Why We Dither

[David Rick]

Discussions of word length reduction and the need for proper dithering are a staple of the Mastering forum. Until recently, it seemed that Remotesters had their hands full just getting all their cables coiled by 1:00 AM, but a recent GIGANTIC THREAD in this forum convinced me that a little refresher on audio resolution wouldn't hurt.

That unmentionable thread also convinced me that most working audio engineers don't get much out of a mathematical treatment except a headache. But trying to explain the subject in words leads to endless misunderstandings, strained analogies, and the urge to strangle the very people that we should be drinking beer with. Instead, I offer a picture. This comes from a program I wrote about ten years ago, while trying to understand why the latest release of a certain DAW was broken.

The attached figure shows the spectra for various representations of a 3.6 kHz tone. Note the distortion products that are generated when the digital signal is truncated at the 16-bit level. Proper dithering makes the distortion products go away, at the cost of an increased noise floor. Dither with "psychoacoustically optimal noise shaping" pushes the noise energy into spectral regions where the ear is less sensitive to it.

(Anticipating questions, the 3.6 kHz tone was generated at 0 dB; its level appears louder due to the FFT coherent processing gain. The dither, being noise-like, displays at its true level. Also, the funny shape of the original noise floor is due to the particular Chebyshev window I used in the spectral analysis.)

David L. Rick
Seventh String Recording

[Ozpeter]

Thanks, Dave.

Discussions of word length reduction and the need for proper dithering are a staple of the Mastering forum.

I didn't know there was one!

And I shall say no more.

[okydoky]

Originally Posted by David Rick

Discussions of word length reduction and the need for proper dithering are a staple of the Mastering forum.

hi,

did you at least warn them?



right.

[MichaelPatrick]

Rick,

Something that's I've wondered about forever...

All WAV editors allow you to save as 16bit. But do they do anything more in the process than simply cut off the last 8 bits?

Put another way, in the process of requantizing, is truncation enough after dithering, or is there some other magic going on?

[d_fu]

Originally Posted by MichaelPatrick

All WAV editors allow you to save as 16bit. But do they do anything more in the process than simply cut off the last 8 bits?

Depends... Any DAW will (or should) give you an option.

Put another way, in the process of requantizing, is truncation enough after dithering, or is there some other magic going on?

Dither replaces simple truncation, if you will. 8 bits are "thrown away", and either you just cut (truncate) or dither, causing different behaviour of the resulting 16 bit file's LSB.

[MichaelPatrick]

Originally Posted by d_fu

Dither replaces simple truncation, if you will. 8 bits are "thrown away", and either you just cut (truncate) or dither, causing different behaviour of the resulting 16 bit file's LSB.

I see two step process:

1. Add dither noise (noise shaping optional).
2. Truncate.

I know both steps are required, but what happens between those steps, if anything?

Do the 16 vital bits need to be recalculated after adding the dither noise, or are they already good 16bit PCM (i.e. the file is ready to truncate)?

[JEGG]

Originally Posted by MichaelPatrick

Rick,

Something that's I've wondered about forever...

All WAV editors allow you to save as 16bit. But do they do anything more in the process than simply cut off the last 8 bits?

Put another way, in the process of requantizing, is truncation enough after dithering, or is there some other magic going on?

Truncation is the only thing that happens after dithering. In other words, you add noise before truncating, as opposed to not adding noise before truncating.

Depending on your dynamic range, and what sort of fades you use, dithering may be completely redundant. Most location sites are way above the LSB, even if very generous (low) levels are used in the recording process.

The fact that there are different dither types, and that dithering is claimed to be completely inaudible, while at the same time different dither types claim different results, leads me to conclude that it is not necessary at all: it is not neutral and inaudible if it produces different tonal results. the exception being using various sorts of fades (lengths) and absolute silence.

And then, will you boost your playback equipment 40 dB or more over normal levels to check the dither? Will you listen at acoustic peak levels of 120 dBA (at least) and up so that you might hear a glint of from the claimed benefits of dither? Will you race to the volume know and mix it at every fade and track change? And if you worried, maybe you could only apply dither at those points. I wouldn't.

However, if you moving lots of files around in a DAW that vary in bit depth, it might be wise to add appropriate dither (non noise shaped) everytime material moves between depths. Your DAW software may do this automatically. Your material may undergo several bit depth changes due to internal processing of the DAW.

