Quote Crow:

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My choice of sine waves in my example was unfortunate; replace that with a complex waveform and my point will be clearer.

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Any complex waveform can be decomposed into a sum of sine-waves of different frequencies. Your complex waveform can thus simply be completely described by simple sine waves of varying frequencies. Simple sine waves and only simple sine waves.

The limitation here is mostly how small (in time) irregularities you can represent. You can't describe a sine-wave with less than two samples per cycle. So, the sample frequency sets a limit on the complexity of the waveform by limiting the highest frequency that can be represented. Bit depth sets another limit. Quantization error/noise depends on bit depth. This affects how soft sounds you can represent.

Lars

Phew! After reading this thread I thought I was going nuts. Hugh's comments on this subject have put my mind at rest again, thankfully...

Quote Feefer:

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Dude (and you come off as a Dude, BTW), I'd think long and hard before calling Roger Nichols to the carpet on either his knowledge or experience: he's worked for the major labels for decades, and has FORGOTTEN more about digital audio and recording engineering than some anorak freshman straight out of of basic audio theory classes (earning a "C", no doubt) could hope to know. The "Immortal" Roger Nichols been working in the studios as an engineer before most of us were waddling about in diapers, and the major audio manufacturers were banging on his door for his technical assistance to help them usher in digital audio gear!If nothing else, he has the respect of Donald Fagan/Walter Becker, and if he's good enough to be the engineer for Steely Dan records, then that's good enough for me.

---

Well yeah, there's that, too.

--------------------
Gear list: If you can't find it, grind it

Quote Lars Farm:

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Any complex waveform can be decomposed into a sum of sine-waves of different frequencies. Your complex waveform can thus simply be completely described by simple sine waves of varying frequencies. Simple sine waves and only simple sine waves. Lars

---

Yeah, hats off to Monsieur Fourier, but this is completely off topic!

Quote Feefer:

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The SUBJECT of his article is to point out issues encountered when transferring between digital formats. OF COURSE HE'S TALKING ABOUT ANTIQUATED GEAR, since that's the same gear that was used to make the original recordings he's archiving!

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But he is not! He is comparing 16 bit to 24 bit. He is not comparing "a unique combination of a 12-bit converter with an additional four bits of an 8-bit converter for gain ranging."

Get your blinders off and accept that Nichols might be wrong!

Quote:

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In his case, he's archiving digital recordings made in the early 1980's on 3M multitrack recorder, and he's simply saying that understanding the workings of the gear that the original music was recorded on will only aid in ending up with a more accurate rendition of the original material in current digital format. Yes, he recorded on that gear back when it WAS state-of-the-art, and knows it's inner workings quite intimately.

---

I agree with that but it is just an introductory paragraph. In the rest of his article he is comparing straight 16 bit with straight 24 bit. He is not comparing 24 bit to "16 bit" implementation of the 3M digital machines!

This should have been a hint to you if you were not so starstruck:

Quote:

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With most digital audio now being recorded at 24-bit, nobody thinks about the ultimate 16-bit destination and what that conversion does to the sound quality.

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Do you see now?

Quote:

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Now if he was unaware of problems with the earlier gear, or was a young whipper-snapper engineer with no first-hand experience of the 3M machine, he might have been tempted to use a digital interface board to do the transfers digitally, thinking a digital transfer would be preferable. Bit no, he decided NOT to do that, since it would've induced non-linear errors that the 3M's original D-A converters compensate for.

---

I am not disagreeing with his choice but he could have summed it up by saying that the 3M implementation is not compatible with modern implementations of digital audio.

Quote:

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So in his words, "analogue transfers it was to be". He recorded to 24-bit from the analog outs.... Why? To make a more accurate archive by recording in 24-bit with modern gear....

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Again, I do not disagree with his choice. I do disagree with his explanation.

Quote:

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You also referred to his last article, where he mentioned hard drives.

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Lets stick to one article at a time.

Quote:

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Dude (and you come off as a Dude, BTW), I'd think long and hard before calling Roger Nichols to the carpet on either his knowledge or experience: he's worked for the major labels for decades, and has FORGOTTEN more about digital audio and recording engineering

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Bla bla bla. It doesn't change the fact that his explanations are not correct.

Quote:

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than some anorak freshman straight out of of basic audio theory classes (earning a "C", no doubt) could hope to know.

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Don't shoot the messenger. Anyway, do not assume anything about me just because you can't follow my arguments.

UnderTow

Quote UnderTow:

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Get your blinders off and accept that Nichols might be wrong!

---

how about considering that YOU might be wrong... (and Are)

as others have already noted.

this

Quote:

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Quote:


Just to refresh your memory, 24-bit audio gives you 256 times more resolution in the position of each sample on the waveform.




This isn't correct. It only gives more resolution to low-level signals. This can be easily demonstrated by converting a 16 bit file to a 24 bit file. The extra 8 bits are just filled with zeros. There is no requantization of the audio. A (loud) signal which lives in the upper bits of a 16 bit audio file does not gain any resolution by having extra zeros added in the extra bits.

---

clearly shows that you lack a full understanding of numeric data systems. or perhaps appropriate terminology.

to put it bluntly. and in Base 10 to be utterly crystal clear...

if in addition to expressing integer values, you are capable of expressing partial values, like 0.00001 to 0.99999 then you are capable of expressing 15.00001 to 15.99999 as well.

this by definition is finer resolution than only being capable of expressing integers

and it's effectively this that the extra bits allow.

In addition, the fact that you seem to fail to appreciate WHY your example of simply converting a 16 bit file to a 24 bit file, (and back) in the suggested manner is SO not relevant, shows a decided logical blind spot.

Since this is a core tenet of your entire argument... I won't bother pulling the rest apart.,..

I would suggest an apology might be in order....

Max

--------------------
if you don't know who i am, i aint gonna tell you.

Quote UnderTow:

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Get your blinders off and accept that Nichols might be wrong!

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Why does this matter so much? Why are you banging this drum so hard? Is it personal or what?

We all know what sounds good, or not. Maybe 0.00001% of the population give a flying toss about the underlying science as to WHY is sounds the way it does. A fractionally higher percentage of the population of sound engineers might give a toss, but I assure you it is very marginal.

Yes, he might be wrong, or at least guilty of some infelicitous language. So what? I'm not going to frame his article and build a candle-lit shrine round it. It's tomorrow's fish and chips wrapper.

--------------------
Dynamite with a laser beam...

Quote Max The Mac:

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Quote UnderTow:

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Get your blinders off and accept that Nichols might be wrong!

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how about considering that YOU might be wrong... (and Are)
as others have already noted.

---

I posted some wrong stuff and I think I have cleared that up. And I did say sorry for the confusion. So I did appologise for that. If that wasn't clear, I appologise again.

Quote:

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clearly shows that you lack a full understanding of numeric data systems. or perhaps appropriate terminology.

