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Dear John:

How are you doing? I hope you are still kicking with REW, one of the best acoustic measurement applications out there, and it keeps on getting better. I keep on using it and I keep on getting great results.

Two months ago I found out that your method of determining dBFS RMS for sine waves and pink noise is not according to the IEC standard 61606 and also AES standard AES17-1998. I found out that you are 3 dB off from the standards when I tried to compare line level and distortion measurements made in Spectrafoo with those made by REW, on the same computer, with the same interface, so the only variable was the software.

Let me explain: For over 75 years, precision analog equipment measuring in decibels has used a sine wave for its calibration. If the equipment is peak sensitive, then the peak level of an 0.775 volts RMS sine wave was used as the 0 dB reference, so 0 dBu measured with a peak meter read the same as 0 dBu measured with an RMS or averaging meter. This produced a convenient and common reference point for analog decibel meters switching between peak and RMS. It is the way that signal to noise measurements are specified (e.g. "the RMS noise floor is -82 dBFS compared to a maximum level that can be recorded in the PCM system of 0 dBFS).

So, audio professionals were already into this standard and had (have) no problem understanding and using it. It's been intuitive for me for years and years. But computer software designers who never worked in professional audio often went for the right triangle rule: "The RMS level of a sine wave is 0.707 times its peak, so it is 3 dB below the peak level so I'll set the RMS to be -3 dBFS when the peak is 0 dBFS". But the key to understanding the IEC and other professional approach is not to think that way. To understand that a decibel REFERENCE is just that, a reference. So IEC defines the decibel reference for both peak and RMS to be the same, 0 dB. It's also true for simple averaging. In other words, a sine wave whose peak level is, say, -10 dBFS will have an RMS level of -10 dBFS. BY DEFINITION. Once you work with this approach for a while you'll see how much more convenient it becomes to calculate signal to noise ratio when using RMS measure for both the sine wave reference and the noise reference. Otherwise you will be 3 dB off of every other professional meter.

The same principle applies to marrying VU meters and peak meters for analog and eventually digital audio. For example, a sine wave at -20 dBFS (as read on a standard peak reading digital meter) was applied to a VU meter and the meter (which is an averaging meter) was set to read 0 VU. From that point it was defined that the peak to average ratio of the system could be determined by comparing the level of the peak meter with program material versus the VU meter. The average level was said to be -20 dBFS.

The vast majority of professional measurement equipment adheres to this standard so you will be in the good company of Dorrough, Audio Precision, Stanford Research, Spectrafoo, and countless others. Professionals such as myself already expect the decibel reference levels to be calibrated in this manner.

The specifications for signal to noise and distortion for IC chips, ADC and DAC are also made using the IEC standard. If you were to measure a chip with the current version of REW, you would be 3 dB off, which is quite an error.

In summary, the standard says, according to Wikipedia:
http://en.wikipedia.org/wiki/DBFS

"Peak: For the case in which the RMS value of a full-scale sine wave is designated 0 dBFS, a full-scale square wave would have an RMS of +3 dBFS.[8][9] This is the definition specified in AES Standard AES17-1998[10] and IEC 61606 and used in Dorrough meters,[7] Analog Devices[11] and Wolfson[12] digital microphone specs, etc."

I once wanted to download the standard, but it is in six parts and each part costs a couple of hundred dollars! Ridiculous, if they want to promulgate a standard it should be affordable to the user.


I started looking at the places in your system which are affected by this error: The signal generator of course, when generating a sine wave or pink noise, differs from other standard generators by 3 dB. The maximum level that you can generate you've made to be -3 dBFS because you assume that above that the peak level would exceed full scale, but as you can see from Wiki, that is intentional and understandable. So when you generate a sine wave, its RMS level can go up to 0 dBFS. When you generate pink noise, its maximum peak level cannot of course exceed 0 dBFS peak, but its RMS will be measured by the IEC standard to be x number of dB below full scale where full scale is define as 0 dBFS RMS/0 dBFS peak with sine wave.

If you have a square wave generator, at full scale peak, its RMS level will read +3 dBFS if I'm not mistaken, and this is perfectly legitimate and conforms to the standard. Since the standard was defined with a sine wave and other waves have different crest factors. Another reason for the consistency of the IEC standard. It defines which waveform shape will have the same RMS and peak level in decibels (by definition).

When calibrating SPL with a sine wave calibrator that I have like the ACO pacific, the SPL is self correcting, you will be correct, and I assume your SPL meter is RMS reading. However, the warning message you give after SPL calibration, "caution, the highest SPL you can measure is xxxx " may be off by 3 dB if and when you recalibrate to the IEC standard. I'm not sure about that, you will have to tell me since you don't know what the waveform of the external signal is. I'm feeding a sine wave from a mike calibrator.

I hope you will give a good thought to this proposition. It would be nice to be standardized and compatible so readings can be compared. Sincerely, I believe that long-time precedent, international standards and audio engineer's approach all favor the IEC/AES standard. Only a few lone wolves working in isolation have come up with a non-standard generator.

