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.

[2Bdecided]

So, in short, you want to run an experiment to see what effect a low pass filter has?

[ChiGung]

So, in short, you want to run an experiment to see what effect a low pass filter has?

Yes.

As particular sample rates, do have implicit unavoidable lowpasses -the process of comparing the capabilites of different samplerates, refactors as comparing effects of different lowpasses. It is almost the same thing, although actualy doing the full downsample (as well its implied lowpass) investigates an attained quality of the full process, so would preferable for this charge for actual proof of subsample source/record ambiguity.

[Woodinville]

So, in short, you want to run an experiment to see what effect a low pass filter has?

Yes.

As particular sample rates, do have implicit unavoidable lowpasses -the process of comparing the capabilites of different samplerates, refactors as comparing effects of different lowpasses. It is almost the same thing, although actualy doing the full downsample (as well its implied lowpass) investigates an attained quality of the full process, so would preferable for this charge for actual proof of subsample source/record ambiguity.

So, if the lowpass filter is above the point where your ear captures information, then what have we found?

The second is that you seem to doubt whether lowpass->sample->reconstruct can be shown to have the same effect as just the lowpass. Without quantization, the theory says that the two processes are identical. If you wish to question this then a mathematical treatment will probably be necessary before your demonstration is accepted.

This mathematical treatment can be found in many places. I believe Taub and Shilling deal with it. Certainly Jayant and Noll address it, but not quite in a form a novice will recognize. Any good older book on modems will discuss it in great detail (PSK being exactly what would discover such differences, including quantization, noise, and distortion).

There is a lot of good mathematical treatment out there.

Interesting, in this case however you know what the checkboard looks like, unexpected deviations from a clean checkboard appearance, would introduce innaccuracy. It is a selective example not fully similar to resolving details in waveforms - which we can have few presumptions about.

So, do you LOOK at your audio, or do you listen to it?

So you will observe how the bandwidth limitations of samplerates damages timing and/or survival of time locatable conditions/events in waveform records vs waveform sources.

Once more, it is trivial to calculate this from first principles.

You DO understand that phase shift at a given frequency is a way of measuring time delay, yes?

Now, can you measure the phase shift (removing the ft, or pure delay, part) of your processing?

If you can't, it's not changing the in-band time resolution.

Now, a given level of quantization can be directly related to a given amount of phase uncertainty. Figure out for yourself what that equals at 16 bit quantization levels for a full-scale signal, now. Just go ahead and do it.

[ChiGung]

So you will observe how the bandwidth limitations of samplerates damages timing and/or survival of time locatable conditions/events in waveform records vs waveform sources.

Once more, it is trivial to calculate this from first principles.

The damage is trivial for you to calculate? Well, i wouldnt say that my method of actualy discerning it was trivial or too involved, but Im just the one who has pressed the issue to be acknowledged arent i?

You DO understand that phase shift at a given frequency is a way of measuring time delay, yes?

I dont accept phase shifts can be directly interprated as a 'time delay' because they applies to long multisample sinusoidal patterns (frequencies), phase shifts never alone detail any isolatable instants. Phase shifts are time relateable attributes of frequencies, not instant isolateable positions or durations in linear time.

Now, can you measure the phase shift (removing the ft, or pure delay, part) of your processing?
If you can't, it's not changing the in-band time resolution.
Now, a given level of quantization can be directly related to a given amount of phase uncertainty. Figure out for yourself what that equals at 16 bit quantization levels for a full-scale signal, now. Just go ahead and do it.

Im not interested in performing your excercises.
The resulting flaw of your own excercising, is that you neither can acknowledge that timing resolution of locateable conditions in real waveforms has significant 'subsample' uncertainty regarding the unknown frequencies which are unrepresentable at any given samplerate.

[Woodinville]

Im not interested in performing your excercises.

Then you're not interested in the answer to your question.

The resulting flaw of your own excercising, is that you neither can acknowledge that timing resolution of locateable conditions in real waveforms has significant 'subsample' uncertainty regarding the unknown frequencies which are unrepresentable at any given samplerate.

The exercises I provided you allow you to do exactly what you want to do.

If you don't want to do them, you aren't going to get your answers.

I dont accept phase shifts can be directly interprated as a 'time delay' because they applies to long multisample sinusoidal patterns (frequencies), phase shifts never alone detail any isolatable instants. Phase shifts are time relateable attributes of frequencies, not instant isolateable positions or durations in linear time.

Actually, given an amount of phase shift at any given frequency, you have precisely specified duration in time.

But this seems to suggest you're stuck in a larger problem. You do realize that all physically realizable waveforms (we're talking audio here, not cosmology, after all) can be represented by an integral of sine waves, do you not? You do realize that you can decompose any physically realized waveform into its sinusoidal components, yes?

Your failure to understand that phase shift and time delay are DEFINED to be related would suggest, as well, that you "don't accept" the language of the field. This is not a good place to start. Perhaps you could start by accepting the language, and then state what your problem is in terms of generally accepted language. Language, after all, is no good for communication if you use different meanings, and if you are using the same meaning as everyone else, a phase shift of x at a given frequency is exactly, precisely specifying a given amount of time.

[ChiGung]

The exercises I provided you allow you to do exactly what you want to do.
If you don't want to do them, you aren't going to get your answers.

i'm scheduled to dip my head in a clow clap and sprinkle ants in my pants just before i get your answers prof

The positions have been stated, time may clarify.....