How Is RMS Measured?

[SouthSIDE Glen]

I'm a bit confused ,. only because peak metering is what gave digital a bad start. Sure , you could pegg the old VU meters and it was'nt a big deal. Not so with digital peak meters!

What gave digital - and FS peak metering - a bad start IMHO was the *assumption* that so many users made that 0 equals 0 regardless of the meter type and the lack of understanding of the conversion factors between VU, dBu and dBFS. It sure didn't/doesn't help that there is no standard conversion factor from analog to digital levels, either.

G.

 

[flatfinger]

What gave digital - and FS peak metering - a bad start IMHO was the *assumption* that so many users made that 0 equals 0 regardless of the meter type and the lack of understanding of the conversion factors between VU, dBu and dBFS. It sure didn't/doesn't help that there is no standard conversion factor from analog to digital levels, either.

G.

Gottcha the devil's in the details

 

[dgatwood]

Since AFAICT, nobody really answered the original question....

RMS:

Root
Mean
Square

This is the same thing as the quadratic mean. To calculate this correctly, take a period of audio (choose the period as desired) and do the following:

• Take every sample within the period and compute the square of the value.
• Add those squares together into a single total value---the sum of the squares.
• Divide that total by the number of samples. This is the mean (average) of the squares.
• Take the square root of the result to get the root of the mean of the squares.

It's that simple. The RMS value for a whole track just involves a very long period and a heck of a lot of summing.

Now if you mean for a meter, that's a little different. RMS metering is really a rolling average metering. That means that you choose a period---maybe 1 ms, for example---and perform an RMS calculation for that entire period and display the results. Every time you get a new sample, you update your mean to include the new sample and discard the oldest existing sample.

As a result of doing things this way, short highest peaks are reduced in magnitude, short troughs increased n magnitude, etc. The whole thing acts kind of like an amplifier with a horribly slow slew rate.

The key question is "What period should I use?" I have no good answer to that question.... The nice thing is that because you are squaring everything, all your values are positive, so you don't have to worry about any frequency being cancelled out entirely by a poor choice of periods. The question is how long a signal should have to be at a given level before you consider it to no longer be a transient that you want the filter to diminish. *shrugs*

 

[dgatwood]

What gave digital - and FS peak metering - a bad start IMHO was the *assumption* that so many users made that 0 equals 0 regardless of the meter type and the lack of understanding of the conversion factors between VU, dBu and dBFS. It sure didn't/doesn't help that there is no standard conversion factor from analog to digital levels, either.

Indeed. So much analog gear had many, many dB of headroom, while digital gear has zero (assuming dBFS). Years of engineers being taught "oh, it's okay if it peaks into the red every now and then" go out the window when peaking into the red means actual clipping. *sigh*

 

[noisedude]

Since AFAICT, nobody really answered the original question....

RMS:

Root
Mean
Square

This is the same thing as the quadratic mean. To calculate this correctly, take a period of audio (choose the period as desired) and do the following:

• Take every sample within the period and compute the square of the value.
• Add those squares together into a single total value---the sum of the squares.
• Divide that total by the number of samples. This is the mean (average) of the squares.
• Take the square root of the result to get the root of the mean of the squares.

It's that simple. The RMS value for a whole track just involves a very long period and a heck of a lot of summing.

Now if you mean for a meter, that's a little different. RMS metering is really a rolling average metering. That means that you choose a period---maybe 1 ms, for example---and perform an RMS calculation for that entire period and display the results. Every time you get a new sample, you update your mean to include the new sample and discard the oldest existing sample.

As a result of doing things this way, short highest peaks are reduced in magnitude, short troughs increased n magnitude, etc. The whole thing acts kind of like an amplifier with a horribly slow slew rate.

The key question is "What period should I use?" I have no good answer to that question.... The nice thing is that because you are squaring everything, all your values are positive, so you don't have to worry about any frequency being cancelled out entirely by a poor choice of periods. The question is how long a signal should have to be at a given level before you consider it to no longer be a transient that you want the filter to diminish. *shrugs*

That last paragraph is what the question was asking, and what we've been discussing. So if a meter is reading whatever as an RMS value, what is that an average of? Is it meaningful or is it taken over a wide range of samples and slow to respond? And an RMS value for the amplitude of a whole track? Is that really a value worth paying attention to?

Now, if I'd thought Glenn was asking how RMS values are calculated, I'd have leapt straight into my teaching narrative for explaining sinusoidal waveforms like ac mains supply. That begins by drawing a sine wave of voltage on the board and working the kids towards realising that the average is zero. Well, from P = IV we know that if we have 0V on average, then on average there's no power coming from this plug socket. Then you point out that if there's no power coming from and no voltage across this plug socket, it's actually totally safe to stick your fingers into.

I guarantee that if you do this absolutely deadpan and straight-faced, that some 18 year-old kid genius will quite happily volunteer to stick their fingers into the socket. And before you let them kill themselves, you point out the need for a more meaningful value for the effective current/voltage/power transfer, and they learn that our 230V power supply actually cycles through a range of 648V, which winds them up even more!!

