I admit I haven't exactly hired an investigator full time to look into this, I have yet to find documentation that goes that deep into it. That DR meter claims to be open source, so they should have it available in the source code itself at least, with hopefully some supporting documentation. That would, unfortunately, only tell us what they are doing, not whether others are doing it the same way or not. Though if it agreed with Sonic Foundry's numbers, that'd be good enough for me (for now ).

I know that the +3db is related to AES-17 and that it is a switchable option on my IXL meters and in WL6 . I've never quite understood what's going on with this.

I'm not a PT guy, but don't I remember reading around here some time ago that there's a similar situation with PT? Something about it using a square wave RMS reference instead of a sine wave reference or something like that, which was the cause of the 3dB difference.

With any luck ( and if I know SS)

Hey, I ASKED the question this time, guys. It's up to your guys to get to the bottom of this one for me .

G.

 

[flatfinger]

You're right , sombody else needs to step up to the plate occasionally !! I tried getting the AES-17 .pdf , but they want $$$ for it ....... I think I got it a while back before they started charging non members . I need to look at some of my backed up files , I know I did some research on this previously .

 

[flatfinger]

Ok ,
I hope you will forgive me if I'm not real concise because I'm no expert , but I'm willing to do some resarch and try and learn something new here.

I google "AES-17 rms meters" and got out my second edition of B.Katz book since I got a lot of hits that mention his "K" system proposal.

THis first one , the Sonoris Meter, http://www.sonoris.nl/catalog/meter-p-34.html

I have a few vst meters that don't agree with each others rms measurment , sometimes it's the aformentioned 3db difference. what this indicates to me is that this is not a simple buisness and that there is no de-facto standard. first there is the weighing system, which one does your meter use , ? ( none ?) is it selectable ?? then ballistics , here is from the site(sonorus meter....

"RMS. This is the standard non-weighted implementation of RMS. Regardless of the samplerate, the bandwidth is 20 Hz to 20KHz (-0.1dB). The RMS calculation window is 1024 samples and metering ballistics are 600 msec. attack and release, as defined in the K-System specification. The 0dBr level is calibrated with –20dBFS pink noise.

Leq(A). This is the first implementation of a K-System meter with Leq. The definition of Leq is: "The level of a constant sound, which in a given time period has the same energy as a time-varying sound". Leq is also used in loudness meters for measuring aircraft noise or industrial noise over a long period. In the Katz proposal the Leq is measured over a 3 sec. interval. This is implemented in the plugin. The (A) stands for A-weighting filter. This filter approximates the loudness sensitivity of the human ear. In practice, you see a nice and rather slow meter, that translates the loudness very well"

The K specification also specifies that there should be a averaging section ( a line not a bar ) that represents the highest level in the last 10 seconds .

So the LEQ is a psychoacoustic "method" and the A is the weighing system.

This looks like a good meter , but I demoed a while back and for $95 the graphics are a bit dull.

Note : the DR meter manual noted that software meters which get hosted in a DAW are a compromise because the programmers give first priority ( as they should ) to audio calculations. SO , software meters can be sluggish as far as screen refreshes , sometimes your compressor's gain reduction meter is indicating reduction that it did a few milliseconds ago ...... trust your ears first .


Like I stated before , the is no standarization!!

 

[flatfinger]

I took a look at my IXL manual , and , for the rms meters , you can configure the length of time in seconds over which rms data is averaged . Not unlike FFT real time analysers , which use FFT , shorter blocks result in a better temporal response which is better for fast transients , but not as accurate for low frequency signals. If you want more accurate information as to the amplitude of your lower frequencies, a bigger block size wil give it to you: but in exchange you get sluggish behavior from the meter in the temporal domain.

I find this pretty interesting in that the default settings are for a short sample size which gives you a nice snappy display that : is'nt giving you as accurate information as it could about lower frequencies where all the energy is at !!!


I'm starting to want analog metering!!!!!!

 

[flatfinger]

Is there a standard?

After about 45 minutes of research , I'd have to say Hell NO!!!!!

 

[flatfinger]

http://www.digido.com/faq/26-Z/110.html

Hello, Jim...
It is a standard, as set forth (I believe) in AES-17.
Sound Forge is not following the rules of the standard AES-17 as set down and they are in error from the official standard by 3 dB. A couple of manufacturers have made this serious mistake. Basically the rule is as follows: The 0 dB reference for either peak OR RMS measurement is that of a sinewave at full scale. Or, to put it another way, if you wish to work with RMS measurements, the 0 dB reference for that is that of a sinewave whose peak value is full scale.
That's the way the rule works! Even if it doesn't seem logical to you; just think of it as a reference, and that it is IRRELEVANT that the RMS value of a sine wave happens to be 3 dB below its peak level. So what... you can (and the AES standard does) define your reference as 0db

It's just a matter of definition.