This is what I've arrived at empirically. I don't feel terribly strongly about it, and I would change my mind at any time if I see the need to.

[d_fu]

Originally Posted by MichaelPatrick

I know both steps are required, but what happens between those steps, if anything?

Nothing...
The process may even be reverse, throwing away 8 bits first, then dithering the LSB of the resulting 16 bit audio before writing it to a file or CD. Not sure hw different software would handle it.

Whichever way, it's one process essentially.

[MichaelPatrick]

Originally Posted by d_fu

Nothing...
The process may even be reverse, throwing away 8 bits first, then dithering the LSB of the resulting 16 bit audio before writing it to a file or CD. Not sure hw different software would handle it.

Whichever way, it's one process essentially.

You've raised another simple yet very important question.

If I'm unbelieving it's only because I can't fully understand the requantization process yet. I trust the tools, but I also really want to know what they're doing with the file.

[MichaelPatrick]

Originally Posted by JEGG

Truncation is the only thing that happens after dithering.

I thought that might be the case.

Do you know if the order is important or why it is important?

d_fu seems to suggest the order is not important - that you can also dither after truncation.

[d_fu]

Originally Posted by MichaelPatrick

d_fu seems to suggest the order is not important - that you can also dither after truncation.

Hmmm... Maybe not... Guess one would have to add dither noise first.

[EDIT]
Of course... What was I thinking? Complete crap, obviously...

[MichaelPatrick]

Originally Posted by d_fu

Hmmm... Maybe not... Guess one would have to add dither noise first.

That's what I thought.

So my remaining question is whether or not the 16bit words are recalculated after dither and before truncation, or should truncation always follow dither immediately as JEGG indicates?

[d_fu]

Originally Posted by MichaelPatrick

So my remaining question is whether or not the 16bit words are recalculated after dither and before truncation, or should truncation always follow dither immediately.

Recalculating would alter the LSB and destroy the effect of the dither.

[MichaelPatrick]

Originally Posted by d_fu

Recalculating would alter the LSB and destroy the effect of the dither.

That sounds like a good argument. For all I know, it may even be dispositive, but I'd like to know what occurs more than why.

My reason for this line of inquiry is: If I know with certainty what my software actually does to the PCM file at each step in the process I won't assume anything and make mistakes.

[David Rick]

Originally Posted by MichaelPatrick

So my remaining question is whether or not the 16bit words are recalculated after dither and before truncation, or should truncation always follow dither immediately as JEGG indicates?

I'm not sure what you mean by recalculating the 16 bit words, Michael. The audio data is presumed to be in some higher-resolution format (24-bit fixed-point, 32-bit fixed-point, or 32-bit floating point) prior to being converted to 16-bit fixed point via truncation or rounding. Dither is the last thing you do at the original resolution. It's been many years since I wrote the demo code, but if I recall correctly, I had to use a particular rounding rule to get the 16-bit result to be properly decorrelated. I'm fuzzy on this after so long, but I think the particular DAW release I was complaining about had implemented an incorrect rounding rule, which broke their dither algorithm.

Originally Posted by JEGG

The fact that there are different dither types, and that dithering is claimed to be completely inaudible, while at the same time different dither types claim different results, leads me to conclude that it is not necessary at all: it is not neutral and inaudible if it produces different tonal results. the exception being using various sorts of fades (lengths) and absolute silence.

I never claimed that dither was inaudible. We know that a "colored" noise floor can affect how we perceive the audio it underlies. My experience is that different dither and noise shaping curves sound different, and my preferences change depending on the audio material. There have even been cases in which I preferred the truncation artifacts, but that is rare.

I don't know how you then reach the conclusion that dither is "not necessary at all". It is necessary if you want to avoid "correlated truncation noise" which is a fancy way of saying "additional distortion". If you decide that additional distortion is ok, whether for philosophical or artistic reasons, then you don't need to dither.

David L. Rick
Seventh String Recording

[JEGG]

Originally Posted by MichaelPatrick

I thought that might be the case.

Do you know if the order is important or why it is important?

d_fu seems to suggest the order is not important - that you can also dither after truncation.

All that's happening is you're chopping off the lower bits. If you then have the LSB bit toggling on and off in weird ways, you're going to have distortion or some very strange sound-or Noise!

You add "random" noise (which is not random, because all dither types sound differently, according to their manufacturers), so that the LSB toggles on and off in a random way.

