Audio Dither Explained 

Kali Doom Thanks Kali. However, the "stair-step" idea is a misinterpretation-I think you understand that. We're looking at digital values in this demonstration, not the output of a D/A converter, and these values can quantize into repeated distinct levels that look like stair steps. Granted, "stair-step" automatically conjures up that poor and incorrect description of D/A output for some, and I could have used something like "plateau" instead. But I don't think it will perpetrate a myth, because it's an accurate description of what I'm showing, and if people get confused, they don't have a grasp of what's being demonstrated anyway. But, I know now to avoid the words "stair-step" in digital audio should the need arise again. Actually, I'm working on a sampling theory and sample rate conversion video (possible as separate videos, depending on how long each part runs) that will make it abundantly clear that samples represent impulses, and exactly why the output of a D/A is a smooth analog waveform. I have older articles on these topics on my website, but video will give the opportunity for a more animated demonstration, with audio.

Thanks for letting me know-glad it as helpful to you!

Thanks for saying. There are examples in my other video on dither: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-KCyA6LlB3As.html

Thank you Sergio!

Hey, I got your message, actually I was replying to a Google+ post by Sigurdór Guðmundsson sharing this video. That's probably why it was confusing to reply to. Anyway, I appreciate that you get that the staircase isn't really what's going on, but since I was taught this this misconception in college, and had to correct it countless times since then, (interns, artists who know enough to be dangerous, etc.) I speak up when I see digital audio visualized with the zero-hold graph. We engineers need to stop putting that visualization out there so we can start to put an end to that idea. Really "diagonally" is not strictly correct either, it's a parabola most accurately. Only one possible solution for the D/A converter to find. But anyway, I'm not meaning to come down on you, Nigel Redmon like it must seem like I was --sorry about that! It's a great visualization of bit depth and dither, the grey/black graphics, I just think drawing the graph like you did leaves people with an exaggerated idea of what these distortions would look like in a waveform, when really they'd be much smoother than all those squared off points and lines.

Justin Newton No, I don't feel at all that you're getting on my case, so to speak. I'm just as sensitive to the point as you are, I'm sure. But to be clear, I didn't connect the dots to be "correct" in any manner at all. The connected line is a visual aid, like circling a point on a chart with a red marker to highlight it. Believe me, if I turned off the connecting line, people would not be able to make heads or tails of the chart-it would be just points dancing around. I tried it. The line is just there so that you can follow from one sample to the next clearly, especially as I change the amplitude.

Justin Newton And yes, I did consider doing band-limited reconstruction to simulate what would come out of an analog converter, but the visual difference for the staircase-ish part is relatively minor with the samples that close together (the dots would be obscuring most of it-I'd have to hide the dots, then I'd have lost what it is I trying to illustrate), and in the animated noise-added view it would be just messy and distracting, zoomed in that closely. The object is to let the eye follow that sample points, not to render an analog view.

Thank you so much, it helps to know-be sure to subscribe if you haven't so you don't miss my (long delayed, but I won't let another year go by) intuitive explanation of sampling theory...

I couldn't find that paper, but thanks!

Thanks, I appreciate you saying!

Thanks! I do appreciate the feedback. And I'm currently working on a couple of major videos after being too busy for a few years, so I'm glad you subscribed.

Appreciate it, Svein

Thanks! I know it may seem impossible, but I'm so close to finishing a new video-and it's prerequisite to another. maybe I'll get faster at doing this with practice...

Business interests want LOSSY. It's how they profit. They have been trying to convince us we can't hear the difference for decades. If you could sell 10% of something and make the same, you probably would. I understand. But full, native resolution recordings are the best, This is lossless, and if you dither from 24bit to 16bit, you technically have loss. No one wants to admit it b/c $$

Thanks, David

Fuck you

Thanks! You should be able to reach the website at earlevel.com...it's probably because the link has "http", from back before the site was secure-only. I'll update it...

Hm, I think that's right except for the factor 0.5. The noise amplitude is ±1 LSB (2 LSB peak to peak). That's the minimum dither level to ensure no signal correlation and no noise modulation. Offhand, I'm not sure about the LSB/2 reference, but take care that sometimes dither levels are expressed in rms.

Thanks, Jonathan. Yes-I've been wanting to do a video on sampling theory, expect to get to it this year. I wrote somewhat of an outline for it, starting here: www.earlevel.com/main/2017/08/16/sampling-theory-the-best-explanation-youve-ever-heard-part-1/

You'll get that very soon! I've been terribly busy, but hope to finish my follow-up video in the next week or so. You'll heard comparisons of dithered and truncated digital audio at different bit levels.

In the case of black and white print media (newspaper, magazine, b&w photocopies for handouts) such dithering is done because there are no gray levels of ink available.

To keep it brief: It's true that 16-bit is enough for audiophile quality, when fully utilized and with linear processing, but it lacks flexibility. But it's not nearly enough for heavy non-linear processing for example (for instance, say you record clean electric guitar, and want to apply an amp simulator for a overdriven sound-it will raise the 16-bit noise floor to an intolerable level). Maybe a simpler way to view it is that for only 50% more data storage (memory is cheap!), you get 256 times the dynamic range to work with (48 dB more).

I was thinking more about the necessity of dithering when downsampling from 24 to 16, rather than storage constrains. If everything was mastered in 16 bits, there would be no such necessity.

You wouldn't save on dither: When you master to 16 bits, that's when you'd have to dither. In fact, any time you apply processing-including a minor level adjustment-then save to 16-bit, you'd need to add dither. The key point is that a multiply expands resolution. For instance, if you have two fractional decimal numbers, hundredths precision (0.00 to 0.99), and multiply them, the result has a resolution of thousandths. 0.93 x 0.96 = 0.8928, for instance (perhaps that's a sample value and a gain fader value). If you try to fit that back into hundredths (0.89), you've truncated-you need to dither for a better error distribution.

Ok, thanks for explaining!

So if your using a project that is in 16bit 44.1 then you don't need to use dither at all when making the cd quality wav files right?

I did post the follow-up video, ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-KCyA6LlB3As.html. Regrettably, in that one I also said there would be a follow-up video to it, but it didn't happen because I never received some professionally recorded tracks that were promised. I do have another video planned on digital audio sampling (you can read the gist of it on earlevel.com), just been tied up with work for a while. It will happen!

Nigel Redmon hello nigel. Ok, i understand. Your explanation it was very usefull, so i was waiting for more. Thank you for the video.

10

Watch it one more time :-D

Short version: Limited resolution (sample size) results in a grid of possible values. The grid can possibly result in patterns in certain audio material that sound like the audio is distorted. By jiggling the grid a tiny bit, randomly, we don't get error patterns that line up with the audio signal-instead of a distorted signal, it sounds like the clean signal plus a tiny bit of hiss. Analogy: Close one eye and spread your fingers in front of your view, and read this. Your fingers will block some words. Jiggle your hand side to side, quickly, a small amount. Now you can read all the words, even though there is a little blur in front of them. The blur is better than the blocking.

You mean quantize, not downsample. And 24 bits for the final master is a waste. 16 bits already give 96dB of dynamic range _without_ noise shaping. With noise shaping, it rises to approximately 120dB, which is more than enough. To quote xiph.org/~xiphmont/demo/neil-young.html: “120dB is greater than the difference between a mosquito somewhere in the same room and a jackhammer a foot away.... or the difference between a deserted 'soundproof' room and a sound loud enough to cause hearing damage in seconds. 16 bits is enough to store all we can hear, and will be enough forever.”

Thanks!