Hi Guys
I've been reading this thread and Rogers article and trying to work out how 24 bit may be superior to 16 bit for bass sounds.

I know reletivly little about digital conversion but I have a theory that may suggest something to support Rogers article.
I don't want to spread missinformation so please correct me if I'm wrong !!!

My thoughts are (assuming no dither);-

What happens to a signal that is between two quantise levels, at the peak of its waveform for a long period (most likely with a slow bass note)

If you look at my

example
(the pink area is a low bit 'recording' and the green area is a higher bit recording)

At the top of the waveform the 'low bit recording' never reaches the next highest quantise level. My understanding is that the top of the recorded waveform will be flat this would introduce a mild distortion which would muddy the sound slightly. The same would happen to higher frequencies but the distortion would be at a higher frequency possibly above human hearing or just making the sound slightly harsher.

Would these distortions (if they exist )be noticeable after dithering??

What do you think ???

I hate to make fun of this thread, because it is infact pretty amazing to see the "battle of minds" if you will.

I would say however, we all phrase things differently, we all have our "opinions". But nobody has mentioned

The Flux Capacitor





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There is nothing Grim about this Reaper
We Fell From The Sky

Quote Jumpeyspyder:

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If you look at my

example
(the pink area is a low bit 'recording' and the green area is a higher bit recording)

At the top of the waveform the 'low bit recording' never reaches the next highest quantise level. My understanding is that the top of the recorded waveform will be flat this would introduce a mild distortion which would muddy the sound slightly.

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There would be a red block at the top that goes beyond the blue curve up to the next horizontal red line. However, in reality, besides the effect of dithering to linearise the quantae steps, you have a reconstruction filter on the output of the DAC so what comes out of your converters is not a stepped waveform like in your graph but rather a smoothed curve that would look like the blue line.

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The same would happen to higher frequencies but the distortion would be at a higher frequency

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I'm not exactly sure what frequency the distorton would be at but yes, in an undithered system, the quantization distortion is correlated to the input signal.

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possibly above human hearing or just making the sound slightly harsher.

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Assuming that the converters are limited to audio bandwidth, in a proper system, anything above the bandwidth (above human hearing) has to be filtered out by anti-aliasing filters or it will fold back down into the audible bandwidth.

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Would these distortions (if they exist )be noticeable after dithering??

What do you think ???

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Simply put, the idea of dither is to remove the quantization distortion trading it in for broadband noise. Dithering the signal after any quantization distortion is introduced has no effect on that distortion. It is too late.

Dither, anti-alias filters, reconstruction filters etc are integral part of sampling theory. If they are not part of the system, the system is broken.

PS: Check out this article by Nika Aldrich about dither: http://www.users.qwest.net/%7Evolt42/cadenzarecording/DitherExplained.pdf< /a>

UnderTow

Edited by UnderTow (09/06/06 11:52 AM)

Thanks for the comments Hugh. Very civil. See my comments...

Quote Hugh Robjohns:

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Quote GJordan:

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My first comment, he is doing error as a percentage of the 'step size', since when has this been a valid measure of error for audibility?

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I think Roger was simply using his (bizarrely calculated) 'percentages' as a way of highlighting the relative sizes of the proportional errors.

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Yes, that's what he's doing, but he's totally misrepresenting the proportional size of the errors, as he's calculating them as a proportion of the change in sample value, whereas he should be showing them as a proportion of the actual sample value. But even more correctly, he should be (as you mention later)looking at the rnage of error values and relating this to signal level. If he did that, you would see no dependency to the slope or frequency of the signal in the way he describes.

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Error signals/noise are normally in absolute terms or relative to the signal level, not the instantaneous rate of change of 'voltage' level.

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The voltage increment denoted by the least significant bit in a digital quantiser is, by definition, an absolute, fixed amount, with a clearly defined relationship to the peak signal level. Roger wasn't talking about instantaneous changes as such, just the possible level differences between adjacent samples.

As I undertsand it, essentially he was comparing the difference in error signal amplitudes between 16 and 24 bit quantisation... although as we know, in a properly dithered system there is no error signal, only random noise...