Chopping something off and then adding dither doesn't do anything, except add noise, you've already truncated without benefit of the randomized LSB.

What is the ambient noise level of your recordings? I'll bet it's a whole lot higher than -144 dBFS! I'll bet it's more like -65 to -50 dBFS on a good day. The dither added to properly truncate a file from 24 to 16 bit would be -96 dBFS. Is your room ambience (plus all the mic's, amps, mixers, etc.) below -96 dBFS? I don't think so.

You've already dithered, your ambient noise has done it. Forget it. Fades can be an issue, as there may be some track to track transition issues. Use you ears for this. Will everyone jump up and turn the monitor controller to max to enjoy this silent track to track experience? Of if they do, maybe just dither those sections.

Bouncing and processing things in a DAW station with high internal bit depth is an entirely different matter, that my require dither, and would be nice if the DAW did it with simple dither. There can be some issues with importing files of different bit depth rates as well.

Some dither types, such as Noise Shaping, should only be done once and at the very end. Otherwise it adds up quickly and it's definitely not subtle.

This why everyone can breath easy and record with levels that might hit -12 dBFS or -18 dBFS once every couple of hours. The dynamic range available is huge, you can let all your analogue gear breath easy and sound better, and raise the levels to the point you require after the fact with no noise penality (and usually lots better sound).

[MichaelPatrick]

Originally Posted by David Rick

I'm not sure what you mean by recalculating the 16 bit words

I could be way off base; my mental concept is that, for each sample, 24bits of amplitude information needs to be distilled down to 16bits.

Dither noise (shaping optional) is added to the 24bit words, then the least significant bits (17-24) get tossed by truncation.

If the dither noise tweaks only bits (17-24) that get tossed by truncation, why do it in the first place? If the dithering noise tweaks the first 16 (more significant) bits, why not dither after truncation?

If my notion of the process is wrong, then it seems there may be a re-calculation or re-writing of the first 16 bits that needs the dither noise to be optimal.

[David Rick]

Originally Posted by JEGG

And then, will you boost your playback equipment 40 dB or more over normal levels to check the dither? Will you listen at acoustic peak levels of 120 dBA (at least) and up so that you might hear a glint of from the claimed benefits of dither? Will you race to the volume know and mix it at every fade and track change? And if you worried, maybe you could only apply dither at those points. I wouldn't.

I want to address this separately, because it is a common misconception. It is a mistake to pick a particular dither or noise-shaping spectrum by cranking up the volume. There's even a web-site out there that encourages you to listen to different dither algorithms at high amplification. This is completely wrong! Psychoacoustically optimized dither and noise-shaping algorithms are optimal only when used at the bit level they were designed for. It's obvious, once you remember the Fletcher-Munson curves. When a mastering engineer is deciding which algorithm to use on your CD, he or she should be listening to it at a volume level that's representative of how the end listener will hear it.

It's not just fades that require dither. In a fixed-point system, you can generate artifacts just by bumping the track fader 0.1 dB. The math doesn't care. I don't have to worry about this so much since I stopped working in a fixed-point DAW with destructive processing, but here are the rules I used to follow:

• All intermediate products (files) should be saved at 24-bit resolution.
• Every 24-bit bounce should use flat spectrum TPDF dither at the correct level.
• Send your final mixes to the mastering engineer in 24-bit files, not 16-bit.
• The mastering engineer applies spectrally-shaped dither or noise-shaping only in the final reduction to 16-bit resolution, with all other processing done as above.

David L. Rick
Seventh String Recording

[JEGG]

Originally Posted by MichaelPatrick

I could be way off base; my mental concept is that, for each sample, 24bits of amplitude information needs to be distilled down to 16bits.

Lots of terms to use here, you can use distilled, "rounding up," or converted or truncated, hacked off, etc.

Originally Posted by MichaelPatrick

Dither noise (shaping optional) is added to the 24bit words, then the least significant bits (17-24) get tossed by truncation.

Yes. Assuming your new file will be 16 bit, the amplitude of the dither is at bit 16 (-96 dBFS) (or 15 or so), so bits 15 or 16-24 contain dither.

Originally Posted by MichaelPatrick

If the dither noise tweaks only bits (17-24) that get tossed by truncation, why do it in the first place? If the dithering noise tweaks the first 16 (more significant) bits, why not dither after truncation?

