Why is 16-bit undithered a "rough" wave, while 24-bit is smooth?

[board]

I like to think that I understand how digital audio works pretty well, but please help me understand this:

I was reading these measurements from Stereophile:

NAD M51 Direct Digital D/A converter Measurements

Sidebar 3: Measurements I used Stereophile's loan sample of the top-of-the-line Audio Precision SYS2722 system to measure the NAD M51 (see www.ap.com and the January 2008 "As We See It"; for some tests, I also used my vintage Audio Precision System One Dual Domain.

www.stereophile.com

Figure 6 shows an undithered 16-bit tone, whereas figure 7 shows the same with 24 bit:
"[T]he M51's reproduction of an undithered 16-bit tone at exactly –90.31dBFS was essentially perfect (fig.6), with a symmetrical waveform and the Gibbs Phenomenon "ringing" on the waveform tops well defined. With 24-bit data, the M51 produced a superbly defined sinewave (fig.7). "


Figure 6:

Figure 7:

Why are the two waves so different between 16-bit and 24-bit?

 

[DonH56]

24 bits adds many more levels to the waveform so a -90 dBFS signal uses many more "steps" than the 16-bit version. The ideal SNR of a 16-bit DAC is about 98 dB compared to 146 dB for a 24-bit waveform, and 24 bits has 256 times the levels ("steps") of a 16-bit DAC (16,77,216 levels vs. 65,536 levels). So the steps are likely much smaller and there are many more of them for a 24-bit DAC, making the waveform look much smoother.

Thinking about it another way, the -90 dBFS, the 16-bit waveform only has a few levels (~3 steps), whilst the 24-bit version has many more (~768 steps), thus the smoother-looking waveform.

There are some introductory articles about data conversion linked in my signature.

HTH - Don

 

[Ken Tajalli]

To add to the above:
This happens at acquisition/production. If you output a 16bit signal, and just pad it to 24, it stays the same.
Don will correct me, if wrong.

 

[Matt_Holland]

What does this test actually show, though as all signals should have either applied? Presumably the SNR of the DAC? Isn’t it all rather academic because a dithered signal would show no steps and a smooth waveform, and we can measure SNR or SINAD in other ways.

 

[Berwhale]

My simplistic understanding is that 1 bit equals roughly 6dB (hence 16 bits giving you ~96 dB of resolution). If the signal is down at -90dBFS, then 15 bits of the 16 bit samples are 0's, leaving you 1 bit to represent the signal. With 24 bit samples, you still have 8 bits to represent the -90dBFS signal which means the resulting waveform is much smoother.

 

[Matt_Holland]

My simplistic understanding is that 1 bit equals roughly 6dB (hence 16 bits giving you ~96 dB of resolution). If the signal is down at -90dBFS, then 15 bits of the 16 bit samples are 0's, leaving you 1 bit to represent the signal. With 24 bit samples, you still have 8 bits to represent the -90dBFS signal which means the resulting waveform is much smoother.

Yes, but it’s all academic. The signals were not dithered.

Dither explanation

 

[danadam]

because a dithered signal would show no steps and a smooth waveform

I'd rather say "noisy waveform".

 

[Matt_Holland]

I'd rather say "noisy waveform".

If you squint hard enough it looks perfectly smooth

 

[Ken Tajalli]

If you squint hard enough it looks perfectly smooth

pass that through a HF filter. It'll smooth it out alright.

 

[RayDunzl]

Why are the two waves so different between 16-bit and 24-bit?

Because the 16bit tone is using only 1 bit (and sign bit) -- just +1 or -1 or 0, at that volume level.

The 24bit file has 512 levels within that last bit of 16 bits, 255 "steps" above and 256 below zero, and zero.

 

[amirm]

What does this test actually show, though as all signals should have either applied? Presumably the SNR of the DAC? Isn’t it all rather academic because a dithered signal would show no steps and a smooth waveform, and we can measure SNR or SINAD in other ways.

Not sure what you are asking. If you mean my testing, I use 24-bit test signals unless specified otherwise.

 

[Berwhale]

Yes, but it’s all academic. The signals were not dithered.

Dither explanation

I think -90dBFS audio signal is pretty academic with or without dither.

 

[Matt_Holland]

Not sure what you are asking. If you mean my testing, I use 24-bit test signals unless specified otherwise.

