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Author Topic: What is above Zero DB in a DAW?  (Read 6382 times)

Offline neil wilkes

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Re: What is above Zero DB in a DAW?
« Reply #15 on: September 27, 2005, 08:22:53 am »
Better still, mix to the K-system, then your internal -20 = 0 dBFS has a specific volume reference as well as a numerical one too.

Re 32 bit FP, this is what happens in the mix - once you go out past the master fader, it ain't FP any more unless you export out as FP. It becomes fixed.

Over 0dB digital FS = distortion, and nasty horrible digital scraping fingers down a blackboard type distortion too.
Nothing pleasant like tape saturation.
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Offline Gunnar Hellquist

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Re: What is above Zero DB in a DAW?
« Reply #16 on: September 27, 2005, 02:04:47 pm »
Lets go back to practical things here. There are four "domains" of things to consider.
1) input to the AD-converter
2) how things are processed inside the DAW
3) the special problems in some plugins
4) things output to the DA-converter.

1) and 4) obviously are the real world. In the real world a digital full scale is maximum. Period! Over that and you get nasty distortion. Full scale is coded as the value +1 (and -1 on the negative side of the wave form). Overload your AD you get distortion. Overload your DA you get distortion. This is your responsibility as engineer to set up the volume right.

2) the most common method to work inside the DAW today is using 32 bit float. This goes for ProTools LE and Cubase and Logic and Samplitude and just about every application.

In 32 bit float sound processing, (and please bear with me, I have to simplify things unless we want to do a lot of math), the value 1 is defined as 0dB. Exactly as what you would expect, as 0dB is just another way to write 1. In the same way 6dB is another way to write 2, so +6dB is 2. And -6dB is 0.5. And on it goes. The maximum value you can represent in float is just above 34 followed by 37 zeroes. This is about 770dB.

So essentially we can say that digital INSIDE THE DAW has a very large headroom. But read about 1) and 4) above, anytime you enter or leave the DAW there is probably a real world interface.

And now for number 3).
Some plugins (you have to test yours to see which) does not really like values above 1, sorry above 0dB. They can create all kinds of digital havoc if you feed them too strong signals. Obviously one way to handle this is to never go above 0dB. Another way is to test your plugins and how they react. Both are perfectly valid ways.

Hope this clears things up a bit. And if you know the math behind you will recognize my simplifications. If all you know is digital math, you still have a bit to learn.

Gunnar
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Offline Ronny

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Re: What is above Zero DB in a DAW?
« Reply #17 on: September 27, 2005, 04:32:45 pm »


Spot on Gunnar. Well written in a concise manner, that should be easy for anyone to understand.  
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Offline Fig

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Re: What is above Zero DB in a DAW?
« Reply #18 on: September 28, 2005, 11:12:53 am »
Thanks Gunnar, I like that description

Gunnar Hellquist wrote on Tue, 27 September 2005 13:04


If all you know is digital math, you still have a bit to learn.




Is that a floating point bit? Laughing


Warm analog regards,

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The easiest thing to do is the thing most easily forgotten.

Offline minister

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Re: What is above Zero DB in a DAW?
« Reply #19 on: September 28, 2005, 11:23:30 am »
excellent post, gunnar!
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Offline Shane Ervin

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Re: What is above Zero DB in a DAW?
« Reply #20 on: September 28, 2005, 02:32:31 pm »
Let me re-phrase the question, or rather, split it into three questions:

1)  What is the AES definition of the "0 dBFS" signal level?

2)  Does it make sense for an electrical engineer or sound technician to refer to signal levels ranked as > 0 dBFS i.a.w. the AES definition?

3)  Do all products and software adopt the AES standard for stating digital levels?

Answers:

1)  0 dBFS is the rms amplitude of a full scale SINUSOID whose positive going peak just reaches digital full scale.  The rms level of an arbitrary waveform may be compared to this reference level, in such a manner that rms levels lower than the reference are denoted with a minus (-) sign.