Because you're loosing the benefit of the dither. The dither is to insure that the new LSB will toggling randomly and therefore *independant* of the program material. So when you "truncate," it won't sound "hacked off." When the 16th bit is operating randomly, it smooths things out and permits material at and under the noise floor to be heard in a randomized way. If you truncate first, you've lost all of that information. Dither is additive to the material in bits 16-24. "Rounding up."

Originally Posted by MichaelPatrick

If my notion of the process is wrong, then it seems there may be a re-calculation or re-writing of the first 16 bits that needs the dither noise to be optimal.

Not at all. You are simply minimizing the effect of chopping off of the last 8 bits by introducing randomized noise unrelated to the program material (of course) by randomizing with dither what will later become the new LSB after truncation.

Again, though, a DAW has different issues. If you import a 24 bit file into something that has a much larger working depth, that file will probably be dithered automatically even if it comes back out at 24 bits. But the dither will be something simpler and less audible than dither that might be used as the last step before mastering to 16 bit.

Finally, please always use your ears! And at real world volume levels.

There are some instances where dither is required, others where it is not.

Dithering however, is not a complex procedure. Add noise before you hack. That's about it. (And adding the right kind of noise at the right level.)

[Dale]

dithering is done when changing word bit length.
it is usually a part of mastering as the recording/mixing should always be delivered in the optimal state. ie record at 96/24; mix, deliver mixes to mastering engineer @ 96/24, who then does their thing with tweaks, insertion of metadata then resample to chosen format then to chosen bit rate using dither.

[Ozpeter]

By way of a practical example of what actually happens, some sample values from a stereo piano recording (columns are left and right) -

24 bit -

755.5977 -18.87109
771.3789 -35.04688
779.2891 -57.32031
771.4258 -80.76953
754.8477 -91.69141
725.5312 -108.3125
684.8359 -116.9102
656.5938 -130.1875
618.0977 -131.8125
573.2852 -129.7773
532.6836 -134.0117
488.7656 -131.4766
450.707 -135.2656
419.7422 -143.2656
373.5117 -142.7227
325.1445 -142.3125
265.7422 -146.6875
205.6055 -147.0352
153.6016 -152.6758
101.4727 -151.0078
51.84766 -148.4297
10.74219 -142.6875
-27.11719 -141.457
-68.19922 -141.1953
-108.6016 -144.5898
-148.5938 -149.957
-209.2891 -150.7344
-282.1719 -142.6016
-370.7656 -138.3594
-464.6836 -132.332
-578.3945 -139.5547
-704.8438 -147.6992
-829.7305 -164.4688

16 bit not dithered -

756 -19
771 -35
779 -57
771 -81
755 -92
726 -108
685 -117
657 -130
618 -132
573 -130
533 -134
489 -131
451 -135
420 -143
374 -143
325 -142
266 -147
206 -147
154 -153
101 -151
52 -148
11 -143
-27 -141
-68 -141
-109 -145
-149 -150
-209 -151
-282 -143
-371 -138
-465 -132
-578 -140
-705 -148
-830 -164

16 bit dithered -

756 -19
771 -36
780 -58
772 -81
755 -91
726 -107
685 -117
657 -130
618 -131
573 -129
532 -135
488 -132
451 -135
420 -144
373 -142
326 -143
265 -147
205 -146
154 -152
102 -152
52 -148
10 -143
-27 -142
-67 -141
-108 -144
-148 -150
-209 -150
-282 -143
-371 -139
-465 -132
-578 -140
-704 -148
-831 -164

(Conversion to 16 bit with and without dither in Audition. Without dither, it seems to round up or down, rather than just cutting off the decimals).

[MichaelPatrick]

Originally Posted by Dale

dithering is done when changing word bit length.
it is usually a part of mastering as the recording/mixing should always be delivered in the optimal state. ie record at 96/24; mix, deliver mixes to mastering engineer @ 96/24, who then does their thing with tweaks, insertion of metadata then resample to chosen format then to chosen bit rate using dither.

Dale, I know why we do it and I now MEs know all this stuff. What you're saying is pretty common knowledge among audio engineers. I'm trying to talk in some detail about a few of the individual technical steps in the requantization process.

[MichaelPatrick]

I appreciate everyone trying to fill the vacuum that's in my head on this subject. All the inputs have been helpful (well, almost).

So the desired effect on bits occurs automatically as a direct and immediate result of adding the dither noise. Then the file can be saved as 16 bits (truncated).

Thanks much!

