Dithering is a Mathematical Process - NOT a psychoacoustic process.

[JohnPM]

985.1Hz seems to work... well, at least over 8 seconds, the smallest absolute values are "exercised" twice, and the largest absolute values considerably more than 100 times.

Doesn't 999.8 Hz exercise all 16 bit values at 44.1 kHz in less time (about 3.7 s)? Also seems to work at 48 kHz, 88.2 kHz and 96 kHz.

 

[xr100]

Doesn't 999.8 Hz exercise all 16 bit values at 44.1 kHz in less time (about 3.7 s)? Also seems to work at 48 kHz, 88.2 kHz and 96 kHz.

985.1Hz works at 48kHz also.

At 44.1kHz, all values are exercised at 999.8Hz and 985.1Hz within 3.75 seconds. But, 999.8Hz is nearer to 1kHz. ;-) And actually, looks like 999.8Hz works within 2 seconds.

Download file.

(Link expires in one week.)

 

[Serge Smirnoff]

View attachment 49700

Does this mean you're developing your own DAP?

This is a concept player, which helps to understand the benefits of manufacturing audio devices with “overkill” audio quality:

1. We listen all recorded music “through ears” of creator(s) - musicians/producers/sound-engineers. A “warmth and depth” of sound at a listening point can not be any better or different than that defined by those people. Playback system can not and should not create them, it has to transfer those characteristics of sound untouched, it has to be transparent.

2. The required transparency is much easier to achieve at the engineering level of audio signal, because we are good enough in engineering and much weaker in psychoacoustics. Those local thresholds of audibility for various types of distortion/degradation depend heavily on listeners and the signals used. Hardly any reliable and universally agreed objective audio metric can be created. It is much easier to establish such metric on the engineering level of signal, based on absolute thresholds of audibility. For circuitry designers/engineers it does not matter much what particular level of accuracy for m-signal needs to be achieved: -50dB, -100dB or -150dB. They already can do this. Yes, it requires more R&D but in mass production the chips/solutions will be cheap anyway.

3. When playback channel is transparent the role of sound engineers will skyrocket because of (1). Today they are in shadow, just a technical stuff for most listeners. This is not fair.

4. On top of this transparent channel any audio processing can be added. This is a new market of applications for creative listening: vinyl, tube distortions, spatial enhancers, equalizers, dynamic compressors, concert hall simulators, room correctors, etc. In fact, this is the market of pleasant audio degradations/distortions. Some of them today are sold by high-end industry in the form of their overpriced devices. Definitely such “nice degradations” can be better accomplished in software, not in hardware.

5. The transparency of audio path then can be easily controlled with a single measurable parameter, which will indicate the class of audio accuracy the measured device belongs to. Df-metric helps to define the required levels of accuracy for various listening environments. Such approach is better and open alternative to MQA.

And returning to your question - am I developing such player? Actually, there is no need to develop it, any semiconductor company with sufficient experience can design and manufacture it. They havn't done this already because nobody asked them for. They must be “incentivized” by audio consumers. The player above can be considered as an example of could-be-successful marketing campaign for new audio products using the novel concept of “New High-End” or “New High Fidelity” or just “Honest Audio” / "Honest Fidelity" / “Ho-Fi” ))

 

[Hayabusa]

1. We listen all recorded music “through ears” of creator(s) - musicians/producers/sound-engineers. A “warmth and depth” of sound at a listening point can not be any better or different than that defined by those people. Playback system can not and should not create them, it has to transfer those characteristics of sound untouched, it has to be transparent.

So in short your goal is to replicate the way the creators were listening to their creation.

There is so much information missing to reach this goal:
quality of the ear of the creator (how old is he for instance)
Exact measurements on the monitoring system. (Speakers/headphones/acoustics of the listening room/studio)
The exact sound level the creator was evaluating the recording.

In short: you will never reach your goal.

 

[Serge Smirnoff]

So in short your goal is to replicate the way the creators were listening to their creation.

There is so much information missing to reach this goal:
quality of the ear of the creator (how old is he for instance)
Exact measurements on the monitoring system. (Speakers/headphones/acoustics of the listening room/studio)
The exact sound level the creator was evaluating the recording.

In short: you will never reach your goal.