2)  Yes, it does make sense to speak of digital signal levels above 0 dBFS, since there are waveforms that have an rms-to-peak ratio larger than that of a sinusoid (i.e., a smaller crest factor).  Before I go further, bear this in mind: Stating a signal level is to compare its rms level to that of a reference.  The reference most audio guys find useful is a full scale sinusoid - not a full scale square.

The simplest example, then, is a full scale square.  It has more area under the curve than a sinusoid of equivalent peak amplitude.  Its RMS level is numerically higher than the sinusoidal reference level.  So a full scale square is ranked as +3 dBFS, in AES terms.

For instance, one can contemplate (or test with) a square wave at a level 1 dB below full scale.  That signal's level would be correctly stated as being +2 dBFS.  Notice there's still 1 dB of headroom left, and so there is no "digital clipping" involved in this scenario.

3)  Unfortunately... NO!  Take Sound Forge XP 4.5, or 5.0, for instance.  In those s/w releases, a full scale square is ranked as 0 dB when the STATISTICS command is invoked (after the user first selects an appropriate portion of the waveform).  A full scale sinusoid is ranked as -3 dB in those SF releases.

Where necessary, to clear up the potential for confusion when working with audio engineers more familiar with engineering standards than with pro-sumer audio products and s/w, I employ the unit: dB_STAT, clearly distinguishing the measurement from the preferred AES unit, the "dBFS".
________________
Other musings:
  • The owner's manual of a digital 2-track recorder will state the digital signal level (in the recording media) that corresponds to +4 dBu ( 0 VU to us old-timers) on the balanced XLR outputs (or inputs, when set to "CAL" or input potentiometer by-pass).
  • For the TASCAM DA-30 DAT and MD-801 R MiniDisc, that level is -16 dBFS.
  • No signal, (not even from a sum bus) can be made to have a higher rms level than a full scale square, so you know you're not talking AES's dBFS if a level is stated as +4 or higher.

Offline Ronny

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Re: What is above Zero DB in a DAW?
« Reply #21 on: September 28, 2005, 03:58:53 pm »
Shane Ervin wrote on Wed, 28 September 2005 14:32

Let me re-phrase the question, or rather, split it into three questions:

1)  What is the AES definition of the "0 dBFS" signal level?

2)  Does it make sense for an electrical engineer or sound technician to refer to signal levels ranked as > 0 dBFS i.a.w. the AES definition?

3)  Do all products and software adopt the AES standard for stating digital levels?

Answers:

1)  0 dBFS is the rms amplitude of a full scale SINUSOID whose positive going peak just reaches digital full scale.  The rms level of an arbitrary waveform may be compared to this reference level, in such a manner that rms levels lower than the reference are denoted with a minus (-) sign.

2)  Yes, it does make sense to speak of digital signal levels above 0 dBFS, since there are waveforms that have an rms-to-peak ratio larger than that of a sinusoid (i.e., a smaller crest factor).  Before I go further, bear this in mind: Stating a signal level is to compare its rms level to that of a reference.  The reference most audio guys find useful is a full scale sinusoid - not a full scale square.

The simplest example, then, is a full scale square.  It has more area under the curve than a sinusoid of equivalent peak amplitude.  Its RMS level is numerically higher than the sinusoidal reference level.  So a full scale square is ranked as +3 dBFS, in AES terms.

For instance, one can contemplate (or test with) a square wave at a level 1 dB below full scale.  That signal's level would be correctly stated as being +2 dBFS.  Notice there's still 1 dB of headroom left, and so there is no "digital clipping" involved in this scenario.

3)  Unfortunately... NO!  Take Sound Forge XP 4.5, or 5.0, for instance.  In those s/w releases, a full scale square is ranked as 0 dB when the STATISTICS command is invoked (after the user first selects an appropriate portion of the waveform).  A full scale sinusoid is ranked as -3 dB in those SF releases.

