Monty Rides Again: Battling the persistent "stair-step" myth

[sonics]

I was pleased to see a young man re-present the famous video made by Monty Montgomery about the digital audio "stair-step" myth.
Please encourage all disbelieving "audiophiles" to watch it. Thirteen minutes of pure and simple enlightenment.

Watch out for the famous cassette tape flip, and the legendary mosquito and jackhammer comparison!

https://youtu.be/cD7YFUYLpDc

[Martin Walker]

Brilliant!

[Rich Hanson]

That came up in my feed a few days ago, well worth a watch.

[Hugh Robjohns]

Hallelujah — they've seen the light!

[Martin Walker]

I've now subscribed to his channel, as his other videos are illuminating too, and I like his very practical and straightforward approach

[RichardT]

A question - I think the reconstruction filter will generate the source signal and pure noise only if the quantisation error is random. But is that always the case in all circumstances, for example if the frequency of the test tone is related to the sampling frequency?

[Hugh Robjohns]

A question - I think the reconstruction filter will generate the source signal and pure noise only if the quantisation error is random.

As I explained (and demonstrated in the associated audio files) in this article, quantisation error is essentially random when the signal crosses many quantising levels, but becomes increasingly coherent when the signal is a lower level so generates both harmonic and non-harmonic distortions.

Adding dither enforces randomized errors regardless of the signal level — that's why its done and such an essential part of high-quality digital audio.

But is that always the case in all circumstances

Yes, providing dither is used or the signal crosses many quantising levels.

...for example if the frequency of the test tone is related to the sampling frequency?

Not a relevant factor at all. In my recent audio test file article the sample-peak meter test used a tone at a quarter of the sample frequency... and it plays perfectly without any noise artefacts.

[RichardT]

Thanks Hugh! I think I understand dither now.

[merlyn]

As ever there's more to it. Stairsteps do exist inside the interface in the zero order hold circuit. What Monty showed was that they're effectively filtered out. Stairsteps could have been found by looking inside the interface at the stage immediately before the reconstruction filter. As a simplified de-bunking of digital audio being jaggy once it's converted back to analogue it's OK.

Representing samples inside the computer as stairsteps is wrong, because samples inside the computer are simply numbers, which ideally last for zero time (the aperture). 'Lollipop sticks' are the right way to represent samples inside the computer.

Monty's grasp of dither also seems a bit off.

[Hugh Robjohns]

Monty's grasp of dither also seems a bit off.

His explanation might be simplified to ease comprehension by his non-engineering audience, but I think you'll find his own grasp and understanding is as solid as yours.

[Mike Stranks]

I think the immediately-preceding exchange above illustrates an issue that often crops up here in the Forums. (NB. I refer to the content of the video, not the exchanges here.)

Someone who obviously has very little knowledge or understanding on a topic will pose a question to which the full answer has considerable width and depth. Does one give them the whole nine yards, or merely the three-and-a-bit that covers the essence and answers the question?

If I'm in a position to answer, I usually try and stick with the 'three-and-a-bit' principle, but trying to ensure that I haven't introduced error through simplification.

Things get complicated when those with detailed knowledge and understanding then feel it's necessary to give the 'five-and-a-bit' that wasn't included in the original response. A lively debate can then ensue among the cognoscenti with i's being dotted and t's crossed and "Ah! Yes! But..." statements flowing freely... leaving the poor old OP bemused and confused.

Sometimes, a little imparted knowledge is enough... as long as the OP realises that there is more that could be learned and understood to get the full picture.

[merlyn]

I saw Monty's video back in the day. What I thought was a possible takeaway from the original video was that dither doesn't really matter. Fond of the shocking reveal, he says at one point "No great recording was ever ruined by leaving off dither". Possibly true, but as a video for a wide audience this statement could be interpreted as "Don't bother with dither", which isn't a good takeaway.

[Hugh Robjohns]

Technically true, but in all the places and processes where it really matters dither is performed automatically anyway. It can't be left off.

And in the few places where a user can intentionally or accidently fail to dither, it either doesn't matter because it introduces desirable artefacts, or is very unlikely to be noticed in practice anyway.

I have a CD called Cinemagic by Dave Grusin. It has no dither at all due to a mastering cockup. No one I've played it too has ever noticed....