Hope this helps.

Bob
 

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Bob, thank you for the extremely informative post and the industry and historical perspectives.

This has been an item of confusion for me at times, as it has surely been for others. It would be nice to get REW squared away in this regard.
 

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Discussion Starter · #5 ·
Some audio plugins allow the user to switch between the two modes. That might be one way to resolve the matter.
It might be more trouble for John to manage, but he could set a user preference to "RMS decibel scale", being "AES standard reference" or "RMS = sine wave peak minus 3 dB".

RME's interfaces have a choice of "RMS + 3 dB" or "RMS", which belies the fact that RMS in dB has been a standard longer than RME was around playing with right triangles :). Well, you can see my prejudice. Regardless, it would be good to get this straightened out because many users combine different gear to make their measurements and it would be good for them to agree on each other.
 

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Thanks for the post Bob. I'll admit to taking exception to your use of the word "error" here. REW's signal level representations are not in error. dB FS = dB relative to full scale. Full scale in a digital system is defined by the data range, and redefining full scale with respect to the rms level of a sine wave, whilst convenient, is an arbitrary choice and does offend the mathematician in me. The data path doesn't care what signals you pass through it and has a perfectly well defined scale by virtue of the values that it can pass. And for that matter, the ITU agree with me.

Anyhow, religious arguments aside I'm sure the good folk at the AES thought long and hard before picking their arbitrary redefinition of full scale and I'm not about to try forming a cult around the one true value of the rms level of a full scale sine wave, even if I am right :). So I'll see what I can do about providing an option to control this. And I might even default it to your and the AES' preference.
 

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Discussion Starter · #7 · (Edited)
Thanks for the post Bob. I'll admit to taking exception to your use of the word "error" here. REW's signal level representations are not in error. dB FS = dB relative to full scale. Full scale in a digital system is defined by the data range, and redefining full scale with respect to the rms level of a sine wave, whilst convenient, is an arbitrary choice and does offend the mathematician in me. The data path doesn't care what signals you pass through it and has a perfectly well defined scale by virtue of the values that it can pass. And for that matter, the ITU agree with me.

Anyhow, religious arguments aside I'm sure the good folk at the AES thought long and hard before picking their arbitrary redefinition of full scale and I'm not about to try forming a cult around the one true value of the rms level of a full scale sine wave, even if I am right :). So I'll see what I can do about providing an option to control this. And I might even default it to your and the AES' preference.
John, I appreciate your wondrous, endless mathematical skills as well as your ergonomic programming skills. Every time I visit the preferences in REW, I marvel at their thoroughness and how you have nailed every corner of every if statement! You are a unique individual, very few software analysis tools are as easy to use as REW or as thoroughly documented. Anyone visiting or using this application can tell it is a labor of love on the developer's part.

"Error" was a poor choice of words on my part! I just wanted to alert you to the areas which might be affected by changing the standard to the IEC measure. We all learned how to interpret sine waves in school. Actually, I take friendly umbrage to your claim that this choice is "arbitrary" because the AES and the IEC have decades years of precedent on their side. Remember that peak-reading audio meters did not appear until around the 1940's so the precedent started with the average and RMS reading meters. It turned out there was a good and practical reason for the choice: hundreds of models of audio level meters, both historical and current, which read both average and peak levels. The calibration practice of analog peak reading audio instruments has always been with sine waves originating at 0 dBu. In the analog domain with a sine wave that reads 0.775 volts RMS and 0 dBu and mostly averaging meters. The peak meter came later. The first quasi-peak reading analog meters were seen in Europe with the EBU and ITU-standard quasi-peak meter, and they were (and are) consistently calibrated to read 0 dB with a 0 dBu, 0.775 volts RMS sine wave.

It wasn't until digital recording came about that we had a meaningful numerical definition of peak level, full scale, + or - 32768 for 16 bit, that the tides could have turned the other way, that is, starting with a peak definition and then defining the RMS relative to that. Since there were no RMS-reading digital record level indicators in the first 20 years or so of digital recording. The digital peak level meter was then calibrated to read 0 dBFS with a numerical sample level value. One sample reaching that numerical value, either positive or negative going gave a peak indication of 0 dBFS.

Then, as soon as an RMS digital meter came along, most professionals who had spent any time in the analog audio world continued to calibrate the digital RMS meter to also read 0 dBFS when the peak meter read 0 dBFS and they used a sine wave to do so, in order to adjust their ADC and DAC gain. They measured the analog level in volts/dBu with an RMS or averaging meter. They then set their VU meters to read 0 VU with this sine wave attenuated by 14, 18, or 20 dB below full scale (there are historical reasons for each of those choices which I could explain some time). This enabled the ability to determine signal to noise ratio and peak to average ratio with a common dB reference.

The LUFS loudness measurement standard defined by ITU .1770-3 and the EBU's R-128 loudness standard are also based on this same definition of RMS. So you will be in good company if you change. :) That's the story from Lake Woebegone.
 

