Kuei Yang Wang said:
In other words, you were incapable of simply making your argument and leaving it at that, you had to make it personal and give a kick to the shins.
So when you were claiming that 16-bit digital audio could only have a maximum dynamic range of 90dB, you weren't in fact arguing because it's a documented and known fact that it's greater than 90dB and you were just illustrating a complete ignorance of the facts?
I don't recall your being as indignant and insulting to yourself on that matter as you're being to others on this one.
You mean like when people claim a maximum dynamic range of 90dB for 16-bit digital audio?
What's that they say about people who live in glass houses?
se
You can only have an argument about things that are not fully known. Anything that is documented and know is fact.
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Many engineering 'facts' are incorrect or wrongly interpreted. EEs are particularly susceptible to this, perahps because of the monodisciplinary nature of the subject . Other more 'multidisciplinary' engineers have to approach design as an art as well. I used to accredit engineering degrees and the emphasis on software and design on computer packages make it difficult for undergraduates to see into the physical nature of problems. This applies to all disciplines.
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Many engineering 'facts' are incorrect or wrongly interpreted. EEs are particularly susceptible to this, perahps because of the monodisciplinary nature of the subject . Other more 'multidisciplinary' engineers have to approach design as an art as well. I used to accredit engineering degrees and the emphasis on software and design on computer packages make it difficult for undergraduates to see into the physical nature of problems. This applies to all disciplines.
Koinichiwa Eddy San,
I do not remeber mentioning any names. If you decide what was meant general as "personal" - whom the cap fits....
Actually I was arguing that it only has 93db and we can if you like have the argument again. And I still consider this true and demonstrable. However, I lost any interest in this argument as you choose to simply apply one type of analysis to the problem and refused to aknowledge that the view I have taken is equally valid and more relevant to reality.
BTW, I'll go as far as noting that 16-Bit digital audio is limited to 87db realistic dynamic range excluding headroom and footroom and excluding other tricks such as noiseshaping and dither.
However, this argument is far from basic and involved the difference between a simple numerical calculation of 2^16 65536 = 96.33 db and scaling this under consideration of quantisation noise, the 1/2LSB uncertainty and RMS vs PEAK-PEAK. A fine but noteworthy distinction when comparing to analogue systems and their common measurements and as we noted earlier, a distinction lost on you.
Sayonara
Steve Eddy said:
I do not remeber mentioning any names. If you decide what was meant general as "personal" - whom the cap fits....
Steve Eddy said:
Actually I was arguing that it only has 93db and we can if you like have the argument again. And I still consider this true and demonstrable. However, I lost any interest in this argument as you choose to simply apply one type of analysis to the problem and refused to aknowledge that the view I have taken is equally valid and more relevant to reality.
BTW, I'll go as far as noting that 16-Bit digital audio is limited to 87db realistic dynamic range excluding headroom and footroom and excluding other tricks such as noiseshaping and dither.
However, this argument is far from basic and involved the difference between a simple numerical calculation of 2^16 65536 = 96.33 db and scaling this under consideration of quantisation noise, the 1/2LSB uncertainty and RMS vs PEAK-PEAK. A fine but noteworthy distinction when comparing to analogue systems and their common measurements and as we noted earlier, a distinction lost on you.
Sayonara
Kuei Yang Wang said:
Not mentioning a name does not mean it's not personal. When you went from making the argument about the subject at hand to denegrating certain PERSONS involved in the argument, you made it PERSONAL.
No, you claimed that it was 90.3dB. Or more precisely, 90.30899869919 dB.
Here's how you demonstrated it:
<i>I shall bother doing all the math here, because it seem that plenty of people have not done so before posting.
As said, 16 Bit are realy 15Bit plus "sign", that translates into a
system capable of representing 2^15 discrete levels.
2^15 equals 32768
20 * Log(32768) equals 90.30899869919 (db).
These are the ABSOLUTE limits of the CD Format. Below this (-90.3db) or above this (0db) there is no way to record any Information.
Some people have insisted that CD is capable of a Dynamic Range of more than the (erronous) 96db. This is pure Science Fiction.</i>
Please note that you say this is the "ABSOLUTE" limit of the 16-bit digital audio. Not a practical limit due to allowing a margin for such things as headroom in the recording process, etc. But the ABSOLUTE limit.