---

Yes that was wrong and I shouldn't have posted at 10 to 4 in the morning. But I did explain later on what I meant. Basicly, in my tired state, I was thinking of error magnitudes but describing it as just amplitude. I should have said errors in the amplitutde or something like that.

Quote:

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and it's effectively this that the extra bits allow.

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Yes agreed. My point was that the error gets smaller.

Quote:

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In addition, the fact that you seem to fail to appreciate WHY your example of simply converting a 16 bit file to a 24 bit file, (and back) in the suggested manner is SO not relevant, shows a decided logical blind spot.

---

It was relevant to demonstrate one particular point in response to one remark. My bad terminology confused the whole issue. That doesn't mean I have a logical blind spot. It means I shouldn't post at 10 to 4 in the morning.

Quote:

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Since this is a core tenet of your entire argument... I won't bother pulling the rest apart.,..

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Not really but please do.

Quote:

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I would suggest an apology might be in order....

Max

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Are you saying that the article is factualy correct? If so, and you can explain why, I will appologise. Maybe I do misunderstand that article completely but so far this hasn't been demonstrated AFAICS.

UnderTow

Ok I give up. And I appologise to this forum for ever bringing this up.

UnderTow

Quote UnderTow:

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Ok I give up. And I appologise to this forum for ever bringing this up.
UnderTow

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AMEN!

--------------------
Gear list: If you can't find it, grind it

To quote from the article, ‘As a percentage of the difference between adjacent samples, the quantisation error is much greater for a low-frequency signal than a high-frequency one’.

I’m really curious about this postulation, but unfortunately possibly the only person that is! I can see where he’s coming from with this, but I’m not sure that it’s at all a relevant comparison. Anyone have an opinion on this?

I found it an interesting article, although a bit ‘strange’ in some way I can’t quite describe. I’ve never heard of the guy and I don’t really care how many awards he has, I’m just trying to understand this particular postulation. I’m intrigued and curious to know what others make of this idea of his.

Quote Crow:

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Anyone have an opinion on this?

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Yes but I'll spare you all.

But I still do suggest people that are interested in the subject read the Dan Lavry article I reference in my first post.

UnderTow

Quote UnderTow:

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I posted some wrong stuff and I think I have cleared that up. And I did say sorry for the confusion. So I did appologise for that. If that wasn't clear, I appologise again.

---

we'll start with an apology ( note the single p ) on my own behalf , as I must have missed those in amongst the rest of it... or at least forgotten them by the time i got to this end of the thread.

it does however rather seem that you failed to modify your later position in the light of your previously , now understood , incorrect positions.

in other words... it seemed very much like you kept banging on the same line despite having been shown and having admitted the errors..

in light of which, I really didn't much feel like expanding and wasting everybody's screen space with pointless effort.

I have to agree that posting at 10 to 4 in the morning isn't always the best idea.... I've done it myself on a number of occasions...

it's rather a sweeping statement to say the entire article is 100% factually correct... but in relation to your original core complaints, yes it is.

The why has already been gone over... several times.. and you've already accepted it.

I should add that SOS readers, on the whole, have been rather spoilt ...... because the majority of "deep" technical explanation articles have been pulled out of the hands of one of the most easily understood writers in the field... Hugh...

Probably fair to say that his background as a trainer for Auntie has left him with a generally uncanny ability to put a point across with the minimum fuss and confusion on the vast majority of occasions.... most especially when he has time to think about how he wants to say it.... basically the BBC like people to come out of Wood Norton with some clue about what it is they're doing!

IMHO, if the average reader were to try getting the explanations contained any one of his more technical articles out of the scientific and engineering papers and manuals that originally contained the data , They'd be very tired, certainly confused and probably no wiser than when they started...


This is not to say that Hugh is ALWAYS right, as he himself is happy to point out.... but what he does say, he says very succinctly and intelligibly .



I cannot say that I find the same quality in the Writing of Roger Nichols, I want to be very clear on that... i am NOT his biggest fan..... in terms of his WRITING, but I cannot really fault his technical ability , experience, and general background knowledge.....


However, your initial post, and original "backing up" of your claims were factually and conceptually incorrect. others have stated so, and you've admitted to it piecemeal when shown in detail .... what's left is apparently largely a case of you fighting your corner because you feel put upon, not because you're actually right...

however, in response to your request I quote below your initial argument, and my rebuttals will be interspersed.

Quote:

---

I was shocked by the article and responded as such. Dinner got in the way of a proper explanation. Here it is:

Quote:


With most digital audio now being recorded at 24-bit, nobody thinks about the ultimate 16-bit destination and what that conversion does to the sound quality.




This comment is not supported by any data and is a bit of an insult to all the people that do think about it. He seems to be saying that he is the only person that has thought about this.


>>> Max .
Err Actually it (the sound quality issue ) is supported by all authorities on the subject, and is the reason for the multiple approaches to Dither by various parties, to get subjectively the best result... In context the statement is simple, and in my experience true... very very few people actually consciously consider the Delivery media during the recording process.. just look at how many people argue over Sample rate conversions from 24/96 to 16/44.1 , and how often the non integer relationship of the sample rate is accused of being the ONLY issue, utterly forgetting that there is also a bit depth reduction to be handled as well.
The Phrase "No-one" is often used as a generalisation in this kind of context, and his hardly an insult or defamation of anyone falling outside of the generalisation.

Quote:


The first impression is that you are just changing the noise floor from -144dB to -96dB, which isn't going to hurt the punchy high-level mix that you spent so much time on. But there is much more to this conversion than meets the ear.




This is incomplete to say the least. You could have a recording with a noise floor way above -96 dB FS. It won't suddenly go down to -144 dB FS just by converting to 24 bits.




>>>>>>> Max. First major technical issue., you've seemingly read his comment backwards... he never said what you implied. he never meant or implied it, and your comment is totally irrelevant in the context of the original article. it has no need to be a complete discourse on Digital Audio, it made a point within the article, and was all that was required to do so.

Quote:


Just to refresh your memory, 24-bit audio gives you 256 times more resolution in the position of each sample on the waveform.




This isn't correct. It only gives more resolution to low-level signals. This can be easily demonstrated by converting a 16 bit file to a 24 bit file. The extra 8 bits are just filled with zeros. There is no requantization of the audio. A (loud) signal which lives in the upper bits of a 16 bit audio file does not gain any resolution by having extra zeros added in the extra bits.


>>>>>> Max. We've been here and done that, but this shows it in context. your statement here is utterly wrong.

Quote:


The first time I heard 24-bit, recording Bela Fleck and the Flecktones, I expected to hear more sheen and high-frequency clarity. I was incorrect. The most noticeable difference was in the low frequencies: the mouthwatering sound of the bass, the breathtaking realism of the kick drum, the clarity of vocals, and the low-end improvements that finally make the banjo worth recording. It took me a while to figure out why this was the case, but I finally got to the bottom of it.




This is anecdotal and isn't based on any facts. He seems to base his whole premise on "bad bass" in 16 bit audio on this recording.


