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.

[ChiGung]

Yo, that was me (felimid)

Is there any meaningful time-domain constraint on audio quality that is directly related to the sampling period?

Ask yourself:
"is there any meaningful space-domain constraint on visual quality that is directly related to the pixel width"

(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 (?))

I know i've put more than enough waffle into that thread to explain why I consider, pixel-width or sample width the explicit limit of record resolution.... maybe just one more try if you have time:
The subsample accuracy of frequency resolution (and collections of frequencies) is about the..what do you call it..."potential losslessness" of manipulating recordsafter downsampling, not about the accuracy of reproduction of the original (natural, pre-record, pre-processed sound) of the downsampled record.

I honestly havent been argueing 'for the sake of it' I'd like this to be understood.
But everyone is free to draw their own conclusions.

best regards'

This post has been edited by ChiGung: Oct 5 2006, 23:09

[Axon]

Yo, that was me (felimid)

Oh! Damn. We've come full circle now.

Is there any meaningful time-domain constraint on audio quality that is directly related to the sampling period?

Ask yourself:
"is there any meaningful space-domain constraint on visual quality that is directly related to the pixel width"

(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 (?))

I know i've put more than enough waffle into that thread to explain why I consider, pixel-width or sample width the explicit limit of record resolution.... maybe just one more try if you have time:
The subsample accuracy of frequency resolution (and collections of frequencies) is about the..what do you call it..."potential losslessness" of manipulating recordsafter downsampling, not about the accuracy of reproduction of the original (natural, pre-record, pre-processed sound) of the downsampled record.

I honestly havent been argueing 'for the sake of it' I'd like this to be understood.
But everyone is free to draw their own conclusions.

best regards'

I mainly posted here to try to get a different take on what was spinning in my head about terminology. I didn't want to start a rantfest about the SH forums - although to be honest, the reason I posted here was simply because I perceive that the regulars here are just flat-out more technically competent in audio engineering than SH as a whole. (ie, HA people tend to have one or more DSP textbooks.)

Mike may be right. "Frequency resolution" has a clear frequency-domain definition, so it makes sense that "time resolution" would have an analogous time-domain definition. In which case.. you're right. However, it is surprisingly hard to actually find a definition of resolution itself. I don't recall such a definition in my textbook (Lathi).

And I still have trouble reconciling the notion of time resolution being directly coupled to the sampling rate, against so many things being resolvable at the subsample level - delays, peaks, etc. (Ignoring the fact that some of those things, like peaks, can change drastically after a resample.) Perhaps there are two classes of "resolution" - one is based on the sampling rate and represents what any given algorithm sees, while the other is based on the real-valued signal the signal reconstructs to, and represents values that are related to a large number of samples (due to FIR reconstruction), and so can exceed the sample-rate resolution limitation.

And for either class of resolution, the error in your measurement is also affected by your choice of algorithm - ie, a measurement may change significantly if downsampling 96->44.1 as compared to 88.2->44.1, because of the added ringing.

[legg]

AFAIK, time resolution is most commonly used to refer to the time that a given block represents when converted to the frequency domain. "The short window has a time resolution of 128 samples, while the steady state block has a time resolution of 2048 samples".

As for other uses, I'm sure there are some, I just haven't read the term in other areas.