Where necessary, to clear up the potential for confusion when working with audio engineers more familiar with engineering standards than with pro-sumer audio products and s/w, I employ the unit: dB_STAT, clearly distinguishing the measurement from the preferred AES unit, the "dBFS".
________________
Other musings:
  • The owner's manual of a digital 2-track recorder will state the digital signal level (in the recording media) that corresponds to +4 dBu ( 0 VU to us old-timers) on the balanced XLR outputs (or inputs, when set to "CAL" or input potentiometer by-pass).
  • For the TASCAM DA-30 DAT and MD-801 R MiniDisc, that level is -16 dBFS.
  • No signal, (not even from a sum bus) can be made to have a higher rms level than a full scale square, so you know you're not talking AES's dBFS if a level is stated as +4 or higher.




The AES reference to dBFs pertains to the A/D and D/A conversions. You can have +4dBFs inside a floating point system and without clipping, as long as the signal is attenuated to at least -0dBFs at the DAC and as long as it doesn't exceed -0dBFs at the ADC. Typically when you see +4dB it's referenced to dBu, so that's correct, but between the ADC and DAC, postive values of dBFS are quite possible and used all of the time. If you are working in a 32 float system and you say +4dB, than I would understand it to mean +4dBFs as it's still frequency sample related. However that's a working level, you'd still have to attenuate at the master section to prevent the DACs from clipping. You really need to associate clipping at +0dBFs with the annie to digi and digi to annie conversions, but understand that in a float system that it's not only possible to work above -0dBFs, but quite common when mastering in the digital realm.  
------Ronny Morris - Digitak Mastering------
---------http://digitakmastering.com---------
----------Powered By Experience-------------
-------------Driven To Perfection---------------


Offline Paul Frindle

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Re: What is above Zero DB in a DAW?
« Reply #22 on: September 28, 2005, 09:21:35 pm »
Shane Ervin wrote on Wed, 28 September 2005 19:32

Let me re-phrase the question, or rather, split it into three questions:

1)  What is the AES definition of the "0 dBFS" signal level?

2)  Does it make sense for an electrical engineer or sound technician to refer to signal levels ranked as > 0 dBFS i.a.w. the AES definition?

3)  Do all products and software adopt the AES standard for stating digital levels?

Answers:

1)  0 dBFS is the rms amplitude of a full scale SINUSOID whose positive going peak just reaches digital full scale.  The rms level of an arbitrary waveform may be compared to this reference level, in such a manner that rms levels lower than the reference are denoted with a minus (-) sign.

2)  Yes, it does make sense to speak of digital signal levels above 0 dBFS, since there are waveforms that have an rms-to-peak ratio larger than that of a sinusoid (i.e., a smaller crest factor).  Before I go further, bear this in mind: Stating a signal level is to compare its rms level to that of a reference.  The reference most audio guys find useful is a full scale sinusoid - not a full scale square.

The simplest example, then, is a full scale square.  It has more area under the curve than a sinusoid of equivalent peak amplitude.  Its RMS level is numerically higher than the sinusoidal reference level.  So a full scale square is ranked as +3 dBFS, in AES terms.

For instance, one can contemplate (or test with) a square wave at a level 1 dB below full scale.  That signal's level would be correctly stated as being +2 dBFS.  Notice there's still 1 dB of headroom left, and so there is no "digital clipping" involved in this scenario.

3)  Unfortunately... NO!  Take Sound Forge XP 4.5, or 5.0, for instance.  In those s/w releases, a full scale square is ranked as 0 dB when the STATISTICS command is invoked (after the user first selects an appropriate portion of the waveform).  A full scale sinusoid is ranked as -3 dB in those SF releases.