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I wasn't really clear here, but I was meaning instantantaneous change = change from one sample to the next. And this is what he's using as his base for calculating the error size. And this 'instantaneous change' is not necessarily a single 24-bit LSB, but many.

Also, he isn't comparing the error signal amplitudes, he's actually comparing the change in error from one sample to the next. Calculating the error signal amplitude doesn't involve any differencing between sample values; the error is the difference between the 'right' sample value and the actual value, for a single sample. For a single sample this is the instantaeous amplitude. If you look at these over many samples you can see how the signal behaves and calculate other useful measures (RMS level, peak-peak max, frequency content, etc.)

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but remember the peaks and troughs of the waves have very small differences between samples. The errors he talks about, are basically at the same signal level irrespective of frequency.

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Sorry, don't follow the first sentence at all. If you compare the area where an analogue signal passes from the negative half cycle to the positive half cycle (the zero-crossing region) then, when sampled, adjacent samples of a low frequency signal in this are are likely to have relatively similar quantisation values -- becaue the rate of change of the signal is reltively low. Adjacent samples of an HF signal are likely to have significantly different quantisation values because the rate of change of the signal is relatively high.

As I see it, this was the fundamental assertion on which the rest of Roger's thoughts were based... and this bit, at least, is correct.

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Yes, if you compare samples at the zero-crossing region (for a single sinewave), but not if you compare samples at the top of the sinewave, where the voltage is changing from increasing to decreasing (and vice-versa at the botttom). I didn't see anything in the article alluding to having to measure at zero-crossings. But again, my point is that this difference is irrelevent to the level of quantization error signal. This difference does not define the level of the main signal.

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Also, his whole premise that the noise level is 'less', and hence less audible, for higher frequencies is, er, inaccurate.

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Quite

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Phew, I'm glad we agree on that. I'm just trying to point out why his explaination that it is, is wrong.

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Let's ignore dithering for now, and just focus on the quantization noise aspect, as the article does (rightly or wrongly).

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This is treading the same dodgy ground as Mr Nichols... and strictly, we should be talking about quantising error rather than noise, to avoid further confusion. By definition, noise is random whereas quantisation error is statistically related to the input signal. A correctly dithered system exhibits a noise floor. An incorrectly (or absent) dithered system exhibits no noise floor at all, but signal errors (distortions) which are related to the source sound.

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OK, a little bit of terminology mismatch here. I'd have to check the technical texts, but I thought the technical definition of noise in a signal, is anything that is not part of the actual signal you are trying to capture/measure. And this is not necessarily random. But, no big deal. I'll be sure to refer to quantization 'noise' as quantization error, and error signal.

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A/D output is the same as adding (mixing) a noise signal to your 'prisine' signal.

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This is getting messy. The output of an A-D is a sequence of binary values. However, in a properly dithered system, the signal encoded in those binary values is, essentially, the source signal plus a very small amount of random noise.

In an undithered system, the encoded signal is essentially the source plus a raft of source-related distortions. The amplitude of those distortions remains fixed (and related to the size of the LSB) -- and so take on a greater significance and audibility as the source signal decreases in amplitude.

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Let me restate it better, the signal represented by the A/D output (i.e. the perfecty reconstructed signal) is the same as your 'pristine' analog signal (approriately bandwidth limited of course) mixed with the error signal (i.e. the reconstructed version of the error signal). Remember I am not incorporating dither here. I'm just rying to illustrate that the effect of quantising (without dither) is just the same as, in a 'perfect' analog domain, mixing another undesired real signal to your desired signal. Hence, the error signal can be, and should be, analysed as any other signal (which the acticle does not do).

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If you regard 24-bit as perfect (or effectively perfect), you can hear this error signal for 16-bit quantisation by simply having a full 24-bit signal, truncating it to 16-bit then taking the difference between this and the original.

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First, in a perfect world, an undithered 24 bit system exhibits the same problems as an undithered 16 bit system...low level signals will still produce quntisation errors and the same distortions. The only difference is the absolute amplitude of those distortions.

