[Ryokan]

Lets imagine you work part time in a job that pays you $940 per month, but the employer can only pay you cash with $100 bills. (this is the same as 16 bit audio compared to 24 bit audio that would mean exactly $940 payment because all bills and notes are available). Without dither the $940 would be rounded to nearest multiple of $100 and that would suck for you because you'd get paid only $900 every month. One solution is you get $1000 40 % of the time and $900 60 % of the time: After 5 months you have been paid $900 + $900 + $900 + $1000 + $1000 = $4700 = $940 * 5. All good, but what about rises to your salary? At same point you may make $956 for example and the earlier method doesn't work anymore. What if the amount of hours you make change from month to month? Is there a method to even out the salary in the long run even when the salary changes? Yes!! It is dithering! In this case it would work like this:

Every month your employer uses a random number generator to come up with a random number between -50 and 50 and adds that to your salary before rounding it to the nearest multiple of $100. On average nothing gets added, because random numbers between -100 and 100 averages to zero statistically,

The genius of this method is that the salary dictates the probability of the salary + random number getting rounded "up" or "down". If your salary raises a bit, the probability of it getting rounded "up" (say to $1000) increases. There is no really "rounding error" (quantization error/distortion) because it gets evened out statistically. Instead we have the dithering noise (-$50 to $50 added randomly). Since we have thousands of samples per second in digital audio, dither evens out rounding errors every small fraction of a second (audibly there is no rounding error).

Hopefully this was in easy to understand terms.

Thank you 71 dB. So 24 bit, and higher, doesn't need dither?

 

[VNandor]

How does adding dither compensate for quantization distortion? In easy to understand terms, thank you.

While making parallels between audio recordings and pictures can lead to misunderstandings, I think it makes sense to point out the similarities of how dithering is used for pictures. Dithering is also used for pictures, in fact the mathematical principles behind how dithering works for audio is the same as how it works for pictures.
Take a look at this image I got from Wikipedia (hopefully you can click on it for full resolution).

The left picture is the original picture which contains a lot of different colors. The middle and the right picture both contain only 216 different colors. The only difference between them is that the picture on the right has dither applied to it.

The middle picture is generated from the original picture in a simple way. The computer looks up the original pixel's color, then picks the closest one to that color from the 216 available colors. It does that for every single pixel to get the full picture. The right picture is made up by the same 216 colors as the middle one but it does look noticeably different. The interesting similarity between the middle and the right picture is that, in a way, they are "wrong by the same amount" compared to the original picture. By that, I mean a specific thing.

Let's say that you calculated how much the first pixel's color of the original picture is different compared to the first pixel of the second picture. Maybe you found that it's off by 0.5%. After that you do the comparison between the second pixel of the original picture vs. the second pixel of the middle picture, you get some number again. You do this calculation for all the pixels, and add up all the differences to arrive at a number that represents how much off the second picture is compared to the original.

If you did the same calculation between the original and the third picture, you would find that the overall error is very close (math does not guarantee the overall error to be exactly the same) to the error you calculated for the second picture. Despite having the same amount of error, the third picture does look better.

Dithering in audio is similar in that sense. The undithered audio contains the "same amount" of error as the dithered audio but the error is distributed in a different way. In audio, if the dithering is done a certain way, the error you get from dithering would be the same as the error you would get from recording with "infinite" bit depth, then adding a tiny bit of white noise to the recording. Which is why people say that a dithered signal can be the same as a perfect signal plus a certain amount of noise.

I've written this out for you as much as for myself, hopefully it makes sense and also accurate. Dithering somehow wasn't covered in any of the courses I've taken.

Edit: I want to point out that the effect of dithering is very clear in these pictures but a dithered 16bit audio signal would barely sound different vs. the undithered one, it most likely wouldn't make a noticeable difference under typical listening conditions.

 

[bigshot]

To answer Ryokan's question... A higher bitrate pushes the noise floor lower, so dithering would be pushed down with it.

The number of colors analogy is a little deceptive, because dithering doesn't add resolution the way colors do. It simply lowers the noise floor. The easiest way to think of it is like tape hiss. Dithering reduces the bed of noise at the bottom of the dynamic range. If the bitrate is higher, the noise floor is lower and dither operates at a lower level to extend the noise floor a little bit lower.

The truth is that dither is overemphasized. In my sig file is a video that has examples of a 16 bit song with and without dither. There isn't a lot of difference in real world listening. 70dB without dither is acceptable. 96dB is overkill in the real world.

 

[VNandor]

The number of colors analogy is a little deceptive, because dithering doesn't add resolution the way colors do. It simply lowers the noise floor. The easiest way to think of it is like tape hiss. Dithering reduces the bed of noise at the bottom of the dynamic range.

Dithering doesn't add resolution to the colors either. Both the quantized and quantized+dithered pictures are made up by the exact same kind and amount of colors. It might be misleading for some other reason, but definitely not for this reason. What do you exactly mean "dithering adding resolution"?