[d_fu]

Originally Posted by David Rick

Proper dithering makes the distortion products go away, at the cost of an increased noise floor. Dither with "psychoacoustically optimal noise shaping" pushes the noise energy into spectral regions where the ear is less sensitive to it.

Rather than opening a new thread, I would like to illustrate these effects with a few sample files I created a while ago.

It's a short excerpt from a concert recording. The "original" file is just to ilustrate the sound (i.e. it may not be suitabe for null tests).

The test was performed by reducing the level of a 24 bit file by 50 dB, which causes some of the original signal's level to drop below the -96 dBFS limit of 16 bit resolution, and then converting to 16 bit in various ways. The resulting files were then raised in level again for listening at relatively normal settings.
The undithered example shows how the sound actually drops out, accompanied by ugly quantization noise. The other files demonstrate the effects of various dither algorithms available in Samplitude. The "triangular" variety is performed in three bit depths (relative to the LSB). Pow-R is a noise shaping algorithm. Observe how especially the third variety allows signals below -96 dBFS to be heard clearly, despite the dither noise.

Originally Posted by David Rick

I want to address this separately, because it is a common misconception. It is a mistake to pick a particular dither or noise-shaping spectrum by cranking up the volume.

It may be, but I find it interesting nonetheless to hear how the various dither alogrithms "sound" (e.g. when converting a silent 24 bit file to 16 bit). The differences in the types of noise are quite noticeable. Such "silent" files rendered with the Pow-R e algorithm will show levels in the vicinity of -85 dBFS RMS during playback... Most of that noise is high-pitch stuff, though.

[Ozpeter]

24-96 Mastering - Dither - The Great Dither Shootout

[space2012]

Originally Posted by Ozpeter

24-96 Mastering - Dither - The Great Dither Shootout

+1.
but izotope rx advanced is not included,
and beats them all! with manual settings, has lots of setings.thumbsup

[David Rick]

Listening to Daniel's files is instructive, despite my comments above. All except the POW'R files involve flat-spectrum dither, so they are not restricted to use at a particular bit level.

What Daniel calls "linear" is really Rectangular Probability Density Function (RPDF) additive dither. In contrast to TPDF dither (T for Triangular) it decorrelates only the first statistical moment, so while you can hear the music below the truncation limit, you can also hear that the music is modulating the noise level.

TPDF with a peak level 1.0 bits eliminates the noise modulation. But notice that this doesn't happen at the two lower levels of TPDF. This illustrates an important point about dither: you must get the amplitude correct!. My ongoing complaint about the dither options in Samplitude is that they permit you to make dither choices that don't actually work. For TPDF the peak amplitude must be +/- 1 LSB, not some smaller or larger number. The choices +/- 2 LSB, +/-3 LSB, +/- 4 LSB, etc. are also ok, but you wouldn't want these unless you believed you actually had a 15 or 14 bit DAC. Incidently, you make TPDF 1.0 by adding two independent RPDF 0.5 streams.

One can hear from the examples that the POW'R algorithms do spectral shaping of the residual error, but you should NOT try to choose among them from this demonstration. The POW'R algorithms are designed for minimal audibility at the 16-bit level, and they won't sound good as presented here.

I'm not certain, but I fancied that I could hear a tiny amount of noise modulation in some of the POW'R examples. But it might not be audible at the intended levels -- if the noise is inaudible to begin with, then it doesn't matter that the noise power gets modulated by the music.

Originally Posted by Ozpeter

24-96 Mastering - Dither - The Great Dither Shootout

This is exactly the web site I was criticizing earlier. Conclusions from this "test" are meaningless, unless you routinely produce 8-bit audio files.

David L. Rick
Seventh String Recording

[MichaelPatrick]

Rick, I greatly appreciate your expertise in this stuff. Thanks!

BTW, can you recommend any good dither plugins?

[space2012]

Originally Posted by David Rick

This is exactly the web site I was criticizing earlier. Conclusions from this "test" are meaningless, unless you routinely produce 8-bit audio files.

David L. Rick
Seventh String Recording

meaningless to you.

to me were like night & day revelationsstike.

[Alexey Lukin]

Originally Posted by David Rick

This is exactly the web site I was criticizing earlier. Conclusions from this "test" are meaningless, unless you routinely produce 8-bit audio files.

I disagree. This web-site doesn't encourage listening to overly amplified files. On a contrary, it encourages turning your levels down, until dithering becomes inaudible.