I can understand that. As tenacious as I can be at times, even I would tend to lose interest in an argument that flew in the face of that which has been proved beyond all doubt for decades.
se
Koinichiwa Eddy San,
Ah yes, this one, I thought you referrred to another one.... The one above is easily proven. This is from Stereophiles Website:
Fig.5 MSB Platinum Link Plus, waveform of undithered 1kHz sinewave at -90.31dBFS, 16-bit data
As can be seen -90.31dbfs just registers. There is nothing below this down to digital silence. As this is at 1KHz there would additional steps down to digital silence if anything below -90.31 dbfs.
Make the input signal just the tiniest bit lower and there is ONLY digital silence....
QED.
If you forgive me the sloppiness in my proof to drop the anything after the first digit after the decimal point, it is 90.3db as absolute limit.
As practical limit due to 1/2 LSB unceratinty it is in actuallity another 3db lower, hence 87db....
Of course, from a different angle the simple math of 2^16 = 96db holds also absolutely true but it is important to understand this in the context of the application to a bipolar signal. Or as I flippantly said before, 90db Peak or 96db Peak-Peak theoretically and 87db Peak or 93db Peak-Peak in application.
Sayonara
Steve Eddy said:
Ah yes, this one, I thought you referrred to another one.... The one above is easily proven. This is from Stereophiles Website:
An externally hosted image should be here but it was not working when we last tested it.
Fig.5 MSB Platinum Link Plus, waveform of undithered 1kHz sinewave at -90.31dBFS, 16-bit data
As can be seen -90.31dbfs just registers. There is nothing below this down to digital silence. As this is at 1KHz there would additional steps down to digital silence if anything below -90.31 dbfs.
Make the input signal just the tiniest bit lower and there is ONLY digital silence....
QED.
If you forgive me the sloppiness in my proof to drop the anything after the first digit after the decimal point, it is 90.3db as absolute limit.
As practical limit due to 1/2 LSB unceratinty it is in actuallity another 3db lower, hence 87db....
Of course, from a different angle the simple math of 2^16 = 96db holds also absolutely true but it is important to understand this in the context of the application to a bipolar signal. Or as I flippantly said before, 90db Peak or 96db Peak-Peak theoretically and 87db Peak or 93db Peak-Peak in application.
Sayonara
Kuei,
You are quite right there. 90 dB it is, not 96 dB, if we want the
value to be comparable to those for ananlog signals. I have
never thought about that before, but you are absolutely right.
Well, then there are still some differences like those you discuss,
eg. quantizatino error, and then, for digital it is a sharp limit
between signal or no signal, as you also point out, while for
analog we are rather referring to the noise floor which may still
contain recoverable info.
However, the observation that we should at least drop a bit
because of the numbers being signed is important.
For those who really want to go into the fine fine details, we
have slightly better dynamic range for the negative cycles since
the numbers are 2's complement encoded.
You are quite right there. 90 dB it is, not 96 dB, if we want the
value to be comparable to those for ananlog signals. I have
never thought about that before, but you are absolutely right.
Well, then there are still some differences like those you discuss,
eg. quantizatino error, and then, for digital it is a sharp limit
between signal or no signal, as you also point out, while for
analog we are rather referring to the noise floor which may still
contain recoverable info.
However, the observation that we should at least drop a bit
because of the numbers being signed is important.
For those who really want to go into the fine fine details, we
have slightly better dynamic range for the negative cycles since
the numbers are 2's complement encoded.
Kuei Yang Wang said:
You're making the exact same mistake you did before.
In the graph, you've got TWO domains of -90.32dBFS. One in the postitive domain and one in the negative domain. You're only considering one, just as you did when you considered only one domain of 15 bits in your original claim.
Look, dynamic range is the ratio of the highest level to the lowest level a system can produce. Zero (or the "digital silence" you refer to above) is as much a part of the dynamic range as the peak value.
With 16 bits, we can have a total of 65,536 discrete levels. You can have these all in the positive domain or all in the negative domain or split them up between the positive domain and the negative domain however you like. No matter how you slice it, the ratio between no signal and full signal is going to be 65,535:1, for a dynamic range of 96dB.
se
But Steve, for analog signals dynamics basically is measured
in the positive domain, as you call it, so the 90dB is a more
correct figure when comparing with ordinary/oldfashioned
figures for dynamics. Alternatively we could define it as the
ratio between the peak-to-peak values of the strongest and
weakest signals, but then the weakest signal in the digital
case will vary between +1 and -1, so we still get only 15 bits
dynamic range.
