@fair ,
I believe at that point I provided enough explanations. Your reactions are quite typical of engineers who consider the classic DSP based on Fourier Analysis the only true paradigm.
From where I am sitting you have not provided one explanation because every single explanation or example you have used is wrong, stacking misunderstanding on top of misunderstanding. Fourier analysis is not a paradigm, it is a mathematical translation from time to frequency, it just is. The accuracy, as I previously wrote, is based on suitable bandwidth limitations, and appropriate windowing functions, much which occur naturally in audio, but are still supplemented by the appropriate analog filters, over sampling, and digital processing. People are not just guessing at the implementation and not considering what the underlying waveforms can and do look like. Let me break just one section down to illustrate your logic flaws and misunderstandings. It carries through to the rest of what you have wrote:
Imagine an audio signal which is a sinusoid of frequency 12 KHz, with amplitude described as piecewise function of two segments linear on dB scale. First segment goes from 0 to 100 dB SPL during first half cycle of the the sinusoid. Second segment goes from 100 db SPL to below quantization noise during the next four cycles of the sinusoid.
Try to sample it with 16/44.1. Then try to reconstruct the signal from the samples. Then shift capture time of the first sample by 1/8 of the sinusoid period. Repeat the exercise.
What you’ll find is that, first, reconstruction will be pretty rough, and second, that it will be wildly changing with even small shifts of the first sample capture time.
You start with a flawed premise, proceed to a flawed understanding of digitization, and finish with an incorrect understanding of reconstruction.
Flawed premise: 12 KHz sine wave do not suddenly appear, starting at 0. As I previously wrote, we are dealing with a bandwidth limited and defined system. You cannot go from 0, silence, directly into what looks exactly like a sine wave. That transition exceeds the 20KHz (or whatever we are using). Also, the digitizer, filters, etc. will have been running and settled to required accuracy by the time this tone burst arrives. Whatever you send it, will have been limited in frequency, by design, by the analog filters preceding the digitizer.
Flawed understanding of Digitization: As written above, the digitizer was already running when the tone burst arrives. Whether the sample clock is shifted globally the equivalent of 1/8 of a 12KHz tone, or not, will have no impact on the digitization of the information in the band limited analog signal.
Flawed understanding of reconstruction: When I reconstruct the analog signal, using the captured data, whether I use the original clock, or the shifted one, the resulting waveform that results will be exactly the same. In relationship to the data file, all the analog information will be shifted by about 10 useconds. That will happen equally on all channels. The waveforms will look exactly the same either case. One set of data files will have an extra 10 useconds of silence at the front of them (or at the end).
As I highlighted, the approach you are advocating doesn’t address the need of having some bits left available for encoding the shape of signal faithfully enough to be perceived as distortions-free.
I am sure you believe this, but you used flawed logic, a flawed understanding of the waveform, and a flawed understanding of digitization, reconstruction, and the associated math.
I went back and looked looked at the research. In lab controlled situations, humans can detect, a very specific signal up to 25db below the noise floor, A-weighted. That is not listening to music, that is an experiment designed to give a human the best possible chance. For vinyl, that means in a controlled experiment, maybe you could hear a tone at -95db referencing 0db as max. With CD, the same would be true at -110db (or more) due to the 100% use of dithering.
It a signal consists mostly of harmonic components quickly changing their amplitudes, non-harmonic transients, and frequently appearing/disappearing components, dithering is not as effective.
I cannot respond to this as it is wrong, and I am not certain where exactly you have gone wrong. As I wrote above, you have made errors of logic and understanding in all the areas critical to digital audio. As I wrote previously, dithering can be applied in analog prior to digitization.
The noise considerations started to amuse me lately. Practical examples were a trio of class-D power amplifies, highly regarded by ASR. I bought them over the years, evaluated, and quickly got rid of, due to intolerable for me distortions.
To be sure we are on the same page. Class-D amplifiers are analog amplifiers. They are not digital. I will correct you. Perception of distortion. You are making an assumption of something that is there, without proof it is there.
Not on assumptions. On theories. Fitting experimental facts. The theory I use is more sophisticated than the classic one, taking into account analog characteristics of human hearing system.
Which theory is it that you are using? I noted many flaws in your understanding of critical elements of digital audio, and assertions that are also incorrect. I have already falsified your theory.
Perhaps not important to this discussion, but 16/44.1 is a delivery format. From what my colleagues tell me, is has not been used as a digitization format in decades, and depending on your point of demarcation, it has not been used as a digitization format since the 1980’s, as all the hardware internally samples at a higher rate and bit depth.
@fair do you think that the people working on this technology never do comparisons of input and output waveforms with real music?