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Absolutely, my point is that you can tell someting about the nature of the 16-bit quantization error signal by using 24-bit, as the quantisation error signal level of pure 24-bit is 48dB less than the signal you're looking at, the 16-bit quantization error signal. This is a simple 'mathematical' exercise to investigate the characteristics of the 16-bit quantization error signal that can be done in a 24-bit audio editor.

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Interesting to play with, perhaps, but not really relevant to the
practical difference between recording with a properly dithered 24 bit A-D versus a properly dithered 16 bit A-D -- which was the premise of Roger's article.

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Er, not quite, Roger's article completely ignores properly dithered signals. I thought this was already understood. Otherwise, he's just looking at random noise levels, not quantization errors.

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What the article is suggesting is that when you add this noise to a high frequency signal you hear it less than with a low frequency signal.

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ROger was suggesting that if you count up the number of quantising levels crossed (in terms of 24 bit LSBs), the relative proportion of maximum potential error compared to the overall difference in quantising level for two adjacent samples is far greater for LF signals than for HF signals. The pure logic of what he said seems right to me, but the concept itself is deeply flawed and not applicable to practice.

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Jackpot! This should be requoted in it's own entry. Very well put - although I might have said "and not applicable to anything in audio (theory or practice, dither or no dither)." Hopefully I've covered some of the reasons why.

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If you have a regular quiet mid-range sound that you mix with just a louder low frequency signal, then mix it just with a louder high frequency signal
does that mid-range sound sound quieter with the high freq added, than with the low freq added? From the article's logic it would.

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Well, we might have to take noise masking into account here... but really, you are talking about mixing dissimilar, unrelated sounds. He was talking about distortion products generated by and related to the specific source... but we are getting bogged down debating irrelevant points.

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Right, signal masking does start to come in at this point, but that would be getting too far off into deep technicalities. Ones in which I'm less well versed (that's the domaian of the audio compression research gurus and others).
My main point was that the quantization error signal is a 'real' signal, and since is the prodcut of a non-linear process produces frequency components that are not present in the original signal. But the article is implying that these components are heard less when present with a high frequency signal than with a low one. Of course further investigation would be, what are the frequency components that are produced for different input signals? That is a very complex question. I don't know as much as I'd like about the answer to that question. Be we all know that they don't sound good.

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I have a lot of respect for fighter pilots, but I'm not going to give much weight to their explanations of the nuts and bolts of aerodynamics. Roger Nichols is an ace fighter pilot.

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Amusing analogy! I like it...

hugh

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Thanks.

Quote Steve Hill:

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Quote gerard:

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...anyone got anymore banjo jokes?

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Q. What's the difference between a 4-string and a 5-string banjo?

A. A 5-string burns for longer

Q. What's the definition of an optimist?

A. A banjo player with a pager

Q. What's the definition of perfect pitch?

A. Throwing a banjo into a skip/dumpster without touching the sides.

(The old ones are the best)

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love it!

thanks dude!

Quote GJordan:

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Yes, that's what he's doing, but he's totally misrepresenting the proportional size of the errors, as he's calculating them as a proportion of the change in sample value, whereas he should be showing them as a proportion of the actual sample value.

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I take your points, but can't help thinking this is all a bit pointless. The technical content of the article was flawed in so many ways that picking at one small bit seems churlish...

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I thought the technical definition of noise in a signal, is anything that is not part of the actual signal you are trying to capture/measure.

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Hmmm.. That sounds like a mathematician's definition to me. In the engineering world, there has always been a difference between truly random errors -- NOISE -- and programme-related errors -- DISTORTION. In some cases noise can be benign (as in dither noise) and sometimes rather annoying and intrusive. Likewise, disortion is acceptable (or even desirable) in some situations and highly irritating in others. It all depends on the context and the human subjectivity to it. This is audio we are talking about, after all...

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I'm just rying to illustrate that the effect of quantising (without dither) is just the same as, in a 'perfect' analog domain, mixing another undesired real signal to your desired signal.