Defining the dynamic range of a digital signal as 20log(2^16)
is rather an information-theoretic measure of dynamics than
a practical one.
in the positive domain, as you call it, so the 90dB is a more
correct figure when comparing with ordinary/oldfashioned
figures for dynamics. Alternatively we could define it as the
ratio between the peak-to-peak values of the strongest and
weakest signals, but then the weakest signal in the digital
case will vary between +1 and -1, so we still get only 15 bits
dynamic range.
Defining the dynamic range of a digital signal as 20log(2^16)
is rather an information-theoretic measure of dynamics than
a practical one.
Christer said:
If he's absolutely right, then everything written on information theory from Shannon and Nyquist on down must be equally absolutely wrong. The entire information and communications field has just been turned upside down. Every textbook on information theory will have to be re-written and he has earned the bragging rights as being the first person to have disproved Shannon after 55 years.
se
Koinichiwa Eddy San,
You are making the same mistake as before, why I walked away from this exchange before. The Textbooks, Shannon, Nyquist et al are perfectly correct. However the way they reckon the issues differs from established practices for qualifying and quantifying analogue systems. We either have to add 6 or 9db (depending if you aknowledge the 1/2 LSB issue) to any conventionally qualified analogue dynamic range or subtract them form the digital system.
As the digital system came second chronologically and wants itself (or rather it's creators want) to compare itself to analogue systems it is the Digital System that must be qualified to the same standards as analogue.
And that was the original starting point of the very old discussion when I classed "the 96db Dynamic Range for CD" as one among many audio myth that cannot stand up to close scrutiny.
I am sure that you are aware of situations where a certain mathematical formula is absolutely correct, yet at the same time absolutely inapplicable to the specific condition. The vast majority of Information theory BTW is of that nature, namely it is too abstract and precise to be applicable in 99% of reality. It does not make it "untrue", just not applicable.
So no books need re-writing (yet - who knows what the furture brings), but it seems in your case they definitly need re-reading.
I'll again leave this discussion. As with the Back To Back electrolytic capacitor issue I have made my point. I'll leave it to the august audience to draw their own conclusions....
Sayonara
Steve Eddy said:
You are making the same mistake as before, why I walked away from this exchange before. The Textbooks, Shannon, Nyquist et al are perfectly correct. However the way they reckon the issues differs from established practices for qualifying and quantifying analogue systems. We either have to add 6 or 9db (depending if you aknowledge the 1/2 LSB issue) to any conventionally qualified analogue dynamic range or subtract them form the digital system.
As the digital system came second chronologically and wants itself (or rather it's creators want) to compare itself to analogue systems it is the Digital System that must be qualified to the same standards as analogue.
And that was the original starting point of the very old discussion when I classed "the 96db Dynamic Range for CD" as one among many audio myth that cannot stand up to close scrutiny.
I am sure that you are aware of situations where a certain mathematical formula is absolutely correct, yet at the same time absolutely inapplicable to the specific condition. The vast majority of Information theory BTW is of that nature, namely it is too abstract and precise to be applicable in 99% of reality. It does not make it "untrue", just not applicable.
So no books need re-writing (yet - who knows what the furture brings), but it seems in your case they definitly need re-reading.
I'll again leave this discussion. As with the Back To Back electrolytic capacitor issue I have made my point. I'll leave it to the august audience to draw their own conclusions....
Sayonara
Steve Eddy said:
I did of course mean it that it seems right to me, I hoped that
was implicit. So where is the error? Am I wrong about how
dynamic range is measured for analog signals? Note, BTW, that
I was referring to getting a meaningful measure that can be
used to compare with the measures for analog signals and I
was not referring to the purely information-theoretic content
of the digital signal, which by the way is less than 16 bits on
the average for practically all CDs.
Food for thought, which contains the most information from an
information-theoretical perspective, a CD recorded with music
or a CD recorded with white noise? (For onece I make an
exception and do not label pop- rock etc as noise.
).Deja vu all over again.......
Lets see...... an individual who has no little concern for with the accuracy of the information in his post;.... a reluctance for people to link to references that might require a little effort, but expand the understanding of the subject by separating generalization from facts,...... and calling people bullies (and now terrorist) when they ask him to not to post nonsense when discussing subjects beyond his understanding..........
Wait it's coming back to me ........ Grey Rollins! But he left in a huff over being called to task for repeated posting of nonsense and misinformation. Oh that history would be repeat itself!