Yes, there are many obstacles. But this goal of audio reproduction systems is better to discuss in comparison with other possible alternative goals. BTW, what are they today? To my current understanding all other ones are worse/misleading and suffer from the points you mentioned as well. To have the correct goal (even hard to achieve) is important. At least it shows where to move. In some cases the goal (to replicate the way the creators were listening to their creation) is easily achievable - if some music was created/mixed in headphones and intended for listening in them (binaural recordings as an example), then you will get sensation very close to the original. But once again, I think the right/reasonable goal is important. Those who want to reach it in full can make some efforts by themselves, especially taking into account how much efforts today are wasted for false goals by audiophiles.

 

[xr100]

So in short your goal is to replicate the way the creators were listening to their creation

If you want auditory perfection then it has to go back, say, to the instruments used to "create" the "creation."

 

[Here2Learn]

I don't have an EE/AE background and being late to the thread, it's a long hard read for a layman. I knew dither was used on digital signals to preserve information, but didn't know why/how.

I think this sums up dither nicely. (somebody feel free to scream if something in it is wrong). I found this visual explanation quite elegant:

Sorry @j_j your first posting was not good for me. And other more technically savvy jumped in on finer points which made it harder to follow on the basic questions of what is dither, why we use it, why (as you say) it's a mathematical process and not a psychoacoustic one.

The question I am left with is, are different types of dither just applying an algorithm that produces a different type of probability density function (or dither signal)?

If so, what are the pros and cons relative to the example in the video?

 

[j_j]

I don't have an EE/AE background and being late to the thread, it's a long hard read for a layman. I knew dither was used on digital signals to preserve information, but didn't know why/how.

I think this sums up dither nicely. (somebody feel free to scream if something in it is wrong). I found this visual explanation quite elegant:

Sorry @j_j your first posting was not good for me. And other more technically savvy jumped in on finer points which made it harder to follow on the basic questions of what is dither, why we use it, why (as you say) it's a mathematical process and not a psychoacoustic one.

The question I am left with is, are different types of dither just applying an algorithm that produces a different type of probability density function (or dither signal)?

If so, what are the pros and cons relative to the example in the video?

Take another look at the results when you have a sine wave just under one LSB. That's really the key to how information is preserved, even if you don't understand what "makes noise independent of signal" is, or how that works out.

I'm "at work" at home right now, can't watch the video right now.

 

[j_j]

The video appears to be exactly the same discussion as my own post about 1 lsb sine waves.

 

[Here2Learn]

The video appears to be exactly the same discussion as my own post about 1 lsb sine waves.

Well that was the intention Just to be more apt for a layman with no assumed knowledge. TPD meant nothing to me on first reading and I only know what LSB means because I develop software, but to anybody outside EE/AE or overlapping disciplines, it might not.

For example, I now assume what you meant by TPD is the triangular probability density referred to in the video as Triangular Probability Density Function (TPDF). I needed to find information that described what TPD might be in order to 'get' your post. From my initial post, I was hoping you could answer the latter two questions in lay terms. Are all alternate dither functions going to be TPD's or are other probabilistic shapes used? Why and to what benefit and cost?

 

[j_j]

Well, you want triangular PDF dither, meaning the probability density function (PDF) is shaped like a triangle (symmetric about zero). That is what ensures the lack of signal-related distortion in both amplitude and power.The sigma (power) of the dither is also exactly specified compared to the step size of 1 LSB.

The frequency content of the dither can, however, be varied quasi-independently of the dither PDF within broad ranges, although doing so is somewhat of a tricky thing. The dither frequency shape describes the "background noise" remaining in the signal from the quantization noise.

There is also noise-shaping, which is different than dither, and which can be used in addition to (or sometimes in place of, but there are tricky issues to that) dither, to shape the quantization noise to mimic, for instance, the zero loudness curve. (meaning the same shape as the absolute threshold of hearing, which some people think, with some justification, may be relevant)

One can extend that noise shaping until one gets to SACD or multibit SACD, all of which are noise-shaped PCM systems, but now that is a horse of another color, and rather much more complex than dither. Yeah, it all ties together eventually, of course.

 

[dc655321]

Well that was the intention Just to be more apt for a layman with no assumed knowledge. TPD meant nothing to me on first reading and I only know what LSB means because I develop software, but to anybody outside EE/AE or overlapping disciplines, it might not.

