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What is "time resolution"?
Axon
post Oct 5 2006, 21:50
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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.
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SebastianG
post Nov 15 2006, 17:30
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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
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Posts in this topic
- Axon   What is "time resolution"?   Oct 5 2006, 21:50
- - benski   Subsample delays are relatively easy to implement ...   Oct 5 2006, 22:04
- - Axon   Well, duh. I showed in that thread that 1/20,000 ...   Oct 5 2006, 22:19
- - krabapple   QUOTE (Axon @ Oct 5 2006, 16:50) So I...   Oct 5 2006, 22:28
- - Mike Giacomelli   QUOTE (Axon @ Oct 5 2006, 13:50) Is it ev...   Oct 5 2006, 22:57
- - ChiGung   Yo, that was me (felimid) QUOTE Is there any meani...   Oct 5 2006, 23:07
|- - Axon   QUOTE (ChiGung @ Oct 5 2006, 17:07) Yo, t...   Oct 6 2006, 00:11
|- - legg   AFAIK, time resolution is most commonly used to re...   Oct 6 2006, 00:28
- - Woodinville   QUOTE (Axon @ Oct 5 2006, 13:50) So I...   Oct 5 2006, 23:20
|- - ChiGung   QUOTE ("woodinville")The first issue is ...   Oct 6 2006, 00:46
|- - Mike Giacomelli   QUOTE (ChiGung @ Oct 5 2006, 16:46) QUOTE...   Oct 6 2006, 02:10
||- - ChiGung   QUOTE (Mike Giacomelli @ Oct 6 2006, 02:1...   Oct 6 2006, 04:30
||- - Mike Giacomelli   QUOTE (ChiGung @ Oct 5 2006, 20:30) QUOTE...   Oct 6 2006, 06:27
|- - krabapple   QUOTE (ChiGung @ Oct 5 2006, 19:46) QUOTE...   Oct 6 2006, 06:21
|- - Woodinville   QUOTE (ChiGung @ Oct 5 2006, 16:46) Howev...   Oct 6 2006, 08:26
- - Woodinville   Well, considered for Guassian vs. Gaussian, dt * ...   Oct 6 2006, 00:35
- - kjoonlee   Does "higher sampling rates mean higher tempo...   Oct 6 2006, 00:47
|- - ChiGung   QUOTE (kjoonlee @ Oct 6 2006, 00:47) Does...   Oct 6 2006, 00:57
|- - kwwong   QUOTE (ChiGung @ Oct 5 2006, 18:57) QUOTE...   Oct 7 2006, 05:12
- - 2Bdecided   ChiGung, You can prove sub-sample time domain acc...   Oct 6 2006, 10:30
|- - ChiGung   QUOTE We're assuming the signal is band limite...   Oct 6 2006, 16:32
|- - krabapple   QUOTE (ChiGung @ Oct 6 2006, 11:32) I can...   Oct 6 2006, 16:54
||- - ChiGung   QUOTE But perhaps for starters, you can describe i...   Oct 6 2006, 17:08
||- - krabapple   QUOTE (ChiGung @ Oct 6 2006, 12:08) QUOTE...   Oct 6 2006, 21:11
||- - MedO   QUOTE (ChiGung @ Oct 6 2006, 18:08) Look....   Oct 7 2006, 10:43
|- - Mike Giacomelli   QUOTE (ChiGung @ Oct 6 2006, 08:32) QUOTE...   Oct 6 2006, 20:54
- - Axon   Okay, so this has gone completely f*cking off topi...   Oct 6 2006, 17:49
|- - krabapple   QUOTE (Axon @ Oct 6 2006, 12:49) Okay, so...   Oct 6 2006, 20:51
- - Canar   QUOTE Ask yourself: "is there any meaningful ...   Oct 6 2006, 21:20
- - Canar   Exactly, kwwong. ChiGung, consider this: In the co...   Oct 7 2006, 08:04
