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]

Here are some nice pictures...



I worked at 16-bits throughout.

I started at 441kHz (i.e. 10x CD sample rate). I generated a single impulse. To prove the point, I also generated a second impulse one sample later on the other stereo channel. This is the left hand pair of plots.

I resampled to 44.1kHz (i.e. CD sample rate). The result is shown in the middle pair of plots. Interestingly, Cool Edit Pro's visual interpolation hints at what is represented by those samples - i.e. a 1/10th of a sample time delay between the two channels.

I resampled back to 441kHz. The result is shown in the right hand pair of plots. The peaks of the waveforms are clearly in the correct place relative to each other. Time resolution equivalent to 1/10th of a sample at 44.1kHz clearly survives this sample rate.


Of course the peaks are low amplitude (less energy) and longer (spread out in the time domain) - but this is just what happens when you low pass filter a click.


So, this is a simple, repeatable example proving the sub-sample accuracy of sampled systems, without a sine wave in sight!

Cheers,
David.