should I dither? (I can't make my mind up (groan...))

According to my reading, the word dither (from the old middle English to tremble), and its practical use, goes back to WWII bomb sight computers, where deliberate addition of vibration made the mechanism work more accurately.

Dither effectively eliminates quantization distortion.

that isn't exactly accurate.  It doesn't eliminate quantization distortion, but it randomizes the differences between what the digital resolution can express and resolution of original signal (which typically is a digital file with a greater resolution (those as Steve pointed out dither has demonstrated some of it's most noticeable effects on files that were simply converted with poor filtering algorithms).  Quantization error remains, but perception of it changes.

Which on the surface at least could suggest that dithering while stepping down from 32 bit to 24 bit, particularly if any processing was done on the 32 bit file after the original ADC would actually make sense

But that is not really issue I looking to address here

OK, as much as I'm going to hate myself in the morning I'll try to gradually make sense of what I'm saying, maybe even suggest why it isn't merely pointless (in my opinion)

AndyH (specifically, but of course anyone is free to jump in), an ABX test, on your system, with regard to the OP's initial inquiry would be expected to reveal what?  What are the options?  What could those options reveal about the underlying audio?

Dither effectively eliminates quantization distortion.

that isn't exactly accurate. 

It isn't accurate at all! The best you could say was that it covered it up, I think, and it gets worse; if you have monotonicity errors, then it's going to take more than 1 bit of noise to cover them up, isn't it?

On any modern converter, there is no real-world justification for dithering between 32 and 24 bits at all.

Audiophillia is a faith based creed. Members of the faith believe many audio related fables that cannot logically be related to anything physical; These fabels are either simply accepted on faith or they are based on purely subjective evaluations, A few of these beliefs, though not accepted by those who demand evidence, may have some truth in them. Perhaps we haven’t learned to measure certain aspects of distortion, noise, or whatever that are actually present.

BUT,  research in perception long ago discovered that people often can hear or see subtle things, or sometimes not so subtle things, that are just not there. If they have an expectation or belief or misunderstanding about what they will or should experience, they may well experience something that is not in the energies impinging upon their sensory organs. Expectations are often based on factors that are irrelevant to the case at hand, such as bigger is better or more expensive is better. More recent research has extended these findings, not contradicted them.

You probably know this and certainly could not live in this society without being aware that medical research involving drugs, in particular, and quite a few other treatments, generally requires double blind testing because of these influences. I’m just making these general opening statements about the topic to set the background, and hopefully avoid any further misunderstanding about the context of what I tried to say.

You said that the choice of whether or not to dither is subjective. I wouldn’t dispute that one could proceed on a subjective basis, but if one does some sighted comparisons on dither vs no dither with such audio as is under discussion, he might come to almost any conclusion. Look at the audiophile forums for verification. Sighted tests are generally only subjective.

However, most of those possibly conclusions would be based on imagination (expectation, beliefs, etc.), not on what signals are being processed by his ears. Almost certainly, any conclusion except ‘there is no audible difference,’ would not be true, even though he might be certain that some difference is clearly evident.

Doing blind comparisons will eliminate those influences. If one does the tests correctly, the software will provide evidence that he does hear a difference or that he doesn’t, it is no longer a subjective evaluation. He can come to a conclusion based on reality, not fantasy (although it is the case that some people refuse to accept contrary evidence and maintain their faith regardless).

Note I did say “done correctly.” There are some ways to manipulate double blind tests with the available computer software, and people sometimes base their conclusions on correct procedure but with too few audio samples and/or too few trials, both of which can badly skew results. Hopefully I haven’t written something is this post that can easily be interpreted as wildly different than I intended.

Quantization error is thus decorrelated from the signal and the effects of the quantization error are randomized to the point of elimination. However, although it greatly reduces distortion, dither adds some noise ... . Ken C. Pohlmann, Principles of Digital Audio, 4th edition, p 39.

Is there an error in the statement above or have I just misunderstood it?

What is an example of a monotonicity error?

Dither effectively eliminates quantization distortion.

that isn't exactly accurate. 

It isn't accurate at all! The best you could say was that it covered it up, I think, and it gets worse; if you have monotonicity errors, then it's going to take more than 1 bit of noise to cover them up, isn't it?

On any modern converter, there is no real-world justification for dithering between 32 and 24 bits at all.

Ironic nuance does not travel well on the internet.  I am at least colloquially aware of the inaccuracy. Awareness based less on education in underlying principles then experience processing audio (and to an extent graphics, which was my first exposure to dither)  And I am convinced of the no real world justification of the 32-24 bit dither.