[merlyn]

Mike's point about 'the whole nine yards' is interesting. Three and a bit out of nine is a fail. With three and a bit out of nine, a person has got more wrong than right.

Someone asked me to go through Miller Puckette's The Theory And Technique Of Electronic Music with them. Miller Puckette was a mathematician and the book uses maths quite a lot. I pretty soon realised Miller Puckette's approach wasn't going to work with this particular musician.

At this point I realised that 'The Audio Gnomes' is as good a metaphor as any. There's gnomes inside the computer that carry audio bits around and when processing is required, the gnomes bash the audio into shape with their bit hammers. The great advantage of this metaphor is that nobody in their right mind would think that that was what was actually happening.

Is three and a bit out of nine any better than The Audio Gnomes?

[Wonks]

Mike's point about 'the whole nine yards' is interesting. Three and a bit out of nine is a fail. With three and a bit out of nine, a person has got more wrong than right.

There are misused metaphors here. “The whole nine yards” is a reference to the length of the .50 cal ammunition belts used on WW2 Corsair fighters. If you shot a plane down with far less than the whole belt, then that’s a good thing, not a bad one, as you could go on and shoot something else down. You’ve used just enough ammo to do the job.

The whole primary (and a lot of the secondary) education system is built upon a mixture of facts, half-facts and gross simplifications in order to get general concepts across. A lot of people getting into digital recording in its many forms are at the equivalent of the primary stage of learning, and anything that helps them understand the basic concepts is fine in my book. They can then go on to a fuller, more complete understanding in time.

Often, pitching too full and detailed an explanation to a beginner or someone who struggles with technical information can be counter-productive. The simpler explanations, even if they include an element of fudging and simplification, are often the most helpful.

Of course if you know you are replying to someone who already has a reasonable grasp of the principles, then be as technical and correct as you want.

The answer given needs to be tailored to the needs of the person asking it, though if simplifications are being used, it doesn’t harm to say so.

[amanise]

I've noticed iZotope automatically applying dither every time you save a file with no opt out available. I believe the same happens with Audacity now too. More than happy for that to happen if those software authors think it's worth putting the dev time into.

But I'm gutted there are no Audio Gnomes! How could you break it to me like this??

[Wonks]

Studio Support Gnome would beg to differ.

[amanise]

Studio Support Gnome would beg to differ.

[Mike Stranks]

Mike's point about 'the whole nine yards' is interesting. Three and a bit out of nine is a fail. With three and a bit out of nine, a person has got more wrong than right.

I refer the Hon Gent to the following:

https://en.wikipedia.org/wiki/The_whole_nine_yards

especially the first two lines...

[Wonks]

I appear to have been misled by the internet as to the origin of the phrase, but my description certainly was one of the meanings/usages that seems to have been derived from an older saying.

[Urthlupe]

Don’t stress it m8, we still love those waggly ears…..

Loopy xxx

[sonics]

Surely the appropriate phrase here is "the full Monty"?

In teaching the principles of digital audio the fine details are really not relevant here. What is important is realising the error in describing the output of these digital audio systems as a series of steps. Just the simple process of drawing those little horizontal lines has caused a world of misunderstanding, and a reason for some ignorant people to have a go at digital systems.

If I measured the position of a tyre valve on a rotating wheel at set intervals I could draw it on a graph and connect the value to create a stair-step, but it wouldn't be correct. At no point does the valve position jump from one value to the next. That would be a bumpy ride...oh, wait, unless we increase the rotational speed of the wheel by, say, having smaller wheels! Yes, that's it, I'm going to put tiny wheels on my car and get a really smooth ride...

[Mike Stranks]

I've noticed iZotope automatically applying dither every time you save a file with no opt out available. I believe the same happens with Audacity now too. More than happy for that to happen if those software authors think it's worth putting the dev time into.

Not in the version of iZotope that I use... only if I change the word-length...

[amanise]

I've noticed iZotope automatically applying dither every time you save a file with no opt out available. I believe the same happens with Audacity now too. More than happy for that to happen if those software authors think it's worth putting the dev time into.

Not in the version of iZotope that I use... only if I change the word-length...

My iZoptope is the cut down intro one (I think its called Elements - or similar). It's about a year or so old. I'm not on my DAW or I'd post the version number. Maybe they made the simplified version just do it for simplicity's sake?