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 happened to code a subpixel detector for "x-corners" (checkerboard corners) for the purpose of calibrating cameras. Luckily it can be shown that the areas around these x-corners show the mentioned symmetries which enables me to accurately measure the subpixel position of those x-corners (=saddle points) by analysing an optically-low-passed-&-sampled image of a checkerboard. Simulations showed that the real bottleneck is the censor noise actually. Without (simulated) censor noise I got an accuracy of 1/300 pixel -- possibly restricted by a little bit of aliasing that's left in the image generation / subpixel-detector code.

The interesting part is: If you capture an image at high resolution with some censor noise and use a high quality resampler to reduce the image resolution you'll get pretty much the same locations for those x-corners -- meaning that the subpixel accuracy increased by the same factor I downsampled the image. In fact, lowpassing is an integral part of the detector to minimize the effect of noise it has on the estimated x-corner positions. So, it's not surprising that the subpixel detector's performance (measured in pixels) was better on the smaller image. By your definition of time resolition (spatial resolution for images) this would mean that the two images would have the same spatial resolution. But of course the 2nd one is a downsampled one which doesn't look as sharp. So what good is your definition?

This post has been edited by SebastianG: Nov 15 2006, 17:52