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.

[Canar]

ChiGung, despite your frequent reassertions to the contrary, we are still not following you. Your explanations have not been clear, precise, testable, or verifiable.

So, there are two possibilities: you are misunderstanding and are incorrect, or all the technically competent members who are assuring you and providing mathematical proof of the inaccuracy of your position are misunderstanding you and are providing evidence that is not related to the topic at hand. I would suggest you consider the possibility of the former, as we consider the possibility of the latter and try and understand exactly what you're trying to convey here.

This post has been edited by Canar: Oct 8 2006, 20:12

[ChiGung]

I would suggest you consider the possibility of the former, as we consider the possibility of the latter and try and understand exactly what you're trying to convey here.

Deal

[ChiGung]

I think that it is being claimed, almost unanimously that, 'conditions' (which would indicate 'events' or 'energy spikes') precise location in a PCM record, accurately informs us of their precise location in real time.
I have been trying to explain how this is untrue. That in real time, rather than the sampled approximation of it, the precise time of any condition can differ from what is idealy indicated by the record -by up to a sample interval (or maybe half a sample interval - I am not certain of the amount)

The correlation between the records indication of timing of instantaneous conditions (such as level= x) and the actual timing of indications would be something like this (loosely from intuition):

Indicated time is within 1 sample period of real time: odds ~1/1
Indicated time is within 1/2 sample period of real time: odds ~1/2
Indicated time is within 1/4 sample period of real time: odds ~1/3
Indicated time is within 1/8th sample period of real time: odds ~1/4

I have presented an intuitive guess of probability of accuracy there to drive through what I am generaly talking about - The uncertainty of PCM records, with regards to potential sources having significantly higher bandlimits. As is often the case with Redbook standard PCM (downsampled from production formats) and others.

It is the unknown frequencies above the samplerates implicit bandlimit which cause this uncertainty. We interprate the PCM record as though the frequnecies beyond the bandlimit must always have been flat, but in for example a production formats samplerate at 96kHz, they were not neccessarily flat (or else there would be little point in using those formats.)

The example of the 'tekkie' locating the spike with a record too precisely was a straight forward one.
The rebuttal of the example that the spike could indicate any position therefore it must indicate the true position securely was invalid for the reason that to ensure the precise positioning of the spikes peak with the true peak, all the other samples would have to be employed to refine that single detail, and they cannot normaly be employed just to do that as they have to convey their own detail as well.
Revise the lumpy mattresse methaphor. It is not a silly one.

The situation I have been pointing out is very complex with great subtleties and many gotchas involved. I am very familiar with the technologies limitations because I have spent a great deal of time pondering it and programming for it, particularly over the past year. I have for example completed my own frequency analyser from first principles without reference to any text books or reported methods. It produces very fine output and the mechanics of it are now being employed in my own compression codec. Unfortunately it will be along time since Ill be able to talk about it in detail in public. But you see, (unless im lying ) I am not wishfully lecturing in an area which I have no experience. I dont believe I have said anything unconfirmable or insensible in this thread (at least which is not transient to the arguement -everyones human), there may be certain mistakes or difficulties in expression to get caught up in, but the subject is outside of many peoples familiarity zone -even people involved here. If anyone reads my explainations open mindedly, and links the parts of the explainations which they can interprate and skips the bits they cant, there is a good chance they will acknowledge an under-reported aspect of PCM 'time resolution'.

I will leave this thread now, confident in the explaination Ive invested here.
If it really is a silly as everyone seems to think it is, I guess it will end up in the recycle bin but I do believe that it would be an uncommon shame on HA.org to do so.

Sincerely.
twerpy' smartass' fat-tongued, Cheegunge

[legg]

I have presented an intuitive guess of probability of accuracy there to drive through what I am generaly talking about - The uncertainty of PCM records, with regards to potential sources having significantly higher bandlimits. As is often the case with Redbook standard PCM (downsampled from production formats) and others.

It is the unknown frequencies above the samplerates implicit bandlimit which cause this uncertainty. We interprate the PCM record as though the frequnecies beyond the bandlimit must always have been flat, but in for example a production formats samplerate at 96kHz, they were not neccessarily flat (or else there would be little point in using those formats.)

Preciselly that's why you must low pass the signal BEFORE sampling, otherwise the content above FS/2 will get mixed with the frequencies below FS/2 causing aliasing. On a bandlimited signal there's no "spike" that can not be represented in the sampled version, even if it lies within 2 samples. It isn't rocket science.

The straightforward solution to be able to capture your so called "spikes" is to increase the sample rate, but that by no means imply that the sampling theorem is flawed in any way. The theorem does imply that you must sample fast enough to have perfect reconstruction, at least from a mathematical point of view. In practice we all know that there's no ADC with a perfect delta dirac.

I'm still waiting to see your MATLAB code proving everyone wrong.

This post has been edited by legg: Oct 9 2006, 02:14

[ChiGung]

....snip vaguest part of my post....

Preciselly that's why you must low pass the signal BEFORE sampling, otherwise the content above FS/2 will get mixed with the frequencies below FS/2 causing aliasing. It isn't rocket science.

The straightforward solution to be able to detect "spikes" is to increase the sample rate, but that by no means imply that the sampling theorem is flawed in any way. It does imply that you must sample fast enough to have perfect reconstruction, at least from a mathematical point of view. In practice we all know that there's no ADC with a perfect delta dirac.

I'm still waiting to see your MATLAB code proving everyone wrong.

Another one tries to wriggle under the full case that has set on a plate for you and seasoned liberaly.
Dont say Im talking about detecting 'spikes' just after I have just described the uncertainty of detecting the realtime location of any 'conditions' -such as spikepeaks, level values or waveform gradients -any conditions that could be locateable in an instant of time indicateable by a PCM record.

Ive never gone near MATLAB because I dont need it, I code in low level java/c syntax, and what I code ends up working sir.

Trying to drag it back to who was right or wrong like that is pathetic.