## There can be curious gaps, in what some people understand.

One of the concepts which once dominated CGI was, that textures assigned to 3D models needed to include a “Normal-Map”, so that even early in the days of 3D gaming, textured surfaces would seem to have ‘bumps’, and these normal-maps were more significant, than displacement-maps – i.e., height- or depth-maps – because shaders were actually able to compute lighting subtleties more easily, using the normal-maps. But additionally, it was always quite common that ordinary 8x8x8 (R,G,B) texel-formats needed to store the normal-maps, just because images could more-easily be prepared and loaded with that pixel-format. (:1)

The old-fashioned way to code that was, that the 8-bit integer (128) was taken to symbolize (0.0), that (255) was taken to symbolize a maximally positive value, and that the integer (0) was decoded to (-1.0). The reason for this, AFAIK, was the use by the old graphics cards, of the 8-bit integer, as a binary fraction.

In the spirit of recreating that, and, because it’s sometimes still necessary to store an approximation of a normal-vector, using only 32 bits, the code has been offered as follows:

Out.Pos_Normal.w = dot(floor(normal * 127.5 + 127.5), float3(1 / 256.0, 1.0, 256.0));

float3 normal = frac(Pos_Normal.w * float3(1.0, 1 / 256.0, 1 / 65536.0)) * 2.0 - 1.0;

There’s an obvious problem with this backwards-emulation: It can’t seem to reproduce the value (0.0) for any of the elements of the normal-vector. And then, what some people do is, to throw their arms in the air, and to say: ‘This problem just can’t be solved!’ Well, what about:

//  Assumed:
normal = normalize(normal);

Out.Pos_Normal.w = dot(floor(normal * 127.0 + 128.5), float3(1 / 256.0, 1.0, 256.0));

A side effect of this will definitely be, that no uncompressed value belonging to the interval [-1.0 .. +1.0] will lead to a compressed series of 8 zeros.

Mind you, because of the way the resulting value was now decoded again, the question of whether zero can actually result, is not as easy to address. And one reason is the fact that, for all the elements except the first, additional bits after the first 8 fractional bits, have not been removed. But that’s just a problem owing to the one-line decoding that was suggested. That could be changed to:

float3 normal = floor(Pos_Normal.w * float3(256.0, 1.0, 1 / 256.0));
normal = frac(normal * (1 / 256.0)) * (256.0 / 127.0) - (128.0 / 127.0);

Suddenly, the impossible has become possible.

N.B.  I would not use the customized decoder, unless I was also sure, that the input floating-point value, came from my customized encoder. It can easily happen that the shader needs to work with texture images prepared by an external program, and then, because of the way their channel-values get normalized today, I might use this as the decoder:

float3 normal = texel.rgb * (255.0 / 128.0) - 1.0;

However, if I did, a texel-value of (128) would still be required, to result in a floating-point value of (0.0)

(Updated 5/10/2020, 19h00… )

## How the JACK Sound Daemon is capable of running at 192kHz

Most of my Linux-computers have as their sound-server “Pulse Audio”. But specifically on my laptop named ‘Klystron’, I have set up the JACK Daemon to be able to run as an alternative, yet not to be running by default. I have performed experiments on that laptop, to confirm that I can launch this sound-server, using a GUI named ‘QJackCtl’, but have also had to make modifications to how this GUI executes commands from the user, so that its start-up pauses the Pulse Audio daemon, which has been able to resume successfully after I was done using JACK. Without such a detail, the attempt should not be made.

One fact which I can see in QJackCtl, is that JACK is capable of running at 192kHz, even though it has not interrogated any of the available devices, about their real capabilities are.

The reason this is possible is the fact that individual sound devices are just clients to that daemon, including any number of devices that act as sound-sources, rather than acting as sinks, i.e. that act as inputs rather than as one output.

I also own a USB-Sound-Device named the ‘Scarlett Focusrite 2i2′, which is mainly intended for use in sound capture, but which also has outputs intended for monitoring purposes.

If I was to run JACK at 192kHz, then one simple consequence of that would be, that zero actual sound-devices would remain compatible with it. As to how cleanly an attempt to connect to an incompatible device exits, giving error messages or crashes, I have not tested, because when I tested the Focusrite, I took into account the real limit of that device at 96kHz.

Similarly, the JACK Daemon runs with 32-bit linear precision by default. In this case, when we enable devices to act as clients, which are only capable of 24-bit sample-depth, which is common, the mismatch is safely ignored. JACK already sees to it, that the last 8 bits of precision get ignored.