If you simply read colloquially phrased descriptions of dither and looked at colloquial descriptions of digital files it would be possible to assume that dithering between  32 & 24 might have some impact and the above post was meant to ask the specific question at the end concerning ABX testing

all of which seems like verbal noise . . . except I'm dealing with clients with assumptions based pseudo-objective stances with far greater frequency and intensity then even in the days of analog/tape when everything was magic . .. (not enough reverb for a single, that guy's never had a single longer then 2 min. 54 sec. so cut 10 sec off that and we'll pay you, in some ways I think I am a bit nostalgic for the days when the client was the producer and the producer was militantly proud of ignorance of technology) . . . I quite understand the tone of the SOS oped piece that raised some debate in 'ear training' thread.

As I recommended Pohlmann's book to Andy H back in my first exchange with him, probably close to 8 yr. ago, it was almost comforting to see him quote . . . but a bit disconcerting that in addition to perhaps not understanding it, he does not seem to be aware that he doesn't understand.  Principles of audio and how they relate to recording seems to remain one of those unknown unknowns . . . and it is situation that I find so frustrating in real world economics

one reason I do post on these forums is that unfocused stumbling here helps me craft more succinct, politic replies for face to face use, rather then simply sighing and beating my head against the wall

(perhaps it is slightly mean spirited to mention that my 'note sealed in the envelope' guess was that AndyH would not respond to the specific question.  My debate, kind of obviously was not with dither or its effectiveness, but with how a single user ABX 'test' was anything but subjective, with regard to the OPs inquiry. and on an ancillary note why he felt the need to interject it?  But hey today I get to deal with a situation where a guy proud of the fact that he uses cheap drum kits (for their 'authenticity') has now heard what they sound like when I've done the best that I can to make them fit the arrangement . . . I tried to politely discuss drums, their sound their limitations with the potential rest of the 'sound' of the recording, tried to get him to listen to raw tracks . . . suggest gently that even my authentically not great Mapex set might actually sound better . . . now I am basically done with the project want to get paid and he is sure it's my fault that the drums sound less then stellar (and on more the one level I actually agree with him . . . I'm the person that knew what they were going to sound like going in) . . . anyway I don't drink near enough coffee these days !)

AndyH (specifically, but of course anyone is free to jump in), an ABX test, on your system, with regard to the OP's initial inquiry would be expected to reveal what?  What are the options?  What could those options reveal about the underlying audio?

Perhaps I did not respond to the specific question exactly, as it has several non-relevant or meaningless components, but I did answer the basic question -- again: an ABX test would “reveal” whether or not one’s “guesses” about hearing a difference, or not hearing a difference, are correct -- by providing evidence. Having evidence means one is making an objective, not a subjective evaluation. Those two opposites are the entire point of the controversy.

While I did not use the word “options” in my reply, they are
(1) having objective evidence vs not having objective evidence and
(2) if one gets an audiophile belief from subjective listening, the option of accepting or not accepting contrary evidence.
both of which I did address.

What did I not answer?

“... on your system” That is irrelevant and meaningless. He could not make any tests on my system, he has to use his own, or at least one that is available to him. Using any specific system can leave the open question of whether or not that system is good enough to reveal some differences, but it has nothing to do with subjective vs objective.

What could be ‘revealed about the underlying audio?’ Whatever the “underlying audio” means, it isn’t something addressed by ABX tests. What is addressed is whether or not one is limiting himself to the purely subjective, and possibly coming to fantasy based conclusions.

You and Steve both repeatedly throw in comments about the degree and level of quantization error and it improbable audibility. There is no controversy about that in anything I wrote, and facts about the logic and mathematics of the degree of quantization error, quantization distortion, or the magnitude of the dither noise, are irrelevant to the question of doing subjective vs objective listening evaluations.

With many words you have insinuated that I don’t under about dither and quantization distortion, or much about most of what I write, but you have not said anything specific. Effectively eliminated means that, in effect, the distortion is eliminated, which means that, with dither, the distortion -- the objectionable aspect of the quantization error -- is no longer heard. It is also the case that the distortion is changed, if not gone entirely; it isn’t simply covered over by the dither. For me to believe that isn’t what Pohlman says would require some other believable interpretation of what he wrote.

Note that I never even implied that the quantization errors no longer exist with dithering, or that their magnitude changes. No, it isn’t your responsibility to give me an education, but what I’m getting is slander.


My own experiments with 24 bit to 16 bit conversion seems to verify that the change in the sound of lower level signals is modified in such a way by dither that the conversion no longer produces a strange or peculiar effect in the sound. The dithering has made it go away. I have to assume that the “strange” aspect I hear without the dither is the infamous quantization distortion, as I’ve never read of any other cause for it.

The on screen evidence is even more striking than the listening. Without dither all sorts of strange stuff is added to the signal. With dither, none of that is present. The essentially unhearable dither noise is now there and it cannot be distinguished from the now randomized quantization noise. All the peculiar patterns, the distortion, of the quantization noise with undithered conversion are nowhere to be found. This is easily verifiable.

