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I've read a lot here about added noise when going from 24 bit to 16 bit. I'd like to know why this exists.

When converting a 24 bit signal to a 16 bit signal, why can't we simply round the 24 bit sample value to the nearest 16 bit sample value? Sure there will be the loss of quality because the resulting recording is 16 bit and not 24 bit, but I don't see how the rounding process introduces any extra noise.

Would an ADC at 16 bit not quantize the analog signal in a similar way?

Edit: To clarify my question: Why would converting a 24-bit recording to 16-bit introduce audible artifacts and distortion that wouldn't be present if the original recording were done in 16-bit in the first place?

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Dithering adds amplitude to all the signals in a digital sample. It forces the lower level amplitude values up to the next threshold level. These new higher amplitude signals now represent the sum of the dither noise and the previously existing amplitude. The lower level bits are filled in with the dither noise and become the least significant bits (in terms of amplitude) in the 24-bit signal. Then, as the file is cut from 24-bit to 16-bit, only the lower 8 bits is truncated thus leaving behind the previous signal plus some noise. [Shamelessly copied from here]. See Pelle ten Cate's answer for more detail.

Think about what happens when rounding a number between 0 and 1: The information is either "included" (as a 1) or "removed" (set to 0). I.e., everything below 0.5 is "ignored" and everything greater than or equal to 0.5 is "enhanced" (increased to 1). This is basically what happens to audio without dithering when converting from 24-bit to 16-bit. Some information is completely removed, and some is altered, resulting in missing sounds and artifacts. Dithering adds a random number to each value, meaning that some of the values that would have been rounded down are now rounded up, and some values that would be rounded up are rounded down. This adds noise but prevents the weirdness introduced by pure rounding.

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It wouldn't be off by a factor of 256... at most it would be off by a factor of 1/32, yes? A 3% reduction in quantization accuracy, which would exist in the recording if it were done in 16 bit in the first place. The dithering process now makes sense to me, but I am still confused. I have clarified my question. If you wouldn't mind helping me fix my confusion, I'd greatly appreciate it. Thanks for your reponse. I am re-reading that article now. –  Brad Dec 12 '10 at 18:51
    
I've updated my answer. –  Matthew Read Dec 12 '10 at 19:33
    
@brad: see it this way: with 8 additional bits, you can make 256 combinations (since 2^8 = 256). Therefore, the possible amount of values of a 24 bits signal relative to a 16 bits signal are a factor 256 higher. –  Pelle ten Cate Dec 13 '10 at 9:24
    
I get it now! Thanks! –  Brad Dec 13 '10 at 14:13
    
To clarify: Dither is something we intentionally add to the signal to prevent the distortion mentioned in the question. If you didn't use dither, it would be distorted due to quantization error. With dither, there is no distortion, just extra noise. en.wikipedia.org/wiki/Quantization_error en.wikipedia.org/wiki/Dither –  endolith Dec 15 '10 at 16:53

First of all, there is (edit: was) a potential terminology issue going on here. Please understand the following: Dithering noise is not something that exists, but something you can add to get rid of something that exists. That something is often called the quantization noise caused by rounding errors during the sampling or the conversion back from 24 bits to 16 bits. It sounds like an aggressive noise that is most heard in high frequency range.

A typical way to display a rounding error in a signal, is to think of a picture. Pictures also have bit depths in colors. Imagine you took a picture with your digital camera which has a nice color gradient from blue to green in it. To actually see this gradients, you need millions of colors between blue and green. Now imagine you change the bit depth from e.g. 24 bits colors, to 16 colors. (which is 4 bit.) by truncating the 20 least significant bits. You will suddenly see that instead of the gradient, all millions of colors are reduced to the nearest of the 16 colors in the 4 bits pallette, in this case just blue and green. While this idea works fine on images with sharp edges and little colors, it doesn't work on gradients because it introduces a sharp lines between them at the place the color changes from blue to green.

If you add dithering, there is some noise added to the signal. (Or, in this case, the picture.) Therefore the color values are changing slightly from their original value, each pixel. This means that at the point the sharp color-changing line was drawn, there is now a pattern of the two colors blended together, since the noise introduces a few green pixels on the blue side (because the random dithering made them just a bit greener), and a few blue pixels on the green side (idem) and it looks - well, still terrible, but the sharp color transition is gone.

