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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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legg
post Oct 9 2006, 03:27
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