Here is a useful link demonstrating the sound of quantisation errors, and the effects of dither and noise shaping.

Paul

With many words you have insinuated that I don’t under about dither and quantization distortion, or much about most of what I write, but you have not said anything specific. Effectively eliminated means that, in effect, the distortion is eliminated, which means that, with dither, the distortion -- the objectionable aspect of the quantization error -- is no longer heard. It is also the case that the distortion is changed, if not gone entirely; it isn’t simply covered over by the dither. For me to believe that isn’t what Pohlman says would require some other believable interpretation of what he wrote.

Well, if that's what you think, then clearly you don't understand about this form of distortion. You cannot 'eliminate' it as such; you can only mask it. The original error remains - and if you undid your dithering precisely it would still be there. It is based on what amounts to an encoding error, and masking it is the best you could manage. But effectively eliminated it is not. It's important to understand that there's a difference; just because you can't hear something doesn't mean that it isn't there, at all.

Another way to express it is that dither changes the quantisation distortion from being correlated with the music to being correlated with the dither noise - this makes the quantisation distortion effectively noise itself - see this paper by Hicks. 

There is always some limit to my understanding. Perhaps we are just involved in a question of defining terms. I do understand there is always going to be an error in the value of each sample (save a very rare exception now and again). I understand there will thus always be some difference from the input signal in the reproduced signal. Dither can’t change that fact.

I understand the fact that the first fact can be called distortion since the output of the conversion, and thus any audio produced from the data, isn’t exactly equal to the input signal. However, those facts in themselves turn out not to be a problem in music recording and reproduction unless the bit depth is too low (as in the examples Paul referenced). Generally speaking, the errors are so small and random that no one can hear that the output signal isn’t exactly the same as the input signal.

The problem in “normal” audio recording and reproduction comes when the signal level is very low, thus allowing only a very low bit depth to represent it -- but if we use a greater bit depth, we have more possible quantization values and thus smaller, and thus harder to hear, errors. The very low level signal, of necessity, has only a very small amplitude change as it goes its merry way from note to note (or especially when holding a single note). The mindless converter working with such an input signal just keeps making the same error(s) over and over again. Thus there is some pattern to the errors and, if we manage to perceive anything, we hear that as a chirpy, or squeaky, or squeally, or some such, little sound. With that in it, the reproduced audio sure doesn’t sound quite right.

That aspect of the error is why we need dither and is what we perceive as quantization distortion (in the infrequent instances that we can perceive anything about it). Adding randomized noise, dither, removes that regularity from the error that is always there, eliminating any pattern and thus effectively eliminating any problem. We might, in extreme instances, hear the random noise created by the random errors, but only a real loser complainer worries about that.

Getting my head around the idea that the problem will reappear if the dither is removed is a bit more difficult, however. The error is in the value calculated (derived, whatever) from signal + noise rather than just from signal. That is what makes it random and thus not a problem. I guess it makses sense that if a program, like maybe Audition, recalculates the sample value based on minus the noise, it will come up the value it would have come up with had the noise never been there; that process is very mechanical.

There is such as thing as subtractive dither, although I don’t know if it is much used. Sixteen bit recording doesn’t seem to be much used anymore, so there wouldn’t be much point. Dither is added to the analogue signal prior to the ADC, as normal for proper 16 bit recording, then, through some kind of  feedback or delay mechanism, the same dither noise is subtracted from the digital version after the conversion. The purpose is to get audio without the undesirable effects of quantization distortion and without dither noise. This seems to me to be somewhat like NR. Surely this process does not result in an audio file equivalent to one that was never dithered? That would really seem to be without any purpose.


Four bit music in the reference Paul provided is one way of demonstrating the effects of dither. I like the ability of test tones to provide clear evidence at 16 bit. It would probably be possible to do the same manipulation presented here with music that has a good gradual fadeout, if I had any such music that did not already have either dither or LP background noise to prevent the demonstration from working.

This screen shot was prepared for by generating a 500Hz tone at -90dB, 32bit, then converting one copy to 16 bit with dither, one copy without dither. I appended the files into one file, converted back to 32 bit (to avoid further degradation), and amplified by 70dB. To avoid over saturating the image, I reduced Spectral View Range from the default 120dB to 90dB.

The amplifying by 70dB makes the distortion components very visible. It also makes the dither very visible, but the elimination of the offensive patterns of quantization distortion is still readily seen.

The difference in sound is also much more easily heard after amplifying in the digital domain. On my system, maximum analogue amplification is required to just get a hint of the distortion in the -90dB file, but a quite modest volume control setting is adequate in the pre-amplified version that this screen shot represents. Technically, one still needs ABX testing to obtain evidence that the apparent sound difference is really heard, but no one is likely to bother when the subjective experience is so dramatic.