Where necessary, to clear up the potential for confusion when working with audio engineers more familiar with engineering standards than with pro-sumer audio products and s/w, I employ the unit: dB_STAT, clearly distinguishing the measurement from the preferred AES unit, the "dBFS".
________________
Other musings:
  • The owner's manual of a digital 2-track recorder will state the digital signal level (in the recording media) that corresponds to +4 dBu ( 0 VU to us old-timers) on the balanced XLR outputs (or inputs, when set to "CAL" or input potentiometer by-pass).
  • For the TASCAM DA-30 DAT and MD-801 R MiniDisc, that level is -16 dBFS.
  • No signal, (not even from a sum bus) can be made to have a higher rms level than a full scale square, so you know you're not talking AES's dBFS if a level is stated as +4 or higher.



You are right - it's a minefield of confusion. But this confusion comes primarily from a misunderstanding of the difference between sample value (what most DAW meters read) and actual reconstructed signal this represents at the DAC output. Remember sample values are UNCODED PCM - not signal Smile

The AES relates to the biggest sine wave that can pass through the system analogue in to analogue out - that does not give rise to digital over-modulation in transit within the digital domain. In fact 0dBFS relates only to the sample values this creates - i.e. flat out max - and has nothing to do with RMS for any other wave shape than sine. So 0dBFS for a sinewave will give an output of -3dB wrt to the peak DC output that would be available for sample maximum.

A squarewave can produce 3dB higher RMS values for the same peak sample value - BUT a square signal cannot pass through the ADC filter without being modified - so the actual RMS value of the signal you would get out would REDUCE with freq. I.e. above 10KHz you would only get out a full level sinewave from full level square wave input (because all harmonics above the fundamental would be lost). So the RMS reference to a sinewave will still reliably give you only -3dB less than it seems possible to get out from the system under some circumstances of 0dBFS (e.g. DC).

If you create a hypothetical squarewave function within the processing (i.e. not input via an ADC) this is NOT a signal - it's only a pattern of samples. Such an illegal (0dBFS) signal could try to give an output that was +3dBFS from the DAC  - but the resulting signal would still not be square (above all but extreme LF freqs and DC) and would result in all sorts of trouble at higher freqs in the destination DAC. Because it's illegal the DAC could do all sorts of things, even crap out entirely. This is sometimes called intersample peaking and can result from gain increases and programme limiting etc.. even if the input WAS legal initially.

Ok now - is the RMS idea sensible at all as far as DAW metering is concerned? For instance it is possible to get signals that have very different crest factors and produce very low RMS values that would still produce full sample values - so an RMS meter would be no particular use to anyone.

What you need to know practically are 2 things;

- Am I clipping in the digital domain?
- Am I producing a signal that may not be decoded by the DAC.

To get this information you need 2 meters; one reading sample value (a conventional DAW meter) and another showing you reconstructed value (a special meter with filtering and reconstruction such as that in a DAC).

There was a long discussion about these effects in an earlier thread;

   http://recforums.prosoundweb.com/index.php/m/65289/2578/?SQ= 5bf2792b2cca9eb480b333279b1361ae#msg_65289

There's also stuff I wrote about this in;

   http://www.sonyoxford.co.uk/pub/plugins-sony/products/limite r-Tech_Detail.htm

OK now we get onto the sticky subject of headroom - which means the ability to get signals in the digital domain that are above 0dBFS which will recover if the gain is reduced downline.

IN a fixed point system generally headroom has to be artificially generated. This means losing some level to start with - putting the meter 0dBFS to read at this lower level - then bumping the signal back up again at the output.
We do this within plug-ins for instance that can generate internal signals that are greater then +/-1 and then reduce them naturally (like multiband EQs, dynamics etc).
But in fixed point systems the interfaces between processes may operate at normal (flat out) levels so signals above 0dBFS will get clipped and cannot be recovered. SO in this case say boosting something without reducing it again before the plug-in output will cause clipping even if the plug-itself didn't crap out internally.