>>>>> Max...
Fact, he heard a difference ,
which in his experience, of recording audio, was significant... and his experience is not to be discounted or taken as being irrelevant... it is highly relevant.. it is only based on subjective experience and qualitative assessment that anyone can make a value judgement on anything... I submit that his experience is demonstrably long enough and at a high enough level for that value judgement to be given some credit.
a sort of "Expert Witness" in court kind of scenario... and i submit you were NOT there, and cannot make any kind of judgement based on that at all.
I also get the feeling that frankly, you don;t have a heap of experience with "antiquated" digital systems... or with recording "at the bleeding edge" with early Digital equipment... because those differences are very very real, as anyone who has had that experience will tell you...



Quote:


This 256 times higher resolution of a 24-bit sample is in effect everywhere on the waveform, from the lowest levels to the highest peaks. A sample point nearing 0dB full scale is 256 times more accurate than the same sample recorded at 16-bit.




This is incorrect. The resolution is only added at the lower end of the amplitude scale.


>>>>>> Max.
Been there, done that, again....



Quote:


To cut down on the confusion with bit sizes, let's use the size of the smallest bit in the 24-bit scale as a reference and call it a step. The difference between Sample A and Sample B in the 24-bit recording is 16 steps. The difference between the same samples in the 16-bit recording is 112 steps. That is 96 steps away from where it should have been — a 700 percent error in a low-frequency signal.




Not only can you not compare 24 and 16 bit signals like this (you need to to add dither during conversion to linearise the quantization steps) but the man can't even calculate percentages!


>>>>>>> Max.
Okay this is where I feel the writing style to be the issue rather than the underlying concept or data.... I don't think Hugh would present that idea like this, and I sure as hell wouldn't... it's at this point I had to do a double take... for a while I had the feeling there'd been an editorial cock up with the diagram and text, until Hugh put my head back on the right way round...

Comparing them like this is I suppose, a valid way of presenting the idea... that there can be significant differences between 16 and 24 bit recordings of the same event... but it's definitely not the most concise or easily intelligible way... you CAN compare the two this way... you did it yourself just a moment beforehand... adding 8 zeroes remember? Dither is essentially a solution to a problem, not necessarily central to recording data at either resolution. But the fact that it ignores the existence of Dither as a solution does leave it somewhat short of an ideal description...


Quote:


The voltages generated in a converter are from small resistors that are trimmed by lasers during manufacturing. The small bits that are prone to error are different for every converter, even from the same manufacturer. This means that bit 23 on the converter on track 1 may be different than bit 23 on the converter on track 12.




Is he talking about segmented DACs? He does have this paragraph in his article:

Quote:


Current oversampling converters do not have the linearity and tracking problems that conventional converters have. Usually you are dealing with a 1-bit converter that samples at 256 times the sample rate. This type of converter just looks at the incoming signal and compares it to a reference voltage. The comparing circuit then decides whether the reference voltage should go up or down. This is done very fast many times between samples. Now the reference voltage that matched the incoming signal determines the resulting PCM value. Only one bit, and no linearity errors.




But nearly every soundcard you buy these days uses oversampling. I might be wrong but he seems to be looking at antiquated technology and basing a whole article on that. This just confuses things.


>>>>>> left these two ,lumps together to answer in context.

Max.
Yes and err, no... in a very real, but somewhat general sense, ALL IC's are made that way... optical lithography, and ALL AD/DA systems have chips that are IC's at their heart........ AND no, he's not really talking about poxy PC or Mac sound cards, but real discrete Hardware, before the PC/Mac based DAW could so much as fart digital audio., in fact before the DAW we know it today existed .
The article was not meant as an educational discourse on cutting edge AD/DA , or PC hardware, but as a piece of useful background knowledge, that might one day save someone's bacon... . imagine if YOU had been given the job of re-archiving all this material.... would you have gone for the straight digital to digital transfer, that would seem so obvious a ploy , had you not known about some of the stuff contained in this article.... and others of it's type.... only those with experience with the systems of the day would really understand this without having to be told it... and there are increasingly few of them left and fewer still working almost at "tape op" level... archiving is not usually considered the preserve of the Grammy winning , working recording engineer.... and VERY few college courses teach anything about such "antiquated" hardware or it's operational idiosyncrasies.

A few comments to the response:

Quote:


I've not read the article in question but I can spot faulty reasoning a mile off.




Not supporting my comment is not faulty reasoning. It's just lack of evidence.

Quote:


You have so far failed to provide:

1) Specific parts of the article with which you disagree; all you have said is "the article is not correct"
2) Evidence to support your assertion that "the article [or part of it] is not correct"
3) Evidence to support your assertion that "Nichols does not understand digital audio"
4) Reasons why Nichols "should not be writing technical articles for SOS"




See above.

Quote:


5) Your real name and credentials




This is totally irrelevant. I prefer to let the facts talk rather than reputation. Actually I am against any form of reputation or lack thereof clouding the issue.

Quote:


If you wish to start a sensible dialogue on this article (or anything for that matter) you first need to learn how to construct an argument - simply referencing other people's writing on the general topic of digital audio gives no credibility to your unsupported claims.




Oh stop being so patronising. You have no idea if I can construct an argument or not as I didn't even attempt to argue! (Talking about faulty reasoning ...) Maybe you should have read the article before responding ...

Those articles are long and complex and it would be completely pointless and extremely time consuming to rewrite those articles in my own words just for this purpose.

UnderTow

---

The latter sections really need no comment... initial reactions to your post were about the manner of posting and the overtly aggressive "I'm oh so right and he's oh so wrong and should be hung" style...
all of which were pretty much to the point and fair comment... take it like a man and fess up to that.....

Sadly the ensuing posts did rather demonstrate the lack of sound argument


( a bad pun sorry, it is late, and I too am tired)

and your final comment was somewhat arrogant, or at least, one sided, since you pretty much asked everyone else to do exactly that.... to disprove your claims. virtually discounting their comment unless they did so
.

here endeth the lesson, that'll be £40 thanks.


best regards
Max


rearrange the following words.
Tea in cup a storm

--------------------
if you don't know who i am, i aint gonna tell you.

Quote Max The Mac:

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rearrange the following words.
Tea in cup a storm

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24 bit molehills out of 16 bit mountains?

First up, I'll say that giving up was a good idea. It let me actually think about the content of my post and the tone I was using in that post.

I was in a very bad mood due to stuff that had nothing to do with anyone on this forum or anyone writing for SOS. I should never have let that spill into this forum. Or rather, I should never have posted anything in that state of mind. It clouded my judgement to say the very least!

I apologise to everyone here and Mr Nichols in particular.

Quote Max The Mac:

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we'll start with an apology ( note the single p ) on my own behalf , as I must have missed those in amongst the rest of it... or at least forgotten them by the time i got to this end of the thread.

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No need to apologise. I was talking out of my arse as well as being one.