- - cabbagerat   QUOTE (MedO @ Oct 7 2006, 01:43) No, ther...   Oct 7 2006, 18:00
|- - MedO   QUOTE That assumption is a bit of a problem, in my...   Oct 7 2006, 18:42
- - cabbagerat   QUOTE (MedO @ Oct 7 2006, 09:42) Of cours...   Oct 7 2006, 20:57
|- - ChiGung   QUOTE (MedO @ Oct 7 2006, 09:42) Of cours...   Oct 7 2006, 23:18
|- - MedO   QUOTE (ChiGung @ Oct 8 2006, 00:18) the p...   Oct 8 2006, 00:13
|- - ChiGung   QUOTE (MedO @ Oct 8 2006, 00:13) QUOTE (C...   Oct 8 2006, 00:28
- - Canar   ChiGung, it is increasingly apparent you are not i...   Oct 8 2006, 00:26
- - Canar   I've provided a mathematical example of why yo...   Oct 8 2006, 01:05
- - cabbagerat   For your viewing pleasure, here's a quick demo...   Oct 8 2006, 08:07
|- - ChiGung   QUOTE (cabbagerat @ Oct 8 2006, 08:07) Fo...   Oct 8 2006, 15:02
- - Canar   So because sinc() interpolation is weird, PCM fail...   Oct 8 2006, 15:28
- - cabbagerat   QUOTE (ChiGung @ Oct 8 2006, 06:02) This ...   Oct 8 2006, 15:51
|- - ChiGung   QUOTE (cabbagerat @ Oct 8 2006, 15:51) I ...   Oct 8 2006, 16:10
- - KikeG   As others have said, time resolution of PCM is the...   Oct 8 2006, 17:59
|- - ChiGung   QUOTE (KikeG @ Oct 8 2006, 17:59) As othe...   Oct 8 2006, 18:14
|- - KikeG   QUOTE (ChiGung @ Oct 8 2006, 18:14) So yo...   Oct 8 2006, 18:24
||- - ChiGung   QUOTE (KikeG @ Oct 8 2006, 18:24) Resolut...   Oct 8 2006, 18:55
|- - Woodinville   QUOTE (ChiGung @ Oct 8 2006, 10:14) So yo...   Oct 8 2006, 19:37
|- - ChiGung   QUOTE (Woodinville @ Oct 8 2006, 19:37) Y...   Oct 8 2006, 19:57
|- - Woodinville   QUOTE (ChiGung @ Oct 8 2006, 11:57) Yeah ...   Oct 9 2006, 18:00
- - Canar   ChiGung, despite your frequent reassertions to the...   Oct 8 2006, 20:08
|- - ChiGung   QUOTE (Canar @ Oct 8 2006, 20:08) I would...   Oct 8 2006, 20:28
|- - ChiGung   I think that it is being claimed, almost unanimous...   Oct 8 2006, 21:44
|- - legg   QUOTE (ChiGung @ Oct 8 2006, 15:44) I hav...   Oct 9 2006, 01:32
||- - ChiGung   QUOTE (legg @ Oct 9 2006, 01:32) QUOTE (C...   Oct 9 2006, 02:16
|- - 2Bdecided   QUOTE (ChiGung @ Oct 8 2006, 21:44) The e...   Oct 9 2006, 15:08
- - legg   Fine forget about the code and do try to provide m...   Oct 9 2006, 03:27
|- - MedO   If I understand you right, you are saying that the...   Oct 9 2006, 09:35
|- - ChiGung   Hello all, I left this discussion in a tizz and ha...   Nov 15 2006, 01:16
|- - kwwong   QUOTE (ChiGung @ Nov 14 2006, 19:16) 44kH...   Nov 15 2006, 09:50
|- - kwwong   QUOTE (kwwong @ Nov 15 2006, 03:50) QUOTE...   Nov 16 2006, 10:24
- - 2Bdecided   Here are some nice pictures... I worked at 16-b...   Oct 9 2006, 15:24
- - cabbagerat   QUOTE (2Bdecided @ Oct 9 2006, 06:08) It...   Oct 9 2006, 16:54
- - Axon   So I was mainly pissed off in my earlier post beca...   Oct 9 2006, 17:30
|- - Woodinville   QUOTE (Axon @ Oct 9 2006, 09:30) The form...   Oct 9 2006, 18:41