"I don't know why certain people personalize the truth as if the truth belongs to one individual or another. The truth is the truth regardless of who may say it and what is said should stand or fall based on what is said rather than who says it."
It also has to stand on the credibility and knowledge of the individual who says it. When engineering text, designers, and manufacturers state a premise which is at odds with the statements of an individual, one must weigh his credibility against that of others. For peer review to work it must actually be done by actual peers, with equal or preferably greater expertise in the subject under scrutiny. The truth? You can't handle the truth.
Lets see...... an individual who has no little concern for with the accuracy of the information in his post;.... a reluctance for people to link to references that might require a little effort, but expand the understanding of the subject by separating generalization from facts,...... and calling people bullies (and now terrorist) when they ask him to not to post nonsense when discussing subjects beyond his understanding..........
Wait it's coming back to me ........ Grey Rollins! But he left in a huff over being called to task for repeated posting of nonsense and misinformation. Oh that history would be repeat itself!
"I don't know why certain people personalize the truth as if the truth belongs to one individual or another. The truth is the truth regardless of who may say it and what is said should stand or fall based on what is said rather than who says it."
It also has to stand on the credibility and knowledge of the individual who says it. When engineering text, designers, and manufacturers state a premise which is at odds with the statements of an individual, one must weigh his credibility against that of others. For peer review to work it must actually be done by actual peers, with equal or preferably greater expertise in the subject under scrutiny. The truth? You can't handle the truth.
Attachments
Christer said:
Dynamic range is typically based on RMS values, whether analog or digital. But it doesn't matter. As long as you're using peak values to peak values or peak-to-peak values to peak-to-peak values, you'll get the same result.
Someone didn't just sit down and say "Ok, let's forget about all the other definitions of dynamic range and just make it 20 x log 2<sup>16</sup>."
The definition is the same whether analog or digital.
As I said previously, dynamic range is the ratio of the lowest level a system can produce to the highest level it can produce. In both analog and digital systems, what limits the lowest level they can produce is their inherent noise.
So dynamic range in dB is:
20 x log (noise level/maximum level)
In analog systems, the inherent noise can come from a number of sources from thermal noise to shot noise, etc. In an undithered digital system, its inherent noise is its quntization noise, which will be a maximum of +/-1/2LSB.
So let's take a 16-bit digital system whose full scale output is +/- 0.5 volts or 1 volt peak-to-peak. So we're using 2<sup>16</sup> discrete values to represent a total swing of 1 volt. Which means that each discrete step will have a magnitude of 1/2<sup>16</sup> or 1.5259 x 10<sup>-5</sup> volts. The maximum quantization noise, which is 1/2LSB will be half that or 7.6294 x 10<sup>-6</sup> volts.
So if you want to calculate dynamic range in the positive (i.e. peak) domain, we've got a maximum positive signal swing of +0.5 volts and a maximum noise level of +7.6294 x 10<sup>-6</sup> volts so:
20 x log (+7.6294 x 10<sup>-6</sup>/0.5) = 96.33dB.
If you want to calculate it in the positive and negative (i.e. peak-to-peak) domain, you've got a peak-to-peak signal swing of 1 volt (i.e. (+0.5) - (-0.5)) and a maximum noise level of 1.5259 x 10<sup>-5</sup> volts (i.e. (+7.6294 x 10<sup>-6</sup>) - (-7.6294 x 10<sup>-6</sup>)) so:
20 x log (1.5259 x 10<sup>-5</sup>/1) = 96.33dB.
se
Christer said:Food for thought, which contains the most information from an
information-theoretical perspective, a CD recorded with music
or a CD recorded with white noise? (For onece I make an
exception and do not label pop- rock etc as noise.
Well, since noise by definition is not information, the CD recorded with music would have the most information on it.
BUT...
With just a tiny amount of noise added to a non-dithered digital system, you can actually put MORE information on the CD than without the tiny amount of noise.
se
Kuei Yang Wang said:
And it is qualified to the same standards as analogue. The inherent noise of each system defines its lower limit. The only difference is that the noise in a digital system is of a bit different type than in analogue. And of course in practical terms (which is irrelevant since your claim was the absolute theoretical limit) a digital system also includes analogue noise as well.
But your claim wasn't made in the context of what is practical. It was made in the context of the ideal theoretical absolute maximum.
If the theoretical absolute maximum dynamic range of a 16-bit system is in fact 90dB rather than 96dB, then indeed quite a lot of textbooks will have to be re-written and thousands of research papers will be worthless.
se
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