True rms will give a RMS value that is -3.01 dB of the peak amplitude
for a sine wave.

AES17 specifies that the RMS should be equal to the peak amplitude
for a sine wave (so RMS is 3.01 dB higher for AES17 than for true RMS).

It's only relevant for interpretation of the meter values (and what you are used to...)

 

[flatfinger]

http://www.ak.tu-berlin.de/fileadmin/a0135/Unterrichtsmaterial/KT-Labor_WS0809/1_ADDA/aes17.pdf


FOUND IT !!!!!!!!!!

 

[SouthSIDE Glen]

I'm starting to want analog metering!!!!!!

I'm still wanting to drop this kind of metering altogether. Metering is good for setting gain structure and avoiding clipping, but just about all other measurements are meaningless, IMHO. We're supposed to be using our ears as our measurement devices. Frankly I could care less - except for thread conversations like this - whether my last mix had an RMS of -17dBFS or -14dBFS. It's like deciding which clothes to wear by measuring how many yards of material are used.

That said, though, flat, you have done a great job of chasing this topic down. You have been very instructional and helpful to me, and I greatly appreciate it

G.

 

[flatfinger]

OK , from here
http://www.tomshardware.com/forum/48188-6-calculation







http://www.tomshardware.com/forum/48188-6-calculation



NOTE Because the definition of full scale is based on a sine wave, it
will be possible with square-wave test signals to read as much as +
3,01 dB FS. Square-wave signals at this level are not recommended because tilt or overshoot introduced by any filtering operations will
cause clipping of the signal.



While this suggests that a 0 dB FS peak sine wave would correspond to a
0 dB RMS sine wave, it never explicitly states that, and I think it is
ambiguous. Cakewalk and UAD seem to take my point of view, since the
RMS meters in Sonar 4 ( OK I learned something about my sonar !)and the UAD Precision Limiter plugin display the
RMS level of a sine wave 3dB lower than they display the peak level.
And with those meters, there's no place to adjust the reference level.

If it is common practice that a 0dB peak = 0dB RMS for a sine wave, I
just wish that there were an explicit standard that states that. If
there is such a standard, could someone point me to it? SURE AES-17



Finally!

From Mr. Mike Rivers ( who knows his shit !)

There is only one full scale amplitude, and that's when all the bits
are turned on. This is 0 dBFS because it's no dB different from full
scale. It doesn't really matter whether it's a sine wave, square wave,
triangle, spike, or DC level that turns on all the bits, that's
0 dBFS. The fact that the RMS value of those various waveforms is
different doesn't matter to the A/D converter. It only looks at the
instantaneous voltage at the time it takes a sample. Given a frequency
below the Nyquist limit and a long enough time, eventually a sample
will be taken at the peak of the waveform. That's what counts.

The correlation with a standard VU meter, your "true RMS" voltmeter,
or a voltmeter calibrated for the RMS value of a sine wave is what's
not standard. But then that's why we use peak reading meters
calibrated with reference to full scale when we're looking at digital
levels.

Well there it is . why , when we went digital , we switched to peak metering instead of the good old VU , which was allot harder to implement ( especially without any standard or agreement to do so!!)

This is what the gist of what KATZ IS TRYING SO HARD TO . Get every body to stop wigging out on USING EVERY BIT!!!!!!!!!!!!!! ( heh , thats in my smart alikey avatar !!!!



OK , Glenn
There is your answer!!!!!!!!!!!!!

 

[flatfinger]

I'm still wanting to drop this kind of metering altogether. Metering is good for setting gain structure and avoiding clipping, but just about all other measurements are meaningless, IMHO. We're supposed to be using our ears as our measurement devices. Frankly I could care less - except for thread conversations like this - whether my last mix had an RMS of -17dBFS or -14dBFS. It's like deciding which clothes to wear by measuring how many yards of material are used.

That said, though, flat, you have done a great job of chasing this topic down. You have been very instructional and helpful to me, and I greatly appreciate it

G.

I'm a bit confused ,(EDIT... OK get it .... just use yer damm ears sonny boy !!!!)

Peak metering is what gave digital a bad start and continues to haunt it.

Sure , you could pegg the old VU meters and it was'nt a big deal. Not so with digital peak meters! I use rms meters for most everything! ( still will even though I see the many flaws !!)

 

[SouthSIDE Glen]

OK , Glenn
There is your answer!!!!!!!!!!!!!

OK, accuse me of premature post-ulation if you must, but check my lat post for my reply .

G.

 

[flatfinger]

That said, though, flat, you have done a great job of chasing this topic down. You have been very instructional and helpful to me, and I greatly appreciate it

G.

De Nada !!!!I've only repayed a small measure of my debt to you as I've learned so much reading your post and the great website . Thanks