- - 2Bdecided   ChiGung, Your experiment wouldn't work. By kn...   Nov 15 2006, 13:00
|- - ChiGung   QUOTE (2Bdecided @ Nov 15 2006, 12:00) .....   Nov 15 2006, 13:45
- - 2Bdecided   So, in short, you want to run an experiment to see...   Nov 15 2006, 14:29
|- - ChiGung   QUOTE (2Bdecided @ Nov 15 2006, 13:29) So...   Nov 15 2006, 14:45
|- - Woodinville   QUOTE (ChiGung @ Nov 15 2006, 05:45) QUOT...   Nov 15 2006, 19:42
|- - ChiGung   QUOTE (Woodinville @ Nov 15 2006, 18:39) ...   Nov 15 2006, 19:56
||- - Woodinville   QUOTE (ChiGung @ Nov 15 2006, 10:56) Nice...   Nov 15 2006, 20:01
||- - ChiGung   QUOTE (Woodinville @ Nov 15 2006, 19:01) ...   Nov 15 2006, 20:30
||- - AstralStorm   QUOTE (ChiGung @ Nov 15 2006, 20:30) It i...   Nov 15 2006, 22:43
||- - 2Bdecided   QUOTE (ChiGung @ Nov 15 2006, 20:30) Im f...   Nov 16 2006, 14:22
||- - ChiGung   QUOTE (2Bdecided @ Nov 16 2006, 13:22) My...   Nov 16 2006, 17:10
||- - SebastianG   QUOTE (ChiGung @ Nov 16 2006, 17:10) The ...   Nov 16 2006, 18:22
||- - ChiGung   QUOTE (SebastianG @ Nov 16 2006, 17:22) Q...   Nov 16 2006, 18:51
||- - Woodinville   QUOTE (ChiGung @ Nov 16 2006, 09:51) I be...   Nov 16 2006, 22:48
||- - ChiGung   QUOTE (Woodinville @ Nov 16 2006, 21:48) ...   Nov 16 2006, 23:32
||- - Woodinville   QUOTE (ChiGung @ Nov 16 2006, 14:32) ...   Nov 16 2006, 23:44
||- - ChiGung   QUOTE (Woodinville @ Nov 16 2006, 22:44) ...   Nov 17 2006, 00:15
|- - ChiGung   QUOTE (Woodinville @ Nov 15 2006, 18:42) ...   Nov 15 2006, 20:14
|- - Garf   QUOTE (ChiGung @ Nov 15 2006, 20:14) The ...   Nov 15 2006, 20:18
|- - Woodinville   QUOTE (ChiGung @ Nov 15 2006, 11:14) Im n...   Nov 15 2006, 23:35
|- - ChiGung   QUOTE (Woodinville @ Nov 15 2006, 22:35) ...   Nov 16 2006, 01:20
- - cabbagerat   QUOTE (ChiGung @ Nov 15 2006, 05:45) It i...   Nov 15 2006, 15:22
|- - ChiGung   QUOTE (cabbagerat @ Nov 15 2006, 14:22) T...   Nov 15 2006, 15:51
- - 2Bdecided   I wish you understood the theory CG, because witho...   Nov 15 2006, 16:18
|- - ChiGung   QUOTE (2Bdecided @ Nov 15 2006, 15:18) It...   Nov 15 2006, 17:01
|- - 2Bdecided   QUOTE (ChiGung @ Nov 15 2006, 17:01) QUOT...   Nov 15 2006, 18:06
|- - ChiGung   QUOTE (2Bdecided @ Nov 15 2006, 17:06) Yo...   Nov 15 2006, 18:31
- - SebastianG   I also don't see the point in checking the pos...   Nov 15 2006, 16:48
|- - ChiGung   QUOTE (SebastianG @ Nov 15 2006, 15:48) I...   Nov 15 2006, 17:16
- - SebastianG   I happened to code a subpixel detector for "x...   Nov 15 2006, 17:30
|- - ChiGung   QUOTE (SebastianG @ Nov 15 2006, 16:30) I...   Nov 15 2006, 17:53
|- - SebastianG   QUOTE (ChiGung @ Nov 15 2006, 17:53) It w...   Nov 15 2006, 17:59
|- - ChiGung   QUOTE (SebastianG @ Nov 15 2006, 16:59) Q...   Nov 15 2006, 18:21
- - MoSPDude   I've been trying to follow this as well, and e...   Nov 17 2006, 00:21
- - Woodinville   QUOTE (MoSPDude @ Nov 16 2006, 15:21) If ...   Nov 17 2006, 00:40
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