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.

[cabbagerat]

Of course there is a limit. If there wasn't, you could store an infinite ammount of information in the exact position of that peak. Turning this the other way, you cannot store audio data in a way which completely preserves this information. However, the way it is it should be accurate enough. My point was that you can place your "brightness-peak" on a great number of positions between the pixels.

Well, I hadn't thought of it in the context of information storage, but that's a very nice way to visualize the limit. I would imagine that this is certainly not one of the limiting factors on the quality of digital storage, but there are certainly people who would say otherwise. You can't really pretend that any mechanical analog system (tape, vinyl, etc) could do better.

[ChiGung]

Of course there is a limit. If there wasn't, you could store an infinite ammount of information in the exact position of that peak. Turning this the other way, you cannot store audio data in a way which completely preserves this information. However, the way it is it should be accurate enough. My point was that you can place your "brightness-peak" on a great number of positions between the pixels.

What is 'accurate enough' is a different matter id not like to confuse the main investigation with.

The situation is, that the positioning of the brightness peak in the record is limited by the fact that the record has an implicit bandlimit. The position of the brightness peak in the source image is not implicity restricted by this limitation. (edit: yes the peak could be precisely positioned if we could employ all of the information stored in surrounding samples to do so - but all those other samples have information of their own to carry*) .

Depending on the characteristics of the information conveyable from the origional media (lenses, microphones, physics of air etc) it may be suitably restricted for precise capture/repoduction by certain samplerates, but because the source media may also not be suitably restricted (and very often is not) we have to allow for this possibility. It's surprised me that there has been a strong tendency to discount this as recognising source media may have finer resolution than target samplerates is fundamental to sensible statements of how accurately target samplerates can record the information of various sources.

Back to the 'peak of brightness', or 'peak of level' example (whichever is easier to visualise) The position of the peak in the source image or sound will in almost all cases be altered by the lowpass of conversion.
The record will then indicate a very precise position, but its disagreeance with the source will be unknown, the precise position of the peak in the source may be anywhere between the enclosing sample points

Then this makes clear my objection to stating the time resolution of PCM as near perfect. That the position in time of any time-localisable details, like peaks, attacks, cliffs etc, cannot be known to agree with the position of such details in the source, except when we can assume convienient limitations of the source. >A clause which basicaly passes on the limitations of the PCM record, to the source record. That is if we assume the source and the records limitations are the same, then to determine the accuracy limitations of the record, we must determine the limitations of the source. Only then can it be said that the record has no limitations with regards the assumable source. It becomes a confusingly convoluted case.

Another way of stating the case, is that the gaps between the samples, embody the unstateable frequencies above the implicit bandlimit. (By implicit bandlimit I mean to imply the one enforced by the nyquist frequency cuttoff, not arbitrary ones which may or may not have been applied on the record by extra conditioning)

Regarding the validity of the 'screen resolution' metaphor; when it was introduced earlier this reminder was made: -

(note that regardless of the quality of anyones particular video card system, bandlimited 'acoustic type' interpolation can be applied to visual data as well as audio (and is a rather good way to treat it, if not the optimal (?))

In other words it can be a fair, almost identical analogue, but if its not accessible to some, they may just have to try to skip over it.

Id remind again, that phase never indicates a point in time, it indicates conditions of a period located throughout time. So the fact that phase can be stated in a record quite precisely, does not mean any real position in time can be stated in the record as precisely.

Some are refering to limits of perceptability which are only discernable with physiological experimentation, limits of technical capability are not affected by what it is possible to hear or see.

Other queries have been raised all of which I hope the answers to will become clear, when the overall matter is realised

I exhibited some more underdog fatigue earlier Im glad to see that did not harm anyones curiosity.

best regards'

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extras

This post has been edited by ChiGung: Oct 8 2006, 00:20

[MedO]

the precise position of the peak in the source may be anywhere between the enclosing sample points -as confirmed by med0.

Please don't misquote me. I said that it is possible to record the position of a peak in a bandlimited signal even if the peak is between two samples, but the precision will be limited (as in "Bill Gates has a limited ammount of money").

If you sample at 1hz (and your signal is limited to 0.5hz), you can record and reconstruct a signal with a peak at 5.23 seconds. If you used a low bitdepth, the peak may be shifted a bit (like 0.01s). If you used a high bitdepth, the position of the peak will be more precise. The point I was making was, you cannot have *infinite* precision. But you can get pretty close.