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...

"Error" was a poor choice of words on my part! I just wanted to alert you to the areas which might be affected by changing the standard to the IEC measure. We all learned how to interpret sine waves in school. Actually, I take friendly umbrage to your claim that this choice is "arbitrary" because the AES and the IEC have decades years of precedent on their side.



The LUFS loudness measurement standard defined by ITU .1770-3 and the EBU's R-128 loudness standard are also based on this same definition of RMS. So you will be in good company if you change. :) That's the story from Lake Woebegone.
I like this kind of information very interesting!!
 

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As an electrical and instrumentation engineer, I use RMS in its electrical sense in other areas than audio, and so I tend to agree with John here.

RMS is Root Mean Square; RMS(AES) is a result of an historical practice to make calibrating meters easier and is 3dB greater than "true" RMS. It is, however, widely used in audio and published (hidden) in the AES standard mentioned by Bob, and I think should be included in REW. It should in my opinion be annotated RMS(AES) in the preferences though, to clearly illustrate that the "audio calibration" is being used.

I feel it's a bit like Indiana trying to legislate PI to a fixed number of decimal places -Pi is still PI, whatever you "officially" try to make it, and RMS is still the Root Mean Square of the signal even if you choose to use an offset meter calibration and include it in a standard. It should be denoted as such.



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Discussion Starter · #10 ·
As an electrical and instrumentation engineer, I use RMS in its electrical sense in other areas than audio, and so I tend to agree with John here.

RMS is Root Mean Square; RMS(AES) is a result of an historical practice to make calibrating meters easier and is 3dB greater than "true" RMS. It is, however, widely used in audio and published (hidden) in the AES standard mentioned by Bob, and I think should be included in REW. It should in my opinion be annotated RMS(AES) in the preferences though, to clearly illustrate that the "audio calibration" is being used.

I feel it's a bit like Indiana trying to legislate PI to a fixed number of decimal places -Pi is still PI, whatever you "officially" try to make it, and RMS is still the Root Mean Square of the signal even if you choose to use an offset meter calibration and include it in a standard. It should be denoted as such.



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Just remember, decibels are relative and where you define your 0 dB is perfectly legitimate. If it makes audio easier, why complain?
 

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Just remember, decibels are relative and where you define your 0 dB is perfectly legitimate. If it makes audio easier, why complain?

Yes Bob, but RMS is also relative to the peak content. I'm not complaining really, I've been used to it in audio for years, but it irks me that it is stated as RMS when it isn't, it's an "alternative calibration" (if you will) of RMS.

I use RMS in level and power calculations in electrical engineering, and that is -3dB of a sinewave peak, Vp/√2. I then have to watch myself if I step over the audio divide if (eg) I'm monitoring power amplifier levels. I have to know whether I'm dealing with RMS(AES) when applying voltage gains or I get real-world voltages and power dissipations out by 70% :ponder:

It might sound a bit pedantic. I just wish it was labelled better, or at least differently ;)



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Yes Bob, but RMS is also relative to the peak content. I'm not complaining really, I've been used to it in audio for years, but it irks me that it is stated as RMS when it isn't, it's an "alternative calibration" (if you will) of RMS.

I use RMS in level and power calculations in electrical engineering, and that is -3dB of a sinewave peak, Vp/√2. I then have to watch myself if I step over the audio divide if (eg) I'm monitoring power amplifier levels. I have to know whether I'm dealing with RMS(AES) when applying voltage gains or I get real-world voltages and power dissipations out by 70% :ponder:

It might sound a bit pedantic. I just wish it was labelled better, or at least differently ;)



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I have had the same problem, basically end up doing "double metering" in my head a lot of the time to keep it all straight, or using metering that allows switching back and forth to help me keep it straight. It has been a tad bit less than friendly from my perspective.
 

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Discussion Starter · #13 ·
Fair enough, Planet nine. By the way, John, if you're reading, I noticed this week that the RMS level in the Mini DSP is calibrated according to the AES/IEC standard.... another party heard from :)


Bob




Yes Bob, but RMS is also relative to the peak content. I'm not complaining really, I've been used to it in audio for years, but it irks me that it is stated as RMS when it isn't, it's an "alternative calibration" (if you will) of RMS.

I use RMS in level and power calculations in electrical engineering, and that is -3dB of a sinewave peak, Vp/√2. I then have to watch myself if I step over the audio divide if (eg) I'm monitoring power amplifier levels. I have to know whether I'm dealing with RMS(AES) when applying voltage gains or I get real-world voltages and power dissipations out by 70% :ponder:

It might sound a bit pedantic. I just wish it was labelled better, or at least differently ;)



>
 

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V5.15 beta 12 has a View preference Full scale sine rms is 0 dBFS. The effect rippled through quite a few areas in the code (about 40 files) but I think I've caught them all, let me know if any of the "FS isn't what you thought it was" devotees spot anywhere it isn't handled per AES preferences. :)

Available in the usual place.
 
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