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.

[SebastianG]

I also don't see the point in checking the positions of zero crossings or peaks after lowpassing. This won't prove anything except that if you further limit the bandwidth of a signal these points may move, vanish, or appear at places where there previously havn't been any.

Assuming the lowpass filter's impulse response is symmetric the following is true: If your signal shows a certain symmetry within an interval with the same size of the lowpass' filter response a certain class of points within that interval will be at the exact same position.

Example signal:
first two harmonics of a square wave: you'll get 4 peaks within a cycle
after lowpassing (only the fundamental left): 2 peaks within a cycle (it's a sine)
The zero crossings are the same (two within a cycle) because there's a "point symmetry" at those points. (rotate the curve around the point 180° and it'll be the same)
Tell me what we have learned by that, ChiGung.

In the context of transform coding time resolution usually refers to the partition of the time/frequency plane that's done by a critically-sampled filterbank AFAIK. Without any noise shaping filter tricks this will effectivly limit how well we can control the quantization noise distribution in specific time/frequency regions only by choosing scalefactors. However, noise shaping filters can be and usually are used to improve this. (With "ANS" enabled Musepack can do better in terms of controling the noise's distribution in the frequency domain than what the filterbank suggests --one subband is 670 Hz wide, though ANS manages to shape the noise within a subband. With "TNS" enabled AAC can do better in terms controling the noise's distribution in the time domain than what the filterbank suggests.)

This post has been edited by SebastianG: Nov 15 2006, 17:18