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.

[Axon]

So I was mainly pissed off in my earlier post because it looked like this was about to turn into a rematch of ChiGung vs. the world. Which wound up happening, and it's not like I agree with him on much, but I already went through all of that on SH.tv.

The formula described by KikeG (and others) does help, but it doesn't really satisfy me. It seems to coincide well with what I've computed (with 1/20000 sample delays being feasible) - I suppose that the 1/(fs*2^n) number is a theoretical limit rather than an upper bound on period, and depending on the vagaries of the upsampling/downsampling implementations, the real testable interval may wind up being much higher. (In theory, I ought to be able to get a 1/65536 sample delay working?)

This gives a lot of wiggle room for audiophiles to claim that there could be large differences in performance based on how good the upsampling/downsampling filters are, resulting in numeric performance improvements to the minimum reproducible delay. However, one could pretty conclusively argue that even the implementation-tested periods are lower than the minimum audible delays by a wide margin. And it does give an exact definition to beat people over the head with, which is what I was wanting.

[Woodinville]

The formula described by KikeG (and others) does help, but it doesn't really satisfy me. It seems to coincide well with what I've computed (with 1/20000 sample delays being feasible) - I suppose that the 1/(fs*2^n) number is a theoretical limit rather than an upper bound on period, and depending on the vagaries of the upsampling/downsampling implementations, the real testable interval may wind up being much higher. (In theory, I ought to be able to get a 1/65536 sample delay working?)

Well, consider this...

Let us take a sine wave at nearly half the sampling frequency...

It's slope (using +-1 for amplitude) is 2*pi*f at maximum (crossing zero).

You want to figure out when you can distinguish one LSB. That's when
2*pi*f > 2/(2**bits).

Give or take. Since we have to dither, the numerator of the right side is bigger by some extent.

This is where the number comes from. It's a classic phase analysis problem.

Of course, when we dither, we can also average many cycles and get a better result.

Now, as strange as it seems, the single-cycle example is directly germane to the question at hand.

I leave it to ChiGung to explain to us how this completely controverts all of his assertions completely.