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But it's not. An undithered digital system is inherently non-linear, whereas an analogue system is (generally) linear. You really can't compare the two in the way you are trying to.

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Er, not quite, Roger's article completely ignores properly dithered signals. I thought this was already understood.

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Yes, agreed, ... but he was treating his analysis as if the systems were working properly when his explanation was based on undithered quantisation errors. Basically what we have here is a large bucket of smelly stuff and we have spent five pages poking at it with a stick to see what animal it has come from! But it really doesn't matter -- it's still a big bucket of smelly stuff, and the best thing we can all do is step away...

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My main point was that the quantization error signal is a 'real' signal, and since is the prodcut of a non-linear process produces frequency components that are not present in the original signal.

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Again, this is all flight-of-fancy stuff. Non-dithered digital systems aren't relevant to the practical use of modern digital systems. Other than when cocking things up when changing word lengths, no one is going to come across undithered digital systems. So the artefacts generated by undithered systems, while 'real' enough in broken sysrtems, don't exist in properly working ones, and so aren't relevant in the practical world either.

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But the article is implying that these components are heard less when present with a high frequency signal than with a low one.

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The article was simply Roger's attempt to justify his entirely subjective impression that bass sounded better when recorded with 24 bit systems than with 16 bit systems.

First, I'm not sure we have any agreement that this is an impression shared with anyone else. "4 bit systems certainly sound better than 16 bit ones, but whether the bass is markedly better than the treble I'm not so sure.

Secondly, as we have agreed, his attempts to find a technical justification have been shown to be deeply flawed, both in fundamental concept and its argument. It's probably best to just draw a line there and move on...

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Of course further investigation would be, what are the frequency components that are produced for different input signals? That is a very complex question.

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But utterly irrelevant since who would want to record audio with a broken, non-dithered A-D converter?

Hugh

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Technical Editor, Sound On Sound

Quote Hugh Robjohns:

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But utterly irrelevant since who would want to record audio with a broken, non-dithered A-D converter?

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Exactly. Unless that's all we had in the early 1980's.

Are you saying older 16-bit systems as used in early 80's digital recorders were always properly dithered, completely linear properly-designed systems?

It's been a long time since I read his article (and I'm not digging it up again, Thank You), but I took the two concepts discussed in his article as being related: both pertained to a design problem that plagued early digital recorders, and problems still relevant to anyone in 2006 who deals with digital recordings made on equipment used in the early days of digital audio, or who is familiar with the typical "sound" of these systems.

1) The first issue pertained to problems with archiving, since trying to do a straight digital transfer from 16-bit to 24-bit (as a young engineer might be tempted to do) would be inherently flawed: such data transfer would bypass the D/A converters which were chosen by the designers in an attempt to compensate for the non-linearity of inherently flawed A/D converters. That was his point as to why he did the archival transfers via audio to a 24-bit recorder.

2) I read the second topic (his commenting on the perception that bass sounds better in 24-bit vs 16-bit systems) not as an explanation of the effect those (8) additional bits would make using a "properly-dithered and linear" modern 24-bit vs. properly-dithered 16-bit recorder, but as a statement that the inherent non-linearity of the D/A converters used in older 16-bit machines was not as mitigated as the designers might've hoped, with this as evidence that the 'matched' converter approach apparently had limitations.

In other words, apparently enough error is introduced in the flawed A/D converter that is not overcome by passing thru the "compensating" D/A converter to still allow the types of effects that result in subjectively poorer detail in the low end. The non-linear errors on the front end were still present, regardless of compensation on the A/D end.

Hence the point that people may think they're comparing the quality of 16-bit to 24-bit recorders in a fair manner, but may be making a mistake thinking both machines are properly dithered, as if the ONLY variable they're changing is bit depth. It's obviously not so simple, as they're actually comparing old improperly designed 16-bit systems to modern 24-bit machines.


I don't know if this was his intent, but that's how I read it. Admittedly, if it was his point, he did a poor job of explaining it, as this required alot of reading between the lines (harder to understand than a Steely Dan lyric, I'd say).