Teaching physics is fun.

Anyway - back to making things LOUDER!

 

[pezking]

What gave digital - and FS peak metering - a bad start IMHO was the *assumption* that so many users made that 0 equals 0 regardless of the meter type and the lack of understanding of the conversion factors between VU, dBu and dBFS. It sure didn't/doesn't help that there is no standard conversion factor from analog to digital levels, either.

G.

This is part of the problem. The other part is that generally speaking those who used the traditional methods of metering, and analogue tape, had some kind of education and understanding of what they were doing. Whether it was taught (Electrical engineering comes to mind..) or knowledge learned on the job (apprentice for example) they understood the levels. In this day of Digital Audio, anyone can get hold of a DAW. They're available free of charge - therefore you get a lot of people who just don't understand the numbers and levels that are there (obviously not aimed at anybody here). The tools, and information is all there to use the metering and scales that are there, people just don't use it, and end up using the metering incorrectly.

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

No... PPM has been a standard for Peak Metering, used in broadcasting, and studios (mainly in Europe) for years (well before digital audio). It is a more useful way of metering than the VU. Peak metering is essential in digital audio. The VU meter doesn't respond fast enough to peaks, and therefore you might well not know that you're clipping your inputs.

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.

G.

If you need to make a set of recordings/masters which you want to keep to the same standard, you need meters. One reason why I put tone at a known reference level and frequency at the beginning of many recordings is so that I have some reference of the relative levels of the different recordings.

Back to the original question, specifying the length of time to take the average in samples would not make sense, as you'd get different results if you use different sample rates. I.e. the averaging window would be twice as long at 48kHz compared to 96kHz. Therefore it is most likely defined as a time, and then specified in various numbers of samples for the different rates. I'll do some investigating and see what I can find!

 

[suprstar]

The key question is "What period should I use?" I have no good answer to that question....

If I was designing a device to monitor real time rms, I'd try something like: Use the latest sample, and some kind of weighted average of the previous samples, so that the samples add less and less into the equation as they get older. Probably some kind of logarithmic decay, and you could mess with the constants til you got good results. Faster decay, the vu meters will bounce faster. Mess with the amplitude constant to make up for the decayed samples. etc..

 

[SouthSIDE Glen]

If I was designing a device to monitor real time rms, I'd try something like: Use the latest sample, and some kind of weighted average of the previous samples, so that the samples add less and less into the equation as they get older. Probably some kind of logarithmic decay, and you could mess with the constants til you got good results. Faster decay, the vu meters will bounce faster. Mess with the amplitude constant to make up for the decayed samples. etc..

Awww, now there you go making sense again.....

Actually, guys, take a look at the thread on "loudness war meter" from which this thread sprung. Head over to that website for that "DR meter" and find the link for the manual for the meter. it contains a quite detailed explanation of how they go about it.

Interestingly, for real-time they pull out a thousand samples from the previous three minutes of playback and perform the RMS averaging on those. It doesn't say whether those sample are evenly spaced or random; I assume they are probably fairly evenly spaced, which would mean that in a standard 44.1k file they are pulling out one out of every 132.3 samples over a three minute period.

For entire song calculations they use only the loudest 20% of samples. I'm still not sure I understand quite why they use this loudness weighting; it apparently has some phycho-acoustic basis, but I haven't wrapped my head around that just yet.

G.

 

[flatfinger]

No... PPM has been a standard for Peak Metering, used in broadcasting, and studios (mainly in Europe) for years (well before digital audio). It is a more useful way of metering than the VU. Peak metering is essential in digital audio.

I was'nt meaning the euro standardPPM .... I have that on my IXL meter and have tried it ... It's a good system , just can't get used to it myself ! ( if I had been using them all along though ; just familiarity factor)

I meant the simple digital full scale peak indicators that most DAW's have.

The VU meter doesn't respond fast enough to peaks, and therefore you might well not know that you're clipping your inputs.

The VU is allot better than simple peak metering to me . If you set your reference for zero VU to -14 Dbfs or even all the way down to -18 or 20 Dbfs and your recording in 24 bits , you can afford to peg the VU at +3 and still not clip. That's whats nice about 24bit .. lots of room to spare .


I just don't want the hassle of watching peaks when I'm tracking.



Cheers

 

[pezking]

The VU is allot better than simple peak metering to me . If you set your reference for zero VU to -14 Dbfs or even all the way down to -18 or 20 Dbfs and your recording in 24 bits , you can afford to peg the VU at +3 and still not clip. That's whats nice about 24bit .. lots of room to spare .

I just don't want the hassle of watching peaks when I'm tracking.

Cheers

I have to say I disagree with VU being "better" (obviously it's your opinion and that's cool). Horses for Courses. They obviously each have their place and their use, I just see PPM as a more useful meter in the Digital domain due to the ballistics.

As an aside, if anyone is using Pro Tools and wants a decent metering plugin (free) you can download this: SignalTools