For a floating system the situation is more complex. You can represent a number thats almost arbitarily bigger than the 0dBFS reference because the number system 'auto-rescales' - and mostly recover it again by reducing a levels downline (with only small accuracy error - not clipping).
BUT this doesn't mean you are totally safe from clipping. Some Plug-ins may still internally misbehave (particualrly if they have inherantly non-linear processes) - and if you are using a processing expansion system with fixed point math (i.e. 56K processors or such like) the interfaces to and from the external process may still clip at 0dBFS - because the external processing fixed point max is set to 0dBFS.

For instance in ProTools LE you can pass signals above 0dBFS between plugs cos it's native float - but you can't in PT TDM even if you use native RTAS plugs, because the interface back into the TDM mixer is fixed point.

Likewise if you use some host DAWs, signals above 0dBFS can pass and be legally reduced afterwards - providing all the processes are host as well (because the processing is native float). But if you use external expansion systems like PowerCore etc. processing run on this will be fixed point and signal will likely clip above 0dBFS and will not recover downline.

I hope this helps Smile


Offline Shane Ervin

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AES dBFS discussion
« Reply #23 on: September 29, 2005, 12:35:37 pm »
From Audio Precision's "Audio.tst" newsletter May 1994:
____________
To our knowledge, the unit "dBFS" (decibels with respect to digital full scale) was first used in System OneDual Domain.  This terminology and its exact definition was later standardized by the Audio Engineering Society as AES 17-1991 AES standard method for digital audio equipment - Measurement of digital audio equipment.

It specifies zero dBFS as the rms level of a sinewave signal calibrated so that peaks reach the positive full scale of the digital word.

The real-time meters and the graphs of all System One FFT-based programs are calibrated according to this definition.

This definition has some interesting attributes when:
  • non-sinusoidal signals are measured, or
  • when any digital signal is viewed in the time domain (oscilloscope mode).
If a squarewave is adjusted until its peaks just reach full scale of the digital word, the amplitude will be displayed as +3.01 dBFS.

At first thought, this may be confusing: "How can a signal exceed full scale in a digital system?"

In fact, a signal, including squarewave signals, of course cannot exceed full scale.  The apparent conflict lies in the fact that a squarewave has a crest factor of one; its peak and rms values are equal.  A sinewave has a crest factor of 3.01 dB.  All other typical signals (music, voice, IMD test signals, etc.) have still higher crest factors.

The AES definition is based on the RMS value, which is normally desired since it is power-related and independent of waveshape. A squarewave, and perhaps a heavily-clipped sinewave, are the only waveforms with crest factors less than a sinewave and which therefore can give rms readings greater than full scale.

Note that some competitive digital domain analyzers have not been designed and calibrated in accordance with the AES measurement standard and will display all digital domain signals with a -3.01 dB error.

Time domain (oscilloscope display) of a digital domain signal brings up essentially the same issue and potential confusion. The AES measurement standard does not address time domain displays .

System One Dual Domain FFT program graphs are calibrated so that 100%FS corresponds to the definition stated above.

On these graphs, a sinewave whose rms value is 0 dBFS (100 %FS) will have peak samples in the time domain which reach +3.01 dBFS, which is 141.4%FS.

This is a direct analogy to time domain display of an analog signal.  A one Volt rms sinewave has peaks which reach 1.414 Volts peak, as any oscilloscope will display.

The real-time amplitude meters at the top of the FFT-based program panels are peak-sensitive (rather than rms) meters and respond to both positive and negative peaks, whichever is larger.

These meters are furnished to help users avoid overloads, rather than to be used for quantitative measurements.  On these meters, 0 dBFS or 100 % FS indicate a signal whose positive and/or negative peaks are just touching full scale, regardless of waveform.

If both GENANLR and an FFT program could be simultaneously monitoring a digital signal whose peaks touch full scale:
  • They would both read 100 %FS (0 dBFS) if the signal is a sinewave.
  • The real-time meters would continue to read 100 %FS on all other full-scale waveforms.
  • The rms-responding meters would read less than 100 %FS on waveforms whose crest factor is greater than a sinewave and, as noted above, more than 100 %FS with a squarewave since its crest factor is 1.00.

