Bit-depth info / question

[ecc83]

If you ignore antialiasing needed to comply with the Nyquist requirements, you'll have trouble.

If you ignore reconstruction filtering at the output, you'll have trouble.

If you use dither, you get rid of quantization distortion and can easily resolve signals below the noise floor.

That Dither Thing - [English] (nice demo of the last point)

This is signal processing 101. 16 bits is more than enough to exceed any possible dymanic range that can be reproduced in a quiet room. 44.1k is more than enough to perfectly reproduce signals with frequency content to 20kHz.

How true^
There was more than one letter in the hallowed pages of Wireless World and Hi Fi News (hallowed then!) pointing out that few people could afford speakers that produced 100dBSPLs or the 100W+ amps needed to drive them (assuming speaker sens' of 90dB/W/mtr and that is generous). At the "other" end very few domestic rooms get quiet enough.

They were not of course to know back in the 80's that 80% of CDs made would have that hard won dynamic range smashed into the top 8dB and that levels would be pushed to within a gnat's boxers of 0dBFS!

Dave.

 

[pcnj50a]

Dither doesn't resolve signals in such a way that restores the lost data from truncation, it adds noise to cover up the square wave with something much more pleasant.

No, it actually does restore the "lost" data as the demo in that link shows. If you're a numbers guy, you can see the effect in distortion spectra- the quantization distortion is eliminated at the expense of a higher noise floor (at the +/-1 LSB level). The odd harmonic components go away, they're not just "covered up."

 

[snow lizard]

Dither doesn't resolve signals in such a way that restores the lost data from truncation, it adds noise to cover up the square wave with something much more pleasant.

No, it actually does restore the "lost" data as the demo in that link shows. If you're a numbers guy, you can see the effect in distortion spectra- the quantization distortion is eliminated at the expense of a higher noise floor (at the +/-1 LSB level). The odd harmonic components go away, they're not just "covered up."

I understand what you're saying. I think we're on the same page, just putting different words on the same thing. Dither doesn't resolve the signal so for example if we have a sine wave (or any signal for that matter) at the LSB that gets rounded off into a square wave, the dither doesn't restore it back to the original. Higher resolution can do that to a point, until we reach the limits of the gear on the analog side of the D/A. Adding non-frequency specific noise does not. While we're increasing the noise floor by a miniscule amount that we're not really going to be able to notice in any practical way, dither will effectively kill the nasty spray of harmonic distortion that has farther reaching effects, which is really what we're interested in.

There's a tradeoff involved but it's an easy one to accept. I think we can agree on that.

In any case it's a very good point and I'm glad you brought it up.


Cheers.


Next week:

TPDF - WTF???

 

[pcnj50a]

Nope, we're still on two different pages. If I'm reading you right, you're confusing dither with reconstruction filters.

Dither doesn't resolve the signal so for example if we have a sine wave (or any signal for that matter) at the LSB that gets rounded off into a square wave, the dither doesn't restore it back to the original.

That's right- the dither doesn't, it's the reconstruction filter that does this. After you bandwidth-limit the output of the DAC to 1/2 the sampling frequency (a basic requirement of sampling), you get... your signal. Not a square wave. No dither needed.

Now, let's say we're reproducing a sine wave with a peak amplitude of 1/4 bit. With no dither, we get no output from the DAC. Now dither the LSB and what we get is... a 1/4 bit with 1 LSB worth of noise. It's easy to see on a spectrum analyzer, and if you listen to the stuff I linked to, it's easy to hear below the noise floor.

 

[snow lizard]

I'll have to concede the point. What you're saying is starting to sound a lot like what some of the mastering guys have said on the subject, and the examples and measurements are very telling. I'm starting to form a clearer picture of how the pieces fit together.

It seems that these issues could be easy to deal with by hardware and software design engineers so that end users don't even have to think about it, but that's not where we're at. There's a lot of confusion and misinformation out there, as well as differing opinions on how relevant the issue really is.

 

[pcnj50a]

There's a lot of confusion and misinformation out there

Absolutely. This stuff is complicated, and as you point out, usually doesn't have to be for the end user. But geeks like me find it interesting.

 

[Farview]

The other thing about it is that what happens with the information at the lsb doesn't really matter that much. Chances are that it will be obscured by the self noise of anything it would get played back on as well as trampled by the rest of the signal.

Creating a sine wave at the lsb is kind of the same thing as creating a 21khz wav with a 44.1k sample rate. Any time you go to the edge of the parameters that the design is supposed to work at, it will always turn into a mess. So it enevitably doesn't mean anything.

44.1k sample rate doesn't resolve a 25khz sine wave? Of course not, it wan't designed to.
8 bit audio can't resolve a sine wave at -46dbfs? Of course not, it wasn't designed to.

 

[pcnj50a]

The other thing about it is that what happens with the information at the lsb doesn't really matter that much. Chances are that it will be obscured by the self noise of anything it would get played back on as well as trampled by the rest of the signal...