 

[bigshot]

More colors adds resolution to the image itself at small pixel sizes. When you look at the picture of the duck, it isn't sharp or clear because of the lack of dithering. But that image would look fine with a low number of colors at a larger pixel dimension, like say 5000 pixels across. No dithering would sound OK at high bitrates. The example of the duck is like listening to a 4 bit song with and without dither. In the real world, at 16 bits you wouldn't hear a great deal of difference between with and without dither, and the difference would be a small difference in the noise floor, not the sharpness or clarity of the sound image.

Images aren't good analogies because audio has a fixed listening level. Images can be viewed super close up, or from a large distance. That is completely different. 16 bit audio has a very low noise floor already. You likely wouldn't detect much of a difference, certainly not as much as the difference in that duck.

The importance of dithering is usually overstated. Listen to the examples provided by Ethan Winer. They show exactly what dithering does and doesn't do.

 

[VNandor]

If my understanding is correct, both the middle and the right pictures are supposed to have both the same kind and amount of colors. Maybe I should make an other thread because I can see myself making a lot of comments that are off topic to this thread.

 

[bigshot]

The resolution (specifically the number and size of the pixels) affect the way the image looks too. At low pixel dimensions dithering looks much worse than at large pixel dimensions. If you were going to compare images to sound, 16 bit audio would be like a very high pixel dimension... but it still isn't a good comparison. Easier to just explain it as sound.

Higher bitrate = lower noise floor.
Dithering = a little lower noise floor than without dithering.

Whenever we use a photo analogy, we get in the weeds it seems.

 

[VNandor]

Well, there is a reason I also tried to explain it for audio as well. The picture has a low bit depth because just like with sound, as the number of quantization steps increase, the quantization error decreases, the dither gets less and less work done so its effect becomes less and less noticeable. So I don't think dithering in audio and images differ in that aspect either. I don't think listening tests reveal anything about how dither works but it certainly is telling about the impact (or lack of) on the perceived sound quality.

 

[Ryokan]

This graphic helps show how bit depth reduces noise:
Christian Thomas March 20, 2023.

 

[71 dB]

Thank you 71 dB. So 24 bit, and higher, doesn't need dither?

In principle anytime you go from higher bit depth to lower bit depth, dither is the correct way to do it.

Even with 16 bit dither isn't that important, but why not dither? If the signal contains enough noise, it acts as self-dither. If you record a singer at 24 bit, the mic signal contains so much noise dither is not needed. Dithering itself is a nuanced issue. There are many ways to dither with different pros and cons.

 

[bigshot]

Default dither should work fine. Some DACs have a bunch of different kinds of dither, but there isn't any practical difference between most of them, and the ones that sound different, sound worse.

 

[Davesrose]

More colors adds resolution to the image itself at small pixel sizes. When you look at the picture of the duck, it isn't sharp or clear because of the lack of dithering. But that image would look fine with a low number of colors at a larger pixel dimension, like say 5000 pixels across. No dithering would sound OK at high bitrates. The example of the duck is like listening to a 4 bit song with and without dither. In the real world, at 16 bits you wouldn't hear a great deal of difference between with and without dither, and the difference would be a small difference in the noise floor, not the sharpness or clarity of the sound image.

It's not more colors per se: it's gradient range. Resolution and contrast range is what defines detail. You don't hear about 8-bit, 16-bit, 24-bit color spaces like the olden days, because we've had devices and image formats easily supporting 24-bit color. It was standard for quite some time that computer color spaces were standard dynamic range, or 8bits per color channel (256 shades of tone and 16.7 million color palette). Now with HDR you hear about 10bit or 12bit: that means you are getting a higher color gamut, but more importantly you're getting much higher tonal range (in the case of 10bit, 1024 shades of tone vs 256). The main current image format I can think of that heavily relies on dithering 8-bit color space is animated GIFs. Trying to show 24-bit video clips as animated 8-bit stills.

 

[bigshot]

There really isn't a purpose for 8 bit sound any more either. Video games were where 8 bit was used a lot, and now video games have Atmos!

 

[Davesrose]

There really isn't a purpose for 8 bit sound any more either. Video games were where 8 bit was used a lot, and now video games have Atmos!

It's funny that there's some 8-bit computer enthusiasts collecting old 70s/80s PCs and consoles (check out 8-bit guy Youtube channel). 8-bit guy even gets into programming for systems like the Commodore (he's even made new games for it!). But yeah, most gamers have to have either the X-Box (which supports Atmos) and Playstation (which doesn't want to pay the Dolby license, so they have their own surround scheme).

 

[gregorio]

However, SACDs sound better to me than CDs

OK …

so I think at some point the increased resolution is helpful and it is not clear whether bit depth or sample rate has more influence but I suspect sample rate is more important.

I put a $2 car air freshener in a Porsche. The Porsche performed much better than a VW Polo, “so I think” car air fresheners have a lot of influence over car performance. Obviously this assertion is nonsense, there’s a whole bunch of possible reasons why a Porsche performs better than a Polo and an air freshener isn’t one of them but I jumped on about the least plausible reason, just as audiophiles frequently do. The “so” is just a correlation/causation fallacy.

I think that is not a problem with dual layer SACDs though.

Why?

This graphic helps show how bit depth reduces noise:

The OP of the 24bit vs 16bit thread might help you.

G