________________ end of excerpt <<

Hope this helps.

Offline bobkatz

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Re: AES dBFS discussion
« Reply #24 on: October 01, 2005, 01:00:43 am »
I wish I had a copy of AES-17.


It states that regardless of whether you measure by average, peak, or RMS method, by definition, 0 dB is the value of any wave whose positive peak level is at the maximum digital word. If the wave is symmetrical, it follows this would be true for negative.

What does this definition mean? It means that a sinewave whose peak level is fulll digital scale is defined as 0 dB"fs". And its RMS value is also defined as 0 dBFS!

This approach to defining the dB reference is consistent with practices that go back to the 1940's so it is nothing new at all.

I once had a peak reading analog test meter made in Europe. 0 dB on its scale was defined as the point where a sine wave arrived whose RMS level is 0.775 volts. You calibrate the 0 dB point with a sine wave...

There is lots of precedent to using this approach. Dorrough meters. Sine wave calibrated to -14 dB on the meter reads the same level on the peak and RMS scales. This is ONLY true with the sine wave as that was the wave chosen for the calibration.

It seems to me the only companies that have not yet absorbed the AES-17 approach are software companies that never lived with analog gear for an point of time. To them, since the RMS value of a sine wave is .707 x its peak level, then they want to calibrate the RMS 3 dB down from its peak.

But this is equally arbitrary and has no precedent in any decibel voltmeter built by any analog manufacturer over the past 40-60 years.
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Offline Shane Ervin

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Re: AES dBFS discussion
« Reply #25 on: October 01, 2005, 02:08:26 pm »
Hi Bob!

Largely spot on, except for one fine point of detail that, were it not for the importance in fostering a good understanding of the subject (for readers other than you!), I would have let slip by.

Here, I'll get started, it's quick...

Quote:

What does this definition mean? It means that a sinewave whose peak level is full digital scale is defined as 0 dB"fs".


Careful here:  the "sinewave", per se, is not the object of the definition.  Rather, the "area under the curve of the squared waveform" (think: calculus integration) is defined as the reference area (aka: power quantity) that, when divided by the time base of integration, and having taken the square root, is what we, as an audio community, want to call the 0 dBFS "signal level", in rms terms.

Thinking in terms of evaluating the integral as the time base shrinks to a point is very helpful in rationalizing the apparently conflicting notion of a signal's "peak level" ... on an "RMS" scale.

In the limit, as the time base of integration shrinks to a single sample centred on a waveform's peak, evaluating the integral produces the peak value as you would expect.  For this reason, the peak value of a full scale sinusoid is +3 dBFS (... and not: 0 dBFS; that's the result when the time base of integration is over a half, or full, cycle - something the "RMS" definition requires).

Other musings:
______________

I'm with you on the notion that it's a sad thing that software developers who lack engineering experience and judgement can often pass off their work as "software engineering".  We in Canada are starting to do something about that.

No less a company than Microsoft itself has run afoul of the Association of Professional Engineers of two provinces (Quebec, and Newfoundland and Labrador).  In recent court cases stemming from MS's use of the term "Microsoft Certified Systems Engineer", it was held that, since these computer workers were not registered professional engineers, Microsoft had no right to use the legally reserved term: "engineer".  (Memorial University's CS dept. was somehow involved in the Newfie case, but I don't recall the details).  Anyway, chalk one up for the good guys.

Btw, Certain exceptions are permitted such as: "Recording Engineer" and "Sound Engineer", since these terms would not likely lead a lay person to believe that the label holder is a member of the professional association and therefore legally entitled to practice professional engineering in that jurisdiction.

Offline bobkatz

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Re: AES dBFS discussion
« Reply #26 on: October 02, 2005, 01:19:30 pm »
Shane Ervin wrote on Sat, 01 October 2005 14:08

Hi Bob!