...8 bit audio can't resolve a sine wave at -46dbfs? Of course not, it wasn't designed to.

The source noise (e.g., mike or mike preamp noise) actually can act as dither! Usually it's more than the LSB of a 16 bit system. So again, it's not a matter of "trampling" or "obscuring," it's a much more subtle and wonderful result. With dither, you CAN resolve a sine wave at -46dB in an 8 bit system.

 

[snow lizard]

The other thing about it is that what happens with the information at the lsb doesn't really matter that much. Chances are that it will be obscured by the self noise of anything it would get played back on as well as trampled by the rest of the signal.

Creating a sine wave at the lsb is kind of the same thing as creating a 21khz wav with a 44.1k sample rate. Any time you go to the edge of the parameters that the design is supposed to work at, it will always turn into a mess. So it enevitably doesn't mean anything.

44.1k sample rate doesn't resolve a 25khz sine wave? Of course not, it wan't designed to.
8 bit audio can't resolve a sine wave at -46dbfs? Of course not, it wasn't designed to.

Truncation and the effect of harmonic distortion begins before you reach the LSB. Harmonic distortion is cumulative.

There are always going to be ways to argue against it until you can hear otherwise. There are always going to be ways of masking the issue until you get past the limitations. If you simply track at too hot a level you're probably going to add enough distortion to the signal that isn't a byproduct of truncation to a point where dither wouldn't really make a difference. Happens all the time and the people doing it aren't even aware. Once people experience the effect of good gain staging they don't view it as a subjective difference, but a magnification of clarity. The same arguments can be applied to acoustic treatment.

Dither isn't restricited to audio systems and it isn't snake oil. It can be measured and demonstrated. Here's a half decent link for a basic explaination:

Dither - Wikipedia, the free encyclopedia

The pictures of the cat are hard to argue against subjectively.

You can eliminate the need for dither by increasing the resolution. I haven't seen a DAW with a 16 bit mix engine, or 24. We know why. Yet there are still 24 bit converters that either have options for dithering, or else they're already dithering.

Plugins are another issue.

Someone stepped in and said "well I can't hear it so it's snake oil". And thus was formed the great divide between the two halves of teh internets.


And to be clear I think you're a good guy Jay, so I'm not trying to be overly pedantic here but anyone trying to learn about it should be aware that there are different viewpoints and a legitimate body of technology and science behind it spanning decades. People will come to their own conclusions.

 

[Farview]

I do believe in dither, and I completely understand it. I think Im just unclear about the point you are trying to make. Your experiment doesn't prove anything other than the fact that you need more than one bit to accurately produce audio. From what I gathered, you thought that something was wrong with that. There isn't.

Of course for dither to work, you have to start with more bits of information and truncated it downwith the dither.

 

[dgatwood]

Getting back to 16 vs. 24, I've seen a lot of reference on the audio forums that 24 bit improves the performance of plugins.

I'm pretty sure they're wrong. Plug-ins always run in a 32-bit float environment (or higher) in basically every audio system on the planet. Thus, the extent of the difference between 24-bit and 16-bit recording is the lower noise floor. To the extent that you're riding in the mud, your audio is going to suck anyway, and if you aren't, there's not likely to be a significant effect on the way any plug-in functions (except maybe quantization tools, and probably not even then).

Higher sampling rates, however, can make a difference in the accuracy of plug-ins that perform certain time-domain operations, such as pitch detection and correction, because plug-ins actually do run at the sample rate of the source material.

 

[dgatwood]

Each bit is 6 dB. This is linear.

The way a binary word works is 2 (the number of values available in a bit, 0 or 1) to the power of how many bits you have. This is exponential, not linear.

A linear change in decibels results in an exponential difference in voltage. A 6dB change in volume translates to doubling the voltage. A single bit = 6 dB. Therefore, when you double the voltage, you also double the numeric value that represents it, give or take. If that mathematical relationship is not maintained, your audio sounds very... unusual. I actually wrote a plug-in that changed audio non-linearly like that. The result was fascinating. At values close to 1, it sounded like compression/expansion, but quickly turned into... something very awful sounding. Of course, it might also have had computation bugs. Hard to say.

 

[snow lizard]

I do believe in dither, and I completely understand it. I think Im just unclear about the point you are trying to make. Your experiment doesn't prove anything other than the fact that you need more than one bit to accurately produce audio. From what I gathered, you thought that something was wrong with that. There isn't.

Oh, sorry. I thought that by saying what happens at the LSB doesn't matter you were dismissing dither. My bad.


My "experiment" was a demonstration of the relationship between bit depth, signal level and resolution. There isn't anything wrong with it. That's how it works. By suggesting that "my DAW is broken" (it isn't btw) I thought that you just didn't get it.

Anyway, sorry for the confusion.