Likewise, I don't know if this explanation is even technically valid. I do think some of the technical boffins here got lost in the details, and lost the forest for the trees rather than going with the gestalt of what he was saying. We'll let you guys tear it apart, and see if the concept survives scrutiny.

As another disclaimer, I also don't know if his words were published exactly as submitted, or if someone made attempts to "clarify" his article: it's possible the editor didn't really get his point in the first place, and just made matters worse by trying to 'fix' it! Maybe a statement on this would be helpful.

But anyway you cut it, it's a mess.

Perhaps the better question is why SOS didn't work out these concerns amongst it's editorial staff BEFORE running with an article that some must've felt was full of holes and hot air? Is this not the job of the editors? Why didn't they contact RN BEFORE to clarify what he meant? I know everyone wants to give RN a black eye over this, but it's just as embarrassing to SOS, IMO.

On second thought, maybe we should just move on, as it's really quibbling at this point.

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 Feefer:

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On second thought, maybe we should just move on, as it's really quibbling at this point.

Chris

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unless anybody has got any more banjo jokes they want to share?


anybody?

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I know everyone wants to give RN a black eye over this, but it's just as embarrassing to SOS, IMO.

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I happen to agree here, and also wondered why it was not scrutinized a bit better before going to print.

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James
"Never interrupt your enemy when he is making a mistake" ~Napoleon Bonaparte~

Quote Feefer:

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Perhaps the better question is why SOS didn't work out these concerns amongst it's editorial staff BEFORE running with an article that some must've felt was full of holes and hot air? Is this not the job of the editors? Why didn't they contact RN BEFORE to clarify what he meant? I know everyone wants to give RN a black eye over this, but it's just as embarrassing to SOS, IMO.

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Agreed. I'm sure alot of people that have read this article and don't visit the forum or this thread are confused and/or misinformed.

If SOS have any respect for their readers and correctness of information, a full unconditional retraction in print is in order. Anything less would be very disapointing and an insult to the readership.

UnderTow

perhaps we can pick the best banjo jokes for the printed correction?

shall we have a vote on the top 5 banjo jokes?

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Are you saying older 16-bit systems as used in early 80's digital recorders were always properly dithered, completely linear properly-designed systems?

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No, definitely not. Many of those early systems were pretty ropey and did the 'digital cause' a lot of damage which we are still fighting today...

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1) The first issue pertained to problems with archiving, since trying to do a straight digital transfer from 16-bit to 24-bit (as a young engineer might be tempted to do) would be inherently flawed: such data transfer would bypass the D/A converters which were chosen by the designers in an attempt to compensate for the non-linearity of inherently flawed A/D converters. That was his point as to why he did the archival transfers via audio to a 24-bit recorder.

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Yes. It was an interesting observation, but an entirely correct one. With that particular recorder's design, the digital data on tape was (slightly) non-linear because of the inherent A-D inaccuracies.

However, I'm less convinced of the validity of finding a replay machine 20 years later in which the D-A converters would compensate perfectly for an unknown set of A-D converters.... It's one thing to optimise each channel's A-D and D-A on a single machine, quite another to match every machine everywhere...

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2) In other words, apparently enough error is introduced in the flawed A/D converter that is not overcome by passing thru the "compensating" D/A converter to still allow the types of effects that result in subjectively poorer detail in the low end. The non-linear errors on the front end were still present, regardless of compensation on the A/D end.

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Hmmm... see my comment above!

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Hence the point that people may think they're comparing the quality of 16-bit to 24-bit recorders in a fair manner, but may be making a mistake thinking both machines are properly dithered, as if the ONLY variable they're changing is bit depth. It's obviously not so simple, as they're actually comparing old improperly designed 16-bit systems to modern 24-bit machines.

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Indeed so. Lots of things have improved in 20 years. Dither is one, but so is the anti-alias and reconstruction filtering, clocking accuracy and stability, and all manner of converter issues such as droop and step non-linearities.

I won't comment on the last question....

hugh

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Technical Editor, Sound On Sound