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.

[Woodinville]

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.

Having read that thread, or some of it, it's clear that there are several issues being confuted by people who do not want to let go of their pet belief system.

The first issue is that of pure delay. You've killed that. You can point out that if you store the data in 16 bit signed, that yes, there is a limit, it's directly related to the sampling rate times the number of levels available for quantization... i.e. directly related to the SNR and the sampling rate.

The second is that of jitter. You need to beat on these people to point out that jitter is different for each sample, and your time delay is not.

Time delay has been reported as audible down to 5 to 10 microseconds in binaural settings with a great deal of care and signal prep involved. No lower.

The cited nanosecods, etc, are just stuff and nonsense.

What you need to do with the jitter crowd is to point out that the spectrum of the jitter is the big deal.

You can have 1 part in 1000 (relative to sample period) if the jitter has only frequencies below 1 Hz.

You can hear much more than that if you have high frequency jitter, and a high frequency signal.

Looking onward, we see the twirp who insists that things have to be periodic in order for subsample resolution to work.

Perhaps he needs to be acquinted with both the Nyquist theorem and the fact that for all real signals, Fourier synthesis works.

I'm not going to get an ID to go argue with those guys. Blah.

This post has been edited by Woodinville: Oct 5 2006, 23:21

[ChiGung]

The first issue is that of pure delay. You've killed that. You can point out that if you store the data in 16 bit signed, that yes, there is a limit, it's directly related to the sampling rate times the number of levels available for quantization... i.e. directly related to the SNR and the sampling rate.

Just me doing the arguing in that thread really. On the fly (though it was never a prime point) I hedged that what you refer to as 'delay' is dependant on the measure size like you state.
However you seem also unwilling to acknowledge too, that such 'delay' is no definite attribute of the undownsampled source, it is an attribute summed circumspectly from the phases of frequencies surviving the downsample. The frequencies which didnt survive the downsample, contained the information required to resolve the true subsample detail of 'time localised energy spikes'.

The second is that of jitter. You need to beat on these people to point out that jitter is different for each sample, and your time delay is not.

Comments about jitter came right at end... or maybe its grown...eek, anyway there enough on the plate already.

Time delay has been reported as audible down to 5 to 10 microseconds in binaural settings with a great deal of care and signal prep involved. No lower.

Informative, although I have never argued the against the subsample time resolution of frequencies surviving the implicit lowpass of the sample rate. The arguement was about whether such precision can be fairly refered to as 'time-resolution'

Looking onward, we see the twirp who insists that things have to be periodic in order for subsample resolution to work.

Ahem* that would be me, but an unkindly misrepresented myself.
Again, my point is -"subsample resolution" of what exactly? the subsample levels implied in PCM have to assume all energy above the nyquist frequency is zero - so yes 'things' do have to be periodic, specificaly the component periods of the frequencies which inform the spaces between samples all have to be less than 2 samples in length - because shorter frequencies are not informed by the record. Subsample detail of the waveform is for standardisation purposes assumed to be consistent with the remaining information, because the origional information is lacked. So what can 'time resolution of PCM' refer to? any synthetic measurement we can take? Is there not already a fair candidate for this term?

Perhaps he needs to be acquinted with both the Nyquist theorem and the fact that for all real signals, Fourier synthesis works.

I am acquainted with it thanks, and understand some limitations. Just trying to pass that on.

I'm not going to get an ID to go argue with those guys. Blah.

You didnt need to

This post has been edited by ChiGung: Oct 6 2006, 00:49

[krabapple]

The second is that of jitter. You need to beat on these people to point out that jitter is different for each sample, and your time delay is not.

Comments about jitter came right at end... or maybe its grown...eek, anyway there enough on the plate already.

Actually they appeared as early as the third post in the thread.