What is "time resolution"? Options

[Axon]

So I've become involved in a rather colorful argument (I'm Publius in the thread) with somebody on stevehoffman.tv. The original thread revolved around shooting down an old audiophile canard, about how subsample delays cannot be represented in PCM. In the course of that debate, I've begun to question a couple things.

• Is it ever accurate to use the term "time resolution" in any sort of technical context? To the best of my knowledge, it has no universally agreed upon technical definition. Most of the times I've seen it used are either for SACD/DVD-A marketing fluff, or to describe FFT window lengths. I'm tempted to just go quasi-logical-positivist on everybody and say that it is a completely meaningless phrase.
• Is there any meaningful time-domain constraint on audio quality that is directly related to the sampling period? Subsample delays (as I've shown above) are not meaningfully related. Bandwidth is a frequency-domain attribute. Pre-echo potentially gets more audible at lower sampling rates, but this is not a concern with sigma-delta ADCs, and it is of debatable audibility at 44.1 to begin with. Some DSP operations may be harder to implement at lower sample rates, but most of the issues involve seem implementation-related. I'm suspecting that there are no clear general limits as to what can and cannot be accomplished in PCM, except with respect to very domain-specific or system-specific situations; and so any claims of 44khz always being limited in ways different from bandwidth may be regarded with skepticism.

[MoSPDude]

I've been trying to follow this as well, and especially reading 2Bdecided post which I think summarises primarily what ChiGung wants to test, this is how I understand the issue.

A lot of this seems to not have much to do with PCM but more sampling theorem in general, as a quick reference I've been using my books and notes, for an online reference - wikipedia (Nyquist–Shannon sampling theorem) as it provides the mathematic descriptions accordingly. Theoretically, a band-limited signal sampled at greater than twice the highest frequency component when reproduced through the sinc interpolation, which requires knowledge of all samples over all time, is a perfect representation. Practically, we don't know all samples across all time and DACs use various methods to reproduce the signal, but not perfectly.

If we do these tests digitally, and the real-world source is band limited below the Nyquist frequency, then the Nyquist–Shannon sampling theorem will hold and values representing that signal will theoretically reproduce an exact perfect signal, including any sub sample shifts in peaks due to filtering. Quantisation will have an effect in terms of increasing noise. If the source signal was not band-limited, aliasing will occur - and the sampled signal will certainly not represent the original signal.

In terms of the peaks moving after a low pass filter etc, I was taught these such things were due to the phase characteristic of the filter where indeed the phase change specified at a specific frequency will give an exact definable time shift. As 2Bdecided said, it would be difficult to track EXACT peaks, but I imagine you could compare magnitude/phase plots of a set period of time with an arbitrary signal before and after an LPF or whatever filter, along with the magnitude/phase plot of the transfer function of the filter. What people are saying when they mention 'records' etc. is that a communication medium also has a transfer function and an appropriate magnitude/phase response - eg age/wear changes these responses.