Anyone that doesn’t trust the additional steps after converting to 16 bit can up the Spectral View range to 160dB or more to more easily see the distortion components in a -90dB file. Whether or not the distortion can also be heard no doubt depends on the equipment you have to listen to it. It is also easily to duplicate this process, but convert from 32bit to 24bit, to demonstrate that dithering makes no appreciable difference when going to 24bit.

Since this is so easy to do in Audition/CoolEdit, I have not attached the audio file from which I made the screen shot, but I will download it if requested.

Ideally the screen shot would be imbedded where I wrote about it rather than provided as an attachment but I guess that requires I have it stashed somewhere on the internet for the forum software to retrieve. I don’t have any such place. If there is a way, I would appreciate knowing about it for future reference.

I start getting amused more and more about the dithering discussion (the discussion itself is dithering also) and I am prepared getting beaten for my statements. The almost only word of truth is the statement of the textbook cited:

Quantization error is thus decorrelated from the signal and the effects of the quantization error are randomized to the point of elimination. However, although it greatly reduces distortion, dither adds some noise ... . Ken C. Pohlmann, Principles of Digital Audio, 4th edition, p 39.

Quantisation error is inherent in digital signal representation and cannot be removed by any means. However, since this error in some cases has a periodic structure, this may be more noticable in a subjective way. The point is that it occupies distinct spectral regions.

This is very well demonstrated by Andy’s spectral presentation of the –90 dB 500 Hz signal. While the undithered signal presents these distinct regions very clearly, the dithered part has these signals smeared all over the spectrum.

Beyond that, his sample is of limited value. Preparing a signal of –90 dB on 32 bit format, (which is in fact 24 bit / 16.8 – 144 dB range) produces a S/N of 54 dB. This corresponds to a 9 bit figure and is therefore a very rough resolution that could have been produced the same way using a – 42 dB signal at 16 bit. It‘s obvious to have some quantisation effects visible.

From a practical point of view one should bear in mind  that all analog recording media have a S/N in the range of  55 to 75 dB regardless of being LP, tape with or without any kind of Dolby. This is still at least some 20 dB better than a 16 bit digital recording such as a CD – which theoretically has a S/N of 94.4 dB. It is a matter of taste whether this is sufficient. I live in my own house and am therefore only limited by my dear wife in making noise. But even except her I cannot make use of the full 94 dB of any CD though I have a pair of 15“ Tannoys driven by 150 W amplifiers.

Beyond that, everybody who ever made recordings himself can testify that it is very rare for the level meter idling below – 75 dB regardless of good microphones and preamps. This is simply because our world is too noisy.

I am mathematically inclined and have done a good number of experiments but they have been bound to the 8 bit format as used for telephone and ISDN. There the quantisation problems count.

But within audio of at least 16 bit - and even more for the transfer of LP’s the whole discussion is not worth making such a huge amount of bubbles ! All other deficiencies in recording and playback – even with very good equipment - are at least one order of magnitude more important.

I should apologize for an error in my reply. The 54 dB S/N is the figure for the 24 bit representation. It could be preserved in the 16 bit representation only if normalized prior to the downscaling. This is not the common procedure. Therefore the resulting S/N is 6 dB (more exactly 4.4 dB) only. That is behind Andy's figure. Still the quantisation noise is more than 20 dB lower than any analog recording. Sorry, if I troubled anybody !

[the effects of the quantization error are randomized to the point of elimination.]

I start getting amused more and more about the dithering discussion (the discussion itself is dithering also) and I am prepared getting beaten for my statements. The almost only word of truth is the statement of the textbook cited:

Quantization error is thus decorrelated from the signal and the effects of the quantization error are randomized to the point of elimination. However, although it greatly reduces distortion, dither adds some noise ... . Ken C. Pohlmann, Principles of Digital Audio, 4th edition, p 39.

The bolded bit is what I think may have confused Andy. There is a world of difference between 'an effect randomised to the point of elimination' and actual elimination itself.

But as for the rest of what you've said (with corrections) in terms of what happens in the real world - well that could hardly be disputed at all, could it?

Confused Andy? I don’t believe I write that badly, so that no one is capable of understanding it. You’ve once again repeated what I wrote. We are just quibbling about the definition of terms such as:
the quantization error itself is the distortion, which is true in the same sense that tape hiss in the best analogue tape recording is distortion, vs the distortion is the undesirable result when the quantization error is highly correlated with the signal.
Which I acknowledged more than once, and spelled out in painful detail.

If this isn’t the case, no one seems willing to support their claim beyond just saying: we know, you don’t.

And what does the S/N ratio have to do with this anyway? Has that been part of the controversy in some way? There certainly has been no slightest controversy over the fact that the answer to the OP question on whether or not to use dither is that it can’t make any appreciable difference. I just pointed out the best way to assure oneself of that fact.