Exactly this happens in audio as well, Try recording a 16 bits signal, (make sure it is loud enough, so get it to 0 dB FS and add a compressor if necessary) and truncate the least significant 15 bits, reducing it back to 1 bit. You get a 1 bit signal that you really can't use. There is no way of recognizing the original back. Now (and this is really miraculous!) mix white noise in the least significant 15 bits (equivalent to -6 dB FS) and then truncate them to the one bit signal. You will hear the exact original signal, mixed in a huge LOT of white noise. But you can actually hear more information from the original than without dithering.

Think of it this way: If you dither in those 15 bits (i.e. add a random value), you actually add information to the 16th (most significant) bit. See it this way.

  • If you truncate those bits, you round all values to 1 or 0 by checking whether they're above or below the sharp line of 0.5.
  • By adding dithering noise, it could possibly be that a 0.4 turns into a 1 as well, and a 0.6 turns into a 0.
    • The chance of a 0.4 becoming a 1 is bigger than the chance of a 0.1 becoming a 1, since you add a random number.

So instead of drawing a fixed line saying all values below 0.5 will be 0, the rest will be 1, you state: All values will be 1 or 0. 0.9999 has most chance of turning into a 1; 0.0001 has most chance of turning into a 0. That is what dithering is.

** The additional question **

You asked: what is the difference between a 16 bits recorded signal, and a 24 bits recorded signal with the last 8 bits truncated? The real (theoretical) answer: there is no difference. If you don't plan to dither, and you are not increasing the signal volume to do something useful with the 8 least significant bits, you can as well record in 16 bits. BUT: There will be a big advantage if you dither.

This said, the real-time rounding mechanism of 16 bits recording equipment is often a bit different from rounding by truncation, since it deals with analog data, so there is still some kind of random bit-flipping in the converter going on, which acts a bit like dithering. Whether this is something you want in your signal depends on your equipment, your ears and most important, your opinion. :) I'm not going into detail about this though, but the conclusion is that you get more quantization noise from truncating a 24 bits signal than you get from sampling a signal to 16 bits. This is not going to be my point anyway.

This sounds disappointing, but the reality is, you are asking the wrong question. The real question should be: What can I get in my 16 bits master when I record in 24 bits, what I can't get if I record directly to 16 bits?

So before you start asking the other obvious question: Yes! Still, do dither! It is the only way to move as much information as possible from the 8 least significant bits of the 24 bits signal, into the 16 bits signal. Think of the photograph with 16 colors. Nobody would recognize it if it wasn't dithered while the bit depth was still high. Also, your camera can't dither by itself, so it can't take recognizable photographs with 16 colors. To get the best: record (i.e. take picture) with high bit depth, dither, reduce. :)

Now: the real bottom line.
Recording in 24 bits gives more detail in low dynamics. Details that you can add to you 16 bits master by dithering, that you can't get when recording in 16 bits directly.
Don't ask yourself the question: Should I dither?
Instead, ask yourself the question: Do I want to record in 24 bits? And always dither if you do, to actually get the advantage of it. :)

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Great answer, very clear. –  Matthew Read Dec 12 '10 at 17:03
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Thanks! I always love to make this analogy, especially here, since most people are merging from StackOverflow, and I expect most of those guys to, well, know what a 16 colors photograph looks like ;) Probably not without the dithering though. –  Pelle ten Cate Dec 12 '10 at 18:10
    
@Pelle, thanks for the response, and clarifying the dithering process. However, I am still confused. I edited my question. I understand the analogy to the picture, and understand what that sounds like. What I don't understand is, why is there a difference between what would have been sampled if the recording was originally done at 16 bit, vs if it was sampled at 24 bit and then reduced to 16 bit via simple rounding. Does the ADC not quantize the signal as best as it can, and would rounding not approximate this quantization? –  Brad Dec 12 '10 at 18:47
    
Edited the question. –  Pelle ten Cate Dec 12 '10 at 19:34
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Let's not forget noise floor. Even if you don't dither, 24bit converters have lower noise floor than 16bit converters - unless they are sickeningly poor quality. –  d-_-b Feb 4 '11 at 6:55

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