 

[snow lizard]

A linear change in decibels results in an exponential difference in voltage. A 6dB change in volume translates to doubling the voltage. A single bit = 6 dB. Therefore, when you double the voltage, you also double the numeric value that represents it, give or take. If that mathematical relationship is not maintained, your audio sounds very... unusual. I actually wrote a plug-in that changed audio non-linearly like that. The result was fascinating. At values close to 1, it sounded like compression/expansion, but quickly turned into... something very awful sounding. Of course, it might also have had computation bugs. Hard to say.

Cool Edit has a bunch of different file formats you can work in. Some of them are non-linear, designed for telephones and such. I suppose converting audio to one of those would yield a similar result.

They don't recommend it in the manual.

 

[Ethan Winer]

There's a lot of confusion and misinformation out there, as well as differing opinions on how relevant the issue really is.

+1 to all the misinformation out there, though relevance is trivial to determine with a few simple experiments. I've done many such experiments, and they're available for download on my web site so you can easily assess relevance for yourself:

Converter Loop-Back Tests
Artifact Audibility Report
The Truth About Record Levels
Hearing Below the Noise Floor
Dither Report
Converter Comparison
Perception - the Final Frontier
AES Audio Myths Workshop(hour-long video)

--Ethan

 

[snow lizard]

+1 to all the misinformation out there, though relevance is trivial to determine with a few simple experiments.
--Ethan

To be honest, I've been a big fan of your internet presence for over a decade and it opened my eyes to the subject of acoustic treatment. You've taken a difficult subject to understand and made it clearer to a lot of people without a lot of math or confusion, so I have to say thank you for that.

I have to admit though, talking about reconstruction filters in a discussion about bit depth is confusing me a little. I understand that the reconstructiuon filter "smooths out the steps" so that what you hear is a representation of the original waveform, not simply a connect-the-dots approximation. This is truth.

I also understand that there are two processes that have to take place to record PCM audio: sampling and quantization. Both create steps.

The sampling steps are used to calculate the waveform and low pass filtering the stuff above Nyquist is a basic requirement.

The quantization steps in linear PCM are basically roughly equal fractions of what has been or will become a volt in the intermediate storage stage.

Can you explain the role of the reconstruction filter on the quantization process? Simply opening a fixed bit file and zooming in to the least significant bit range of any signal in a wave editor that shows individual sample points suggests there isn't one. This seems to be congruent with all of the educational material I've read on the subject.


Thanks again,


sl

 

[Ethan Winer]

I have to admit though, talking about reconstruction filters in a discussion about bit depth is confusing me a little.

We've talked about a lot of things in this thread, including sample rate.

Can you explain the role of the reconstruction filter on the quantization process? Simply opening a fixed bit file and zooming in to the least significant bit range of any signal in a wave editor that shows individual sample points suggests there isn't one.

Not to turn this into a plug for my book, but I explain this in more detail than I can write here. The short version is the output filter not only removes steps visually, it makes the output exactly analogous to the input. If it didn't, the result would be distortion. That modern converters have distortion amounts preceded by many zeroes proves those steps really aren't present.

Understand that the waveform shown in an audio editor program hides much of the detail. The waveforms you see are like a GIF image file, and I believe most programs store only 8 bits of visual data. If they stored the full 16 or 24 bits, the image files you see would be as large as the audio data! So zooming in doesn't show the lowest bits. Further, audio editor programs don't smooth the samples as that would make the image files much larger to draw not only all the samples, but 10-30 smoothed points in between.

--Ethan

 

[snow lizard]

Strange.

I brought a sine wave in 32 bit down to -144 in Cool Edit 2.0 and it let me zoom into it just fine. No truncation whatsoever. I'm also finding truncation in 16 bit at -60. I realize this is not a game changer - I'm not an advocate of riding signals around in the dirt or anything, but on my system it seems that more than the noise floor is affected. Plus my D/A isn't filtering it out.

Oh well, dare to be different I guess.

 

[dgatwood]

Cool Edit has a bunch of different file formats you can work in. Some of them are non-linear, designed for telephones and such. I suppose converting audio to one of those would yield a similar result.

They don't recommend it in the manual.

Non-linear, yes, but they scale the signal back at the end. And therein lies the difference.

It's lossy when you do that, but if you don't scale it back, it's... well, way more than just lossy. IIRC, it only sounded acceptable within about the range o = i ^ 0.95 to o = i ^ 1.05, give or take.

 

[Farview]

Strange.

I brought a sine wave in 32 bit down to -144 in Cool Edit 2.0 and it let me zoom into it just fine. No truncation whatsoever. I'm also finding truncation in 16 bit at -60. I realize this is not a game changer - I'm not an advocate of riding signals around in the dirt or anything, but on my system it seems that more than the noise floor is affected. Plus my D/A isn't filtering it out.


Oh well, dare to be different I guess.

I think some of the confusion might be coming from you attempting to draw conclusions about the behavior of digital audio in general by observing the behavior of an ancient version of cool edit. None of us can replicate your results, so that might point to cool edit being silly instead of giving you much usable information about the behavior of digital audio.