Largely spot on, except for one fine point of detail that, were it not for the importance in fostering a good understanding of the subject (for readers other than you!), I would have let slip by.

Here, I'll get started, it's quick...

Quote:

What does this definition mean? It means that a sinewave whose peak level is full digital scale is defined as 0 dB"fs".


Careful here:  the "sinewave", per se, is not the object of the definition.  Rather, the "area under the curve of the squared waveform" (think: calculus integration) is defined as the reference area (aka: power quantity) that, when divided by the time base of integration, and having taken the square root, is what we, as an audio community, want to call the 0 dBFS "signal level", in rms terms.




Are you quoting the AES-17 spec? I believe that the sine wave is the basis of the entire spec. Sure, you can then use an RMS meter that integrates the area of a complex waveform, but ONLY after you calibrate this meter to a 0 dB based on a sine wave whose peak level is 0 dBFS.

Thanks for your comments on "engineers". I'd like to think that I have the equivalent knowledge after 35 years of "practical study", but I do not have a degree as an "engineer"! And I'm the first to admit it.

I wholely admire some of the Tonmeister curricula in Europe. Those thorough programs genuinely deserve to give their qualifying graduates the degree "Engineer/Producer". The students learn to read scores, interpret performances, and use and fix the equipment and much more. My equivalent education in instrumental music, combined with some college courses in electrical engineering (which was not my major, my major was communications), and the practical experience and study have given me the equivalent of this training----but no official degree to justify the title.

BK
There are two kinds of fools,
One says-this is old and therefore good.
The other says-this is new and therefore better."

No trees were killed in the sending of this message. However a large number of
electrons were terribly inconvenienced.

Offline Shane Ervin

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Re: AES dBFS discussion
« Reply #27 on: October 02, 2005, 02:22:06 pm »
Hi Bob,

(Edit) I'm quoting the letters "RMS" that are indeed the key part of the standard and this portion of the discussion thread (fixed point representation in signal blocks adjacent to ADC's and DAC's).

This is the particular aspect of the definition that I wanted to ensure folks got nicely "squared away" (sorry, I couldn't resist!), especially when the discussion touches on peak levels - something that doesn't naturally fit well with notions of rms level.

So, the comment on which I grabbed the fine paint brush to touch up was the quoted one, since it may have steered some newbies astray.

Referring to a sinewave is the most practical way to approach authoring a definition of a "reference signal level" (for audio engineering).  The AES, naturally enough, chose a sinusoid.  What I felt needed to be clearly understood by other readers was that, to say: "level" is to say: "rms", and, in turn, to say: "rms" is to contemplate taking the integral of the squared waveform over a half, or full, cycle.

 In the end, we're saying that in the digital domain, we're lucky to still enjoy the benefits derived from the important RMS notion of "equivalent heating effect" when comparing an arbitrary voltage waveform (a pressure quantity) to a DC level.

 The ear responds to the rms level of the pressure function, not peaks, making the AES definition of 0 dBFS sensible and useful for perceptual analyses.  An attempt to avoid clipping, on the part of the recording engineer, is a separate exercise that evokes a mindset quite distant from equivalent heating effect.

 The 0 dBFS signal level, then, is not solely associated with a sinusoid (even thought the standard refers to one).  Rather, lots of arbitrary waveforms could have the equivalent heating effect of a sinusoid of equivalent rms level - and it's the area under the curve of the squared waveform that becomes the important focus in such comparisons.

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Musings, cont'd...

In addition to obtaining a degree from an accredited institution, a candidate must spend 3 years after graduation working under the direct supervision of an experienced P.Eng., (plus take courses and pass exams on the subjects of law and ethics) prior to becoming eligible for receiving the title of "engineer".  This gives the public the ability to rely on the P.Eng.'s judgement on  matters of import to their client, employer, other professionals, and society as a whole, something that an independent training regimen is less certain to bestow.