Now, I could be cautious and worry, that because of errors in the Linux drivers, those last 8 bits somehow get mapped to a control register as an error. But then the simple way to test for that, was simply to send some 32-bit sound through JACK, to this output device. What I found when testing this, is that the basic operation of the Focusrite was not disturbed, even though my hearing was not good enough, to tell me when I had my Sennheisers on, whether in fact 24-bit precision was still working. I was mainly testing, that trying to send a 32-bit value, does not disrupt the actual operation.

## Successive Approximation

While Successive Approximation is generally an accurate approach to Analog-to-Digital conversion, it is not a panacea. Its main flaw is in the fact that the D/A converter within, will eventually show inconsistencies. When that happens, some of the least-significant bits output will either be an overestimated one, followed by nothing but zeroes, or an underestimated zero, followed by nothing but ones.

Although circuit specialists do what they can to make this device consistent, there are quantitative limits to how successful they can be. And, whether 24 bits can be achieved depends mainly on frequency. In analog circuits, voltages tend to zero in on an ideal voltage exponentially, even when there is no signal-processing taking place. So the real question should be, ‘Can 24 bits still be achieved, far above 48kHz?’

And, if we insist that the low-pass filter should be purely numeric, we are also implying that one A/D conversion must be taking place at the highest sample-rate, such as at 192kHz, while if the low-pass filter could be partially analog, this would not be required.

Dirk

## My Opinion on the Opinion of Chris “Monty” Montgomery

Chris Montgomery is the Audio Expert, who invented the OGG Vorbis codec. That gives enough reason to accredit him with good advice. I recommend that my readers read his advice here.

I did read the whole thing, but have three comments on it:

1. The Author suggests that 16-bit sample-depth offers a de-facto solution to the limits in dynamic range, simply due to the correct application of dithering. If I cannot trust my hardware to perform correct low-pass filtering, why on Earth would I trust it to perform correct, 16-bit, audio dithering?
2. The Author explains the famous loudness curves, that define threshold of perceptibility, as well as the higher threshold of pain. What he fails to point out is that these curves assume, that the sound being tested for, is the only sound being played over the headphones. If there is another, background sound being played – i.e. the current loudness-level already higher than zero – then the threshold of perception for a given test-sound, is higher – requires a higher level, for that test-sound itself to be heard. Yet, this level is still lower, than the peak level of the background sound. People who design codecs know this, as I am sure the author does. It is the threshold of perceptibility next to a background sound – not the absolute threshold – which gets used in the design of codecs.
3. The Author suggests it would be a misuse of his codec, to encode discrete multi-channel sound. And one reason he states, would be the waste in file-size, while the next reason he states, would be the fact that sound jumps to the nearest speaker, when they are all encoded that way.

This last observation strikes a cord with me. I have already noticed, that OGG Files do allow numerous channels to be encoded in parallel, but that if we exceed 2, we lose the benefits of Joint Stereo. By itself, this does not really count against this Author, whose codec therefore does not offer explicit surround-sound. But the possibility is very real, that the localization of sound will jump to the nearest speaker, if the listener moves and the sound was encoded that way. It is entirely possible, that purposeful encoding of surround-sound by the (competing) AC3 or the AAC codecs, reduces this risk.

But then I would suggest an alternative approach, to people who do not want to use the proprietary codecs, yet who wish to encode their movies with surround.

There exists the Steve Harris LADSPA plug-in library, which includes a matrix encoder for Pro Logic. This matrix encoder accepts 4 input channels, one of which is the surround channel, and outputs 2 stereo channels.

Further, the circuitry must exist someplace as well, to accept 2 stereo, 1 center and 1 surround-channel, and to encode those in real-time, so that the surround-effect can be played back over 6 speakers.

• In principle, it should be possible to OGG-compress 4 channels and not 6, so that these channels can be used as inputs, to a matrix surround-system, like to the LADSPA plug-in, so that listenable surround will emanate from all speakers. Does Audio Software exist, which applies the LADSPA plug-in in real-time?
• Alternatively, it might be possible to mix down Pro Logic sound into Stereo using the Steve Harris plug-in, and then to use FLAC on the resulting stereo.

BTW: What the Author mainly writes, is how incorrect it would be for pure listeners, to download their music in 24/192 format. He does not actually write, that Music / Sound Authors should avoid recording in this format. And so one fact which I have observed, is that there exists a lot of Audio Software – such as Ardour – that stores its sound in some higher, internal format, but which, when instructed to Export that to a 16-bit format, offer Dithering as an option.

This is possible because the Application is numeric and not physical. Thus, If I had used my USB-sound-device to record in 24-bit, I could next Export the finished sound tracks to 16-bit:

But, It would also seem that Chris Montgomery equates the use of such technology, as only being suited for Professionals. I am not a professional, and do not have the extremely expensive tools they do. Yet, I am able to author sound-projects.

Dirk