For example, I now assume what you meant by TPD is the triangular probability density referred to in the video as Triangular Probability Density Function (TPDF). I needed to find information that described what TPD might be in order to 'get' your post. From my initial post, I was hoping you could answer the latter two questions in lay terms. Are all alternate dither functions going to be TPD's or are other probabilistic shapes used? Why and to what benefit and cost?

Since dither is intentionally adding "noise" to signal, one does need a PRNG (governed by some type of PDF/Characteristic Function) to draw variates from as a source of said noise. Noise-shaping does put a bit of a slant on that though.

As @j_j said, drawing dither variates (noise) from a Triangular PDF severs dependencies between input and error signal up to second order (variance or second moment). To contrast, dither drawn from a Rectangular PDF will have an input-signal dependence on its variance, so the noise floor of such a dithered signal will modulate with the input.

Not sure if it's mentioned in this thread (certainly is elsewhere), but a TPDF is simply implemented from an average of Uniform PDFs. And those can be calculated very quickly.

If you're a "show me some code" type of person, I've found this bit from Audacity useful.
If you're comfortable with math, you may want to dive into the details in a canonical paper on the subject of dither in audio.

 

[mansr]

multibit SACD

What now? I've never heard of that before.

 

[Here2Learn]

@j_j and @dc655321 Thanks for the response, both helpful.

What now? I've never heard of that before.

Is that because of the hint in j_j's post that these might be noise-shaped towards the zero loudness curves (updated Fletcher-Munson curves) and therefore may be subjectively perceived as 'better'? I think that would be a whole 'nother thread.

 

[j_j]

Just to throw another handful of dust into the water, a gaussian is the distribution that would eliminate all moments, not just first and second, in terms of signal correlation.

When you bandpass both a tpd or a uniform dither, you start to move toward gaussian.

 

[Here2Learn]

Just to throw another handful of dust into the water, a gaussian is the distribution that would eliminate all moments, not just first and second, in terms of signal correlation.

Sorry, lost me there. Any way to show visually? (The other sentence I haven't quoted seems intuitive)

 

[j_j]

Sorry, lost me there. Any way to show visually? (The other sentence I haven't quoted seems intuitive)

Not really, except that when you average many uniform distributions you get gaussian as a limit.

 

[MRC01]

Here's an experiment: use REW to generate a 622 Hz sin wave in 24-bit resolution at level -114 dB.
Why -114 dB? Because it's well below the -96 dB limit of 16-bit audio.
Why 622 Hz? It's easy to hear, smack-dab center of hearing range, and it's E flat which is a cool musical note. But use your favorite note instead, if you like.

Load this file into Audacity.
Go into Audacity settings, quality, ensure dither is set to Triangle.
Use the Audacity track format menu to transform this 24-bit file to 16-bit. The sin wave is still there. Can't hear it? Use effects/amplify to amplify it by +90 dB so peak levels are just below 0 dB. Audacity amplify maxes out at +50 dB, so apply +50 dB, then another +40 dB. Play it (ensure to adjust volume downward because it will be loud) and you can easily hear the sin wave in the noise.
Find a friend who thinks 16-bit audio can't capture information below -96 dB, and show him this.

To see how dither is critical to this process, see what happens without dither: go into Audacity settings, set dither to None.
Now load the original 24-bit file again, and transform it to 16-bit. After transforming, set dither back to Triangle. Now amplify +50, then +40 like before and listen to the noise. The signal (622 Hz sin wave) is gone. It's pure noise.

In this sense, one can say that dithered digital audio has infinite resolution at any bit depth. Dither is an essential part of digital audio, and the bit depth determines the noise level, not the resolution. Of course, in practice it's not really infinite because when the noise level is high enough masks low level signals. But the point is, 16-bit audio can capture low level detail well below -96 dB.

 

[dualazmak]

I'd have to dig it out IIRC it was called Super Audio Check CD with a large booklet all in Japanese and not one of the YEDs series one of which I have somewhere. It was purchased at the Akihabara along with some of the first CD players. There was a full set of test tracks along with music samples, the CD started with a steam train starting right and leaving left just like some old LP demo disks. IIRC one of my CD players could not handle the 99 tracks.

I just posted two of mine here and here regarding "Super Audio Check CD by CBS/Sony".
You may find here the booklet translated into English by my myself.

 

[Cbdb2]

Interesting video with audio samples. You can hear what dither is doing. Does it matter with most music never below -20dbfs? No.