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]

For your viewing pleasure, here's a quick demonstration that 16/44.1 PCM can resolve 10ns differences in time between two signals. The code is MATLAB, but if you don't have MATLAB, then download Octave (it's free) which will run this code without modification.

CODE

fs = 44100; %sample rate
ts = 1/fs; %sample period
bd = 16; %bit depth
f0 = 1e3; % frequency of wave
bd_scale = 2^(bd-1);
x=0:(1/fs):0.01;
y = round(cos(f0*2*pi*x)*bd_scale);
y2 = round(cos(f0*2*pi*(x+1e-8))*bd_scale);
plot(x, y1-y2, 'r');

Chigung's assertion that you sacrifice the accuracy of other samples is, in my mind, quite a stretch. Do you have a demonstration of this (in code, or in a theoretical treatment)?

[ChiGung]

For your viewing pleasure, here's a quick demonstration that 16/44.1 PCM can resolve 10ns differences in time between two signals. The code is MATLAB, but if you don't have MATLAB, then download Octave (it's free) which will run this code without modification.

CODE

snip statement demonstrating the precise resolution of known variables

Chigung's assertion that you sacrifice the accuracy of other samples is, in my mind, quite a stretch. Do you have a demonstration of this (in code, or in a theoretical treatment)?

I am happy for this practical request.

Regarding:

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*) .

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Visualise a sequence of samples:

a,b,c,d,e,f,g,h,i,j

Suppose we are interested in the records solution between e and f. Perhaps we are looking for the precise location of the summit of a spike or perhaps the precise location when the recorded level achieves a value, like level=0. You must be able to propose a condition of the level to locate in time, in order for any statements about the records ability to locate detail in time to have meaning.

Propose a condition to locate then.
Then arrange any test values you like for all the levels.
Then locate your condition between e and f.

You will be able to do so, to the degree of precision noted frequently throughout this thread.

Then change the value of any single sample.
The location of your condition will change.
The location of the condition can be altered to occur anywhere between the bounding samples by altering the other samples in the record. (note ,depending on the condition sought, it may also be possible to make it not occur at all)

This is because the location of that condition is the result of a calculation which employs simultaneously all of the levels. The information which is used to store the conditions location, is that which is contained in all the samples. But that is an unnatural reading of the record (it is not being interprated just as normal PCM) We are effectly using a long 'read in' and 'read-out' period to achieve the accurate placement of the condition. We are treating the other samples as disposeable, when in normal PCM recording, each sample must have essentialy attributed the same importance as each other.

Its as though, we are trying to discover PCMs ability to precise locate details in time, so we test its ability to locate a single detail in time -arranging the whole record to do that locating. It is an unnormal reading of the record - an overreading of the relevance of the levels indicated conditions at the interval we are focusing on with an assumption of compliance of all the other levels.

To try to alter the indicated travel of the level to fit our intentions, is like trying to poke lumps out of a mattresse and finding when we do so, lumps appear in other parts of the mattresse. We can only arrange the shape we like in one bit of the mattrese by causing distortion in the rest. After doing so, if we could discard the rest of the mattress, then shape we had arranged would dissappear as it was the whole mattresse which informed the shape of the little part we were interested in.