Apologies there’s a typo in my post:

“What does this test actually show, though as all signals should have either dither applied”

I was asking what the graph of the un-dithered sine waves shows us, shown in the report linked to in the OP.

 

[amirm]

Ah. I don't know what the motivation for the test has been. Maybe there was a time that CD players/DACs didn't decode the right order bit of 16 bits correctly. I don't find any use in it.

 

[DonH56]

I don't remember why the test either, though I know I did at one time. I think it was to see if noise obfuscated the lsb-level signal, or nonlinearities corrupted the waveform.

 

[Blumlein 88]

Here is the same test on a 1986 CAL Tempest CD player by Stereophile. A combination of ultrasonic noise and low level linearity issues could give a poor result. For instance what should have been a -90 db signal here was -84.6 db.

Here is a Kinergetics CD player from 1990 with the next generation of DAC chips. Still some linearity issues, less HF noise. By this point and later the test was usually irrelevant. Just a case of crossing T's and dotting I's. From Stereophile.

For instance this 2008 Stereophile test of a Sony PS-1 Playstation. Low level linearity issues below -80 db. Few products had such issues by then.

 

[kemmler3D]

Why are the two waves so different between 16-bit and 24-bit?

In a nutshell, because at -90dB there are only a few of 16 bits left to use, where 24-bit at -90dB still has roughly 8 bits, I guess.

This is not a very consequential difference, because you can rarely hear anything that's 90dB below the signal. This is why it's often said 16 bits is enough for perfect sound quality.

 

[restorer-john]

Here is a Kinergetics CD player from 1990 with the next generation of DAC chips. Still some linearity issues, less HF noise. By this point and later the test was usually irrelevant. Just a case of crossing T's and dotting I's.

If it truly were an 'irrelevant' test by ~1990, all the plots subsequently would look the same, with perfectly resolved (3) individual levels with a perfect zero cross.

But that is not the case and still isn't today, is it?

I would argue if the 16bit -90.31dB is 'irrelevant', then so is any form of low level linearity test, especially a 24bit version- when the overwhelming vast majority of digital music consumed is 16 bit in the first place.

Amir is finding plenty of D/As where they truncate or mute below 14/15 bits, so the test is still valid.

 

[Blumlein 88]

If it truly were an 'irrelevant' test by ~1990, all the plots subsequently would look the same, with perfectly resolved (3) individual levels with a perfect zero cross.

But that is not the case and still isn't today, is it?

I would argue if the 16bit -90.31dB is 'irrelevant', then so is any form of low level linearity test, especially a 24bit version- when the overwhelming vast majority of digital music consumed is 16 bit in the first place.

Amir is finding plenty of D/As where they truncate or mute below 14/15 bits, so the test is still valid.

Yes irrelevant. Amir does linearity, noise and dynamic range tests. Those tell you everything this plot will with less ambiguity. This plot of undithered 16 bits is graphically easier to understand by some people I suppose. And how often is undithered 16 bit going to be a source?

I didn't show the plots once Stereophile was showing that test and then the dithered version. Even those doing poorly on the undithered 16 bit did a more reasonable job with a dithered signal.

There is the odd incompetently done device which will flunk this test or have other issues. With the small number of those and the very unlikely chance you'll be listening to undithered 16 bit this is a test not worth doing. Linearity and noise will pick up those device specific issues.

 

[board]

24 bits adds many more levels to the waveform so a -90 dBFS signal uses many more "steps" than the 16-bit version. The ideal SNR of a 16-bit DAC is about 98 dB compared to 146 dB for a 24-bit waveform, and 24 bits has 256 times the levels ("steps") of a 16-bit DAC (16,77,216 levels vs. 65,536 levels). So the steps are likely much smaller and there are many more of them for a 24-bit DAC, making the waveform look much smoother.

Thinking about it another way, the -90 dBFS, the 16-bit waveform only has a few levels (~3 steps), whilst the 24-bit version has many more (~768 steps), thus the smoother-looking waveform.

There are some introductory articles about data conversion linked in my signature.

HTH - Don

Thanks for the explanation, and thanks to anyone else who has responded and helped explain.
I asked because I wanted to understand why the waveforms looked like that rather than figure out if the test is relevant or not.
Before posting I had also been wondering if the explanation was due to the higher noise floor.
Thanks again everyone. You can keep the conversation going if you like, but I think I got the answer I was looking for .