Quote:

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it does however rather seem that you failed to modify your later position in the light of your previously , now understood , incorrect positions.

in other words... it seemed very much like you kept banging on the same line despite having been shown and having admitted the errors..

---

Yes yes, *lowers head in shame*.

Quote:

---

I should add that SOS readers, on the whole, have been rather spoilt ...... because the majority of "deep" technical explanation articles have been pulled out of the hands of one of the most easily understood writers in the field... Hugh...

Probably fair to say that his background as a trainer for Auntie has left him with a generally uncanny ability to put a point across with the minimum fuss and confusion on the vast majority of occasions.... most especially when he has time to think about how he wants to say it.... basically the BBC like people to come out of Wood Norton with some clue about what it is they're doing!

IMHO, if the average reader were to try getting the explanations contained any one of his more technical articles out of the scientific and engineering papers and manuals that originally contained the data , They'd be very tired, certainly confused and probably no wiser than when they started...

---

Entirely agreed.

Quote:

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However, your initial post, and original "backing up" of your claims were factually and conceptually incorrect. others have stated so, and you've admitted to it piecemeal when shown in detail .... what's left is apparently largely a case of you fighting your corner because you feel put upon, not because you're actually right...

---

Yes. Correct assessment.

Quote:

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however, in response to your request I quote below your initial argument, and my rebuttals will be interspersed.

---

Thanks.

Quote:

---

>>> Max .
Err Actually it (the sound quality issue ) is supported by all authorities on the subject, and is the reason for the multiple approaches to Dither by various parties, to get subjectively the best result... In context the statement is simple, and in my experience true... very very few people actually consciously consider the Delivery media during the recording process.. just look at how many people argue over Sample rate conversions from 24/96 to 16/44.1 , and how often the non integer relationship of the sample rate is accused of being the ONLY issue, utterly forgetting that there is also a bit depth reduction to be handled as well.
The Phrase "No-one" is often used as a generalisation in this kind of context, and his hardly an insult or defamation of anyone falling outside of the generalisation.

---

Indeed. I shouldn't have taken personaly something that wasn't personal at all.

Quote:

---

Quote:
The first impression is that you are just changing the noise floor from -144dB to -96dB, which isn't going to hurt the punchy high-level mix that you spent so much time on. But there is much more to this conversion than meets the ear.

This is incomplete to say the least. You could have a recording with a noise floor way above -96 dB FS. It won't suddenly go down to -144 dB FS just by converting to 24 bits.

>>>>>>> Max. First major technical issue., you've seemingly read his comment backwards... he never said what you implied. he never meant or implied it, and your comment is totally irrelevant in the context of the original article. it has no need to be a complete discourse on Digital Audio, it made a point within the article, and was all that was required to do so.

---

Yup. In a sense I was supporting his statement. It isn't so much that I read his comment backwards, it is that I failed miserably to convey what I was trying to say: That the noise floor of 16 or 24 bit converters is not the only thing that contributes to the overall noise floor. This is certainly not a contradiction to what Mr Nichols says.

Quote:

---

Quote:
Just to refresh your memory, 24-bit audio gives you 256 times more resolution in the position of each sample on the waveform.

This isn't correct. It only gives more resolution to low-level signals. This can be easily demonstrated by converting a 16 bit file to a 24 bit file. The extra 8 bits are just filled with zeros. There is no requantization of the audio. A (loud) signal which lives in the upper bits of a 16 bit audio file does not gain any resolution by having extra zeros added in the extra bits.


>>>>>> Max. We've been here and done that, but this shows it in context. your statement here is utterly wrong.

---

It is indeed. (I do know what I was trying to say but lets just forget it).

Quote:

---

Quote:
The first time I heard 24-bit, recording Bela Fleck and the Flecktones, I expected to hear more sheen and high-frequency clarity. I was incorrect. The most noticeable difference was in the low frequencies: the mouthwatering sound of the bass, the breathtaking realism of the kick drum, the clarity of vocals, and the low-end improvements that finally make the banjo worth recording. It took me a while to figure out why this was the case, but I finally got to the bottom of it.




This is anecdotal and isn't based on any facts. He seems to base his whole premise on "bad bass" in 16 bit audio on this recording.


>>>>> Max...
Fact, he heard a difference ,
which in his experience, of recording audio, was significant... and his experience is not to be discounted or taken as being irrelevant... it is highly relevant.. it is only based on subjective experience and qualitative assessment that anyone can make a value judgement on anything... I submit that his experience is demonstrably long enough and at a high enough level for that value judgement to be given some credit.
a sort of "Expert Witness" in court kind of scenario... and i submit you were NOT there, and cannot make any kind of judgement based on that at all.
I also get the feeling that frankly, you don;t have a heap of experience with "antiquated" digital systems... or with recording "at the bleeding edge" with early Digital equipment... because those differences are very very real, as anyone who has had that experience will tell you...

---

You are entirely correct that I do not have that experience. I havn't been in the business long enough.

Quote:

---

Quote:
This 256 times higher resolution of a 24-bit sample is in effect everywhere on the waveform, from the lowest levels to the highest peaks. A sample point nearing 0dB full scale is 256 times more accurate than the same sample recorded at 16-bit.

This is incorrect. The resolution is only added at the lower end of the amplitude scale.


>>>>>> Max.
Been there, done that, again....

---

Agreed.

Quote:

---

Quote:
To cut down on the confusion with bit sizes, let's use the size of the smallest bit in the 24-bit scale as a reference and call it a step. The difference between Sample A and Sample B in the 24-bit recording is 16 steps. The difference between the same samples in the 16-bit recording is 112 steps. That is 96 steps away from where it should have been — a 700 percent error in a low-frequency signal.



Not only can you not compare 24 and 16 bit signals like this (you need to to add dither during conversion to linearise the quantization steps) but the man can't even calculate percentages!


>>>>>>> Max.
Okay this is where I feel the writing style to be the issue rather than the underlying concept or data.... I don't think Hugh would present that idea like this, and I sure as hell wouldn't... it's at this point I had to do a double take... for a while I had the feeling there'd been an editorial cock up with the diagram and text, until Hugh put my head back on the right way round...

Comparing them like this is I suppose, a valid way of presenting the idea... that there can be significant differences between 16 and 24 bit recordings of the same event... but it's definitely not the most concise or easily intelligible way... you CAN compare the two this way... you did it yourself just a moment beforehand... adding 8 zeroes remember? Dither is essentially a solution to a problem, not necessarily central to recording data at either resolution. But the fact that it ignores the existence of Dither as a solution does leave it somewhat short of an ideal description...

---

Agreed. Just one point: Shouldn't an error percentage be calculated as a difference between the absolute value of the samples (lets say in 24 bits) and the difference the samples have to this value rather than just looking at the number of steps the samples are off and comparing these?

Quote:

---

Quote:
The voltages generated in a converter are from small resistors that are trimmed by lasers during manufacturing. The small bits that are prone to error are different for every converter, even from the same manufacturer. This means that bit 23 on the converter on track 1 may be different than bit 23 on the converter on track 12.

Is he talking about segmented DACs? He does have this paragraph in his article:

Quote:
Current oversampling converters do not have the linearity and tracking problems that conventional converters have. Usually you are dealing with a 1-bit converter that samples at 256 times the sample rate. This type of converter just looks at the incoming signal and compares it to a reference voltage. The comparing circuit then decides whether the reference voltage should go up or down. This is done very fast many times between samples. Now the reference voltage that matched the incoming signal determines the resulting PCM value. Only one bit, and no linearity errors.

But nearly every soundcard you buy these days uses oversampling. I might be wrong but he seems to be looking at antiquated technology and basing a whole article on that. This just confuses things.

>>>>>> left these two ,lumps together to answer in context.

Max.
Yes and err, no... in a very real, but somewhat general sense, ALL IC's are made that way... optical lithography, and ALL AD/DA systems have chips that are IC's at their heart........ AND no, he's not really talking about poxy PC or Mac sound cards, but real discrete Hardware, before the PC/Mac based DAW could so much as fart digital audio., in fact before the DAW we know it today existed .

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Ok, I did not find that Mr Nichols made it clear in his article that he was purely talking about these older converters when he started talking about 16 and 24 bit recording. At least not clear enough. Hence my questions.

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The article was not meant as an educational discourse on cutting edge AD/DA , or PC hardware, but as a piece of useful background knowledge, that might one day save someone's bacon... . imagine if YOU had been given the job of re-archiving all this material.... would you have gone for the straight digital to digital transfer, that would seem so obvious a ploy , had you not known about some of the stuff contained in this article.... and others of it's type.... only those with experience with the systems of the day would really understand this without having to be told it... and there are increasingly few of them left and fewer still working almost at "tape op" level... archiving is not usually considered the preserve of the Grammy winning , working recording engineer.... and VERY few college courses teach anything about such "antiquated" hardware or it's operational idiosyncrasies.

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No, I would have done some research. Anyway, I am guessing that these machines don't interface with any modern connectors and protocols. I would assume anyone presented with the challenge would be obliged to do some research simply because of this.

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The latter sections really need no comment... initial reactions to your post were about the manner of posting and the overtly aggressive "I'm oh so right and he's oh so wrong and should be hung" style...
all of which were pretty much to the point and fair comment... take it like a man and fess up to that.....

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Yes, I hope I have just done that.

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best regards
Max

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And to you. Thanks for taking the time to respond.

Cup in a tea storm

UnderTow

Quote UnderTow:

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First up, I'll say that giving up was a good idea. It let me actually think about the content of my post and the tone I was using in that post.

I was in a very bad mood due to stuff that had nothing to do with anyone on this forum or anyone writing for SOS. I should never have let that spill into this forum. Or rather, I should never have posted anything in that state of mind. It clouded my judgement to say the very least!

I apologise to everyone here and Mr Nichols in particular.

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That's ok just take it out on Hugh(that's what I do) and he'll give you a whooping,educate you and also make you feel good at the same time.
You think mag is called SOS for nothing!

And due credit to Undertow for being big enough of a person to admit he was confused on this. The guy shows some hope, after all.

Wouldn't on-line forums be much more pleasant if more people had the courage to put their egos aside long enough to utter that little sentence: "I'm sorry. I was wrong"?

Chris

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1.5GHz Al 17" Powerbook G4 (2.0GB RAM, Hitachi 60GB 7,200 rpm drive), running Logic Pro 7 under OSX 10.4.5

Quote Crow:

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Yeah, hats off to Monsieur Fourier, but this is completely off topic!

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It was in response to what you snipped from your own statement:-"My choice of sine waves in my example was unfortunate; replace that with a complex waveform and my point will be clearer.". Fourier shows that these are the same.

Quote UnderTow:

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Arf! I am not talking about the amplitude scale nor am I talking about the amplitude resolution! I am talking about an amplitude resolution scale

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But what is an 'amplitude resolution scale' ? This is a meaningless phrase to me (and I suspect everyone else here... ) I suspect this is the core of our communication problem

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So the line decreases. The amplitude resolution of the LSB of each digital word decreases as the word length increases.

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Yep, with you so far...

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Arf! By "at the lowest resolution scale" I mean at the least significant bits. As you go through the bits in a digital word, starting at the MSB and ending at the LSB, the amplitude of the error caused by flipping a particular bit decreases.

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Yes it does... but who or what is going to be flipping bits. This concerns data errors in recorded or transmitted files, and has nothing whatevere to do with tht intrinsic resolution of 16 or 24 bit data. I've commented on this area of confusion before...

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One of my points about the article is that the word dither is not mentioned once. But I agree with what you say. The dither linearises the quantae.

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To be fair, dithering (or not) doesn't really affect Roger Nichol's assertions or arguments.

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Arf! If you properly dither, you won't have quantization errors! So if you have quantization errors, you havn't properly dithered!

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Arf yourself! There will always be quantisation errors, That is inherent when you quantise something because of the discrete nature of the quantisation levels. When the system is correctly dithered, those errors are distributed randomly, instead of being related to the signal amplitude, and hence manifest as noise instead of programme-related distortion.

I don't want to be rude, but there do appear to be several gaps and confusion in your understanding of the core concepts here. But ;et's plough on and try to resolve them...

Hugh

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Technical Editor, Sound On Sound

Quote UnderTow:

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I think you are working under the assumption that I don't understand what I am talking about instead of working under the assumption that I do and trying to follow my logic.

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I can only go by the evidence of what you have written. And from that there appears to be some misunderstandings and confusion. Maybe it is a language or use of language problem... but if we can find a consistent and common terminology perhaps we can all reach a common understanding too.

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Not directly but it is as a bit of mental exercise to understand the subject. You know as well as me that digital audio is not intuitive at first glance.

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I can certainly agree with the first point. As for your mental gymnastics, I think it is further clouding and confusing the subject, not adding clarification.

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As I have explained in earlier posts, I was describing my mental processes to clarify that my terminology was wrong but not my thought processes.

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In the nicest possible way, I'm yet to arrive at that conclusion

Hugh

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Technical Editor, Sound On Sound

Quote UnderTow:

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And this is the crux of the problem. He has a Grammy (or more) and people believe him blindly. That is why he should either, check his facts or have his articles checked by somone at SOS that is more knowledgable about digital audio.

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But we are yet to find a cohesive, well reasoned argument as to what is conceptually or technically wrong in Mr Nichol's arguments. I've not found anything and I have been looking hard...

I agree that the quoted numbers for step size differences in his text and diagrams seem a little abstract, and his percentage error calculation seems unfounded, but the principle of proportionate quantisation errors at LF and HF between 16 and 24 bit quantising seems to me to be reasonable.

Personally, Im not convinced that bass is conveyed significantly better than treble, subjectively, when using 24 bits. But I am convinced that everything generally sounds better... and obviously for the same core reasons. The resolution is considerably improved.

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I am saying that he should not write deep technical articles about digital audio.

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Again, to be fair, it is not a deep technical article. He is describing a subjective effect he noticed, and his attempts to find a reason for that effect. As far as I can see, his technical arguments broadly hold water. I will happily agree that his explanations are less than perfectly clear, but as you have discovered yourself, UnderTow, it is actually very hard to get across complex technical issues in print.

hugh

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Technical Editor, Sound On Sound

Quote Crow:

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Can’t a low frequency signal be much more accurately represented than a high frequency one using the same sample rate?

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No, it can't. But that's not the point of Nichol's argument.

What he is trying to argue is that since a low frequency waveform exhibits only relatively small changes in amplitude between adjacent samples, the aditional amplitude resolution af 24 bit quantising allows these small amplitude changes to be recorded with a smaller error (as a percentage of the amplitude change) than the equivalent HF signal.

Let me try to explain that more clearly...

For the sake of argument let's say that, when quantised to 16 bits, the first sample is rounded down to be quantised to some specific level and the next is rounded up to adjacent quantising level above it. (This rounding is, of course, the quantising error.)

However, if quantised to 24 bits, there will be 255 more quantising levels in between each and every 16 bit quantising level.

When quantised to 24 bits, then, the first sample might be coded to a quantising level which is now, say, 36 levels above the level corresponding to the 16 bit quantise level. There will still be a degree of rounding up or down involved, but clearly the amount of rounding error is now much smaller because the quantisation levels are much more closely spaced.

The second sample might be coded to a level which is 48 levels below that corresponding to the upper 16 bit quantising level.

So, if we measure the distance between the first and second samples described above, in terms of 24 bit quantising intervals, when quantised to 16 bits the distance is 256 steps -- because that is the spacing between the equivalenmt 16 bit quantisation levels.

While when quantised to 24 bits, the gap between these two samples is 172 (256-48-36).

So there is a relatively large percentage error here. The amplitude difference should be 172 'steps', but when quantised to 16 bits, it comes out at 256 steps.

256/172 suggests an error of 149%

In contrast, although the same kind of error mechanism exists for HF signals, there nature is such that adjacent sample are likely to be spaced over many more quantising levels in a 16 bit system.

Again, for the sake of argument, let's say that the first sample is rounded down to one quantising level, and the next sample is rounded up to a quantising level which is 35 16 bit levels higher. If we convert that amplitude difference to 24 bit quantising levels, remembering that there are 255 additional levels between each 16 bit quantising level, 35*255 = 8925 levels.

When quantised to 24 bit accuracy, let's say that the first sample ends up 36 levels higher than the 16 bit rounded value, and that the second sample is 48 levels below the 16 bit value -- in other words, exactly the same size of error as we had inthe LF example previously.

So the step difference between samples in the 24 bit system is 8925-36-48 = 8841 levels.

So the percentage error between 16 bit quantised values and 24 bit quantised values is 8925/8841 = 0.95%


That's it. That's the argument Nichols is making. 24 bit quantising typically results in much smaller percentage amplitude errors for LF signals, than HF signals.

From that premise, he argues that the increased resolution of 24 bit coding is more audible for LF sigals than HF signals, and that agrees with his subjective impressions.

Where is the problem? I'm intrigued to know

hugh

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Technical Editor, Sound On Sound

Quote Hugh Robjohns:

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[Where is the problem? I'm intrigued to know

hugh

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the banjo?

har har...

QUOTE:"UnderTow, it is actually very hard to get across complex technical issues in print."

I would agree Hugh.
I don't know if it really matters that much anyway to most on this forum. The complexities of digital audio are for the boffins who make the gear (convertors, recorders, software, etc..) and while it is a very interesting subject, this discussion proves that unless you know it in all its detail, I reckon we are better off using this wonderful gear which the boffins did invent, comment on the merits and shortfalls and continue to make music.
For my money, we see far too many posts about people judging the sound quality of various bits of gear by the technical spec (and sometimes brand name) - and not the actual sound itself.
The sound is always the most important thing.
Many people on this forum are fairly new to recording. They should be given good practical advice on getting the best from their gear rather than be bombarded with lots of technical mumbo-jumbo. This only adds to the confusion.

PS. If you put a bass guitar through a 16-bit guitar POD, in my opinion it actually gives you a nice tidy bass sound - from the persepctive of the bottom end.

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Jack of all trades, master of some.

Quote UnderTow:

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Get your blinders off and accept that Nichols might be wrong!

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He might be... but I still can't see the flaw in the argument. I can see the flaw in his numbers, but not the argument...

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I agree with that but it is just an introductory paragraph. In the rest of his article he is comparing straight 16 bit with straight 24 bit.

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What he was trying to do was find an explanation to justify his subjective impressions: namely that the LF quality is greatly improved by 24 bit quantising (compared to 16 bit quantising) -- and far more so than the HF quality.

Now that might actually be a point worth debating in its own right. Do others here agree with that?

His (personal) theory for why there might be a greater improvement in LF resolution than HF resolution is an interesting one, and as far as I can see, is hard to argue against....

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I am not disagreeing with his choice but he could have summed it up by saying that the 3M implementation is not compatible with modern implementations of digital audio.

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Er... it was (and is) perfectly compatible. What he was explaning was that the early A-D converters weren't very linear, and that each A-D was matched (by hand) to the respective D-A to try to minimise linearity errors between analogue in and analogue out. The A-D linearity errors are recorded on tape for all time in digital form, and that's why he was able to get better quality by transferring via the analogue domain and carefully optimising the D-A converter set up.

Which is all very interesting, but not actually relevant to his main issue which was about the subjective bass improvement he noticed when working with 24 bits.

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Again, I do not disagree with his choice. I do disagree with his explanation.

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Seems clcear and accurate to me.

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Bla bla bla. It doesn't change the fact that his explanations are not correct.

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... We all have our own opinions, and you are entitled to yours. But if you want to assert fault in his claims you'll have to do rather better than you have so far...

hugh

Edited to add: It has (understandably, I hope) taking me a while to wade through this huge thread and asnwer each relevant point. Consequently, this post was written long before I got to the end of the thread to realise that UnderTow has finally seen the light, thanks to Max's efforts.

So apologies for my continued battering long after the white flag had been raised! -- but I hope the further explanations and clrifications have helped others equally as confused about the claims and arguments.

hugh





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Technical Editor, Sound On Sound

"Where is the problem? I'm intrigued to know"

Ignorance?

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Jack of all trades, master of some.

Quote BigAl:

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"Where is the problem? I'm intrigued to know"

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Hugh and I had a long discussion before we put this article into print. I think both of us were quite surprised by the argument Roger Nichols makes about bass sounding better, but neither of us could fault his reasoning.

Thinking about it, though, there is one thing I'm not sure about. The argument makes sense in the context of a solo bass instrument with no high-frequency content, where the rate of change of the waveform is uniformly fairly slow. But if that is the explanation for bass sounding better at 24-bit, I can't see why the improvement would be noticeable in the context of a mix. After all, the waveform for a full mix typically displays a fairly rapid rate of change most of the time, meaning that the percentage error is low most of the time.

well I still think you should have gotten http://www.russandrews.com in to advise on the mouthwateringness of the resulting bass

Actually, when *ARE* you going to do an interview with Russ Andrews?

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~~~ A weasel hath not such a deal of spleen as you are tossed with! www.feline1.co.uk ~~~

Sam,
It was Hugh who said that.

But on the subject - many of the arguments for using different mic's, preamps, bit-rates etc... only become apparent on solo testing and A/B tests etc...
In full mixes many of these differencies become less important, and there'e something called creativity which at times can upset the rule book.

PS. Saying the bass was better is subjective, regadless of the technical reasoning, even it was 'true' on paper (if you know what I mean).

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Jack of all trades, master of some.

Quote Hugh Robjohns:

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He might be... but I still can't see the flaw in the argument. I can see the flaw in his numbers, but not the argument...

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Well look at it this way: what he's saying is that a bass signal with the addition of some quantisation noise is going to sound worse than a treble signal with the same noise. That noise is pretty much like adding white noise to the signal. So would a bass signal with -96dB white noise added sound somehow much worse than a treble signal with the same noise added?

Well maybe there could be some psycoacoustic arguement about this, but then the same would hold true for analog equipment - the bass should sound even worse than the 16 bit digital signal because the noise floor is higher.

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Midipicks - the all new MIDI Guitar forum...

I still want to hear evidence that the banjo was worth recording. People who make sweeping statements like that should put up or shut up!

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Dynamite with a laser beam...

Hugh, thanks very much for your detailed reply. I need to run my slide rule over the numbers and iron my brain before digesting it all; I’ll get back to you.

Quote Lars Farm:

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Quote Crow:

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Yeah, hats off to Monsieur Fourier, but this is completely off topic!

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It was in response to what you snipped from your own statement:-"My choice of sine waves in my example was unfortunate; replace that with a complex waveform and my point will be clearer.". Fourier shows that these are the same.

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Sorry if I was a bit blunt with you, but I’m interested in the article being discussed here and this thread already has a very poor SNR, so I was hoping we could keep it on topic. In the context of the article being discussed here, I couldn’t see the relevance of your posts.

"On top of old smokey...."

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Jack of all trades, master of some.

Quote Hugh Robjohns:

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Where is the problem? I'm intrigued to know

hugh

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Could it be that while the quantization error for each sample is larger for low frequency waves, the number of samples during the cycle of the wave is much bigger so the error averages out? So in practise, over the whole cycle of the wave, we have the same error percentage over the whole cycle?

There is a relationship between the number of samples during one cycle of a wave and the percentage of error due to quantization at each sample. Maybe someone that knows the exact maths can tell us what that relation is. Hugh?

Also, as the data goes through a reconstruction filter in the DAC, the graphs in the article seem to be a bit misleading. The angles (any angles) in the graph imply (infinitely) high frequency content which isn't realistic AFAIK. How does the quantization error in the waveform look at each point (including points between samples) after reconstruction?

I really do like the waveform preview in Audition/Cool Edit as it shows the wave after reconstruction. You can even see inter sample peaks going over 0 dB FS on some material if you zoom in enough but I disgress.


Hugh, you write the following:

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There will always be quantisation errors, That is inherent when you quantise something because of the discrete nature of the quantisation levels. When the system is correctly dithered, those errors are distributed randomly, instead of being related to the signal amplitude, and hence manifest as noise instead of programme-related distortion.

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Assuming a theoretical ideal system with ideal TPDF dither, are we not effectively increasing the resolution of the system by linearising the quantization steps and trading that in for noise? In other words, arn't the quantae steps "removed" for all practical purpouses?

If I take a 16 bit recording, convert it to 24 bit, reduce the volume by 96 dB or more, convert back to 16 bit with TPDF dither applied and then normalise, I still hear the original recording below the dither noise.

At the point in this process after the volume reduction by 96 dB or more, the entire signal is encoded in the lower 8 bits of the 24 bit words (bits that don't exist in a 16 bit word). Yet, after bit reduction with dither, the original signal is still there. Doesn't this support my comment that the quantization distortion is removed (but traded in for noise)?

And if what I describe above is correct, isn't it so that discussing this topic without including dither is a bit pointless?

UnderTow

Quote Hugh Robjohns:

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However, if quantised to 24 bits, there will be 255 more quantising levels in between each and every 16 bit quantising level.

hugh

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What happens when you then turn it back to 16bit to put on a CD. The level the sample is, cannot be represented in 16bit format? Is that what dither is about? Do the articles undertow mentioned hold the answers?

Quote UnderTow:

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Could it be that while the quantization error for each sample is larger for low frequency waves, the number of samples during the cycle of the wave is much bigger so the error averages out? So in practise, over the whole cycle of the wave, we have the same error percentage over the whole cycle?

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I don't think it's quite that, but nearly. What he's done by looking at a one sample interval is to compare the high frequence component of the quantization noise to the high frequency component of the signal (which is obviously lower in a bass than a treble sound).

You could make a opposite arguement: for treble signals sounding worse if you compare the low frequency component of the quantisation noise (which is just as large as the hf component) to the low frequency component of the signal. But you couldn't do that with a little picture that everybody could 'understand' (and so be mislead by).

In fact you could make a better case that way because treble signals in music are at a much lower level than bass signals (something else the article doesn't mention).


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Midipicks - the all new MIDI Guitar forum...

Quote UnderTow:

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Could it be that while the quantization error for each sample is larger for low frequency waves, the number of samples during the cycle of the wave is much bigger so the error averages out? So in practise, over the whole cycle of the wave, we have the same error percentage over the whole cycle?

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Hmmm... time averaged noise... now that is an interesting concept...

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Also, as the data goes through a reconstruction filter in the DAC, the graphs in the article seem to be a bit misleading. The angles (any angles) in the graph imply (infinitely) high frequency content which isn't realistic AFAIK.

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er... it was a deliberately simplistic diagram intended to explain the difference in quantising errors in an A-D. Wave reconstruction in the D-A isn't relevant to that argument.

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How does the quantization error in the waveform look at each point (including points between samples) after reconstruction?

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The quantisation error only exists at the sampling instants, by definition, and at those points the graph as shown is correct. What is technically incorrect is the straight line used to join the dots.... but I can't help thinking you are looking for flaws here when none really exist (or are relevant at any rate)

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Assuming a theoretical ideal system with ideal TPDF dither, are we not effectively increasing the resolution of the system by linearising the quantization steps and trading that in for noise? In other words, arn't the quantae steps "removed" for all practical purpouses?

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Yes, you can certainly look at it that way. But this view point, and my explanation above are not at odds with each other, just alternative ways of looking at the same thing.

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If I take a 16 bit recording, convert it to 24 bit, reduce the volume by 96 dB or more, convert back to 16 bit with TPDF dither applied and then normalise, I still hear the original recording below the dither noise.

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I won't ask why you'd want to, but yes, assuming your DAW has sufficient internal dynamic range, that would indeed be the case.

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At the point in this process after the volume reduction by 96 dB or more, the entire signal is encoded in the lower 8 bits of the 24 bit words (bits that don't exist in a 16 bit word).

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Not strictly true. The full 16 bit original signal would be encoded using floating point maths to retain the maximum resolution. Only at the point of outputting the 24 bit file would it be truncated and dithered to sit in the bottom eight bits.

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Doesn't this support my comment that the quantization distortion is removed (but traded in for noise)?

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Er... it's a very odd way of demonstrating the point, and I'm not sure what you're getting at anyway. Was there ever any doubt that dithering converts nasty quantisation errors into benign noise? I'm not sure what point you are trying to address here. Sorry.

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And if what I describe above is correct, isn't it so that discussing this topic without including dither is a bit pointless?

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I think what you are trying to describe is correct... but no, dither still isn't relevant to the point Nichols was arguing.

He is arguing that an LF signal coded with 24 bits has less quantising error than when coded at 16 bits, but that the proportionate error for HF signals does not change improve anything like as much. That is true. Yes, if the system is properly dithered, those errors are essentially random noise not distortion artefacts, but the facts remain.

Hugh

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Technical Editor, Sound On Sound

There's a part I don't get:

Ok so we know that there is a difference in the amount of levels 24Bit give us over 16Bit and 24Bit gives us more to represent the sound,but isn't this just part of the A/D D/A conversion aren't there other factors which contribute to the sound that appears at the I/O?
What about the filters,clocks etc?

Would like to know more about how Lo and Hi frequencies are dealt with in analogue and digital domains and what problems they cause.

Thanks

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Music Manic

Quote Hugh Robjohns:

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Quote UnderTow:

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Could it be that while the quantization error for each sample is larger for low frequency waves, the number of samples during the cycle of the wave is much bigger so the error averages out? So in practise, over the whole cycle of the wave, we have the same error percentage over the whole cycle?

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Hmmm... time averaged noise... now that is an interesting concept...

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Well isn't that how we hear things? Isn't that why we talk about RMS values as they are closer representations of how we as humans hear things?

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Also, as the data goes through a reconstruction filter in the DAC, the graphs in the article seem to be a bit misleading. The angles (any angles) in the graph imply (infinitely) high frequency content which isn't realistic AFAIK.

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er... it was a deliberately simplistic diagram intended to explain the difference in quantising errors in an A-D. Wave reconstruction in the D-A isn't relevant to that argument.

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How so? We can only hear stuff after it has gone through the DAC with the relevant reconstruction filters so I don't see how looking at a plot that doesn't represent the final waveform explains what we do or don't hear.

Maybe I am missunderstanding something here. Would you care to explain?

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How does the quantization error in the waveform look at each point (including points between samples) after reconstruction?

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The quantisation error only exists at the sampling instants, by definition, and at those points the graph as shown is correct.

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Yes but how does it affect the wave after reconstruction? Surely this is relevant?

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What is technically incorrect is the straight line used to join the dots.... but I can't help thinking you are looking for flaws here when none really exist (or are relevant at any rate)

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I am trying to understand things. At the moment I don't quite understand why the reconstruction filters are irrelevant.

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Assuming a theoretical ideal system with ideal TPDF dither, are we not effectively increasing the resolution of the system by linearising the quantization steps and trading that in for noise? In other words, arn't the quantae steps "removed" for all practical purpouses?

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Yes, you can certainly look at it that way. But this view point, and my explanation above are not at odds with each other, just alternative ways of looking at the same thing.

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Well if the dithering process linearises the quantization steps, I don't see how the quantization error (when properly dithering) affects the low frequency waves in the way that Mr Nichols seems to be describing. Basicly, I don't understand his explanation and I still doubt it is correct. That might be due to my lack of understanding but that is why I continue this discussion.

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If I take a 16 bit recording, convert it to 24 bit, reduce the volume by 96 dB or more, convert back to 16 bit with TPDF dither applied and then normalise, I still hear the original recording below the dither noise.

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I won't ask why you'd want to, but yes, assuming your DAW has sufficient internal dynamic range, that would indeed be the case.

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Obviously to try and understand things. Not something I would do in every day recording.

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At the point in this process after the volume reduction by 96 dB or more, the entire signal is encoded in the lower 8 bits of the 24 bit words (bits that don't exist in a 16 bit word).

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Not strictly true. The full 16 bit original signal would be encoded using floating point maths to retain the maximum resolution. Only at the point of outputting the 24 bit file would it be truncated and dithered to sit in the bottom eight bits.

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Indeed and that is why you have to save the intermediary file as a 24 bit file to make sure that SF is not just using a 32 bit float intermediary file. (Sorry for not claryfing that in my original description).

Anyway, even with saving the file as 24 bit file, the signal is still there after reopening the file, bit reducing to 16 bit and normalizing.

After conversion to 16 bit, the entire signal is encoded in the lowest 2 bits of the 16 bit format. (2 bits because TPDF has a 2 bit amplitude peak to peak). In other words, the quantization steps have been linearised and are not actual steps any more (and we trade this in for noise).

Do you see what I am driving at? If I am completely wrong, please explain me where my misunderstanding lies.

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Doesn't this support my comment that the quantization distortion is removed (but traded in for noise)?

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Er... it's a very odd way of demonstrating the point, and I'm not sure what you're getting at anyway. Was there ever any doubt that dithering converts nasty quantisation errors into benign noise? I'm not sure what point you are trying to address here. Sorry.

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I am trying to demonstrate the linearization of the quantae steps by dithering. And if I am correct in my understanding, this contradicts Mr Nichols' explanation AFAICS.

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And if what I describe above is correct, isn't it so that discussing this topic without including dither is a bit pointless?

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I think what you are trying to describe is correct... but no, dither still isn't relevant to the point Nichols was arguing.

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I don't get this. If the steps are linearized, then his explanation is incorrect. Again, I might be misunderstanding things but I need convincing of that.

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He is arguing that an LF signal coded with 24 bits has less quantising error than when coded at 16 bits, but that the proportionate error for HF signals does not change improve anything like as much. That is true. Yes, if the system is properly dithered, those errors are essentially random noise not distortion artefacts, but the facts remain.

Hugh

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Hmmm ... I'm still not convinced. I think his argument is only valid in an un-dithered system. But AFAIK, dither is an essential part of digital audio. If we leave it out, we are not talking about practical implementations of sampling theory. (Idem for reconstruction filters in the DACs).

UnderTow

I've just read this entire thread, and it's taken me all day, but I don't understand it AT ALL. I thought digital audio was perfect quality, like CDs? It would help if everyone stopped going on about 'dithering', 'converters', 'bits', 'resolution' and all the rest of it. I mean wtf?? Doesn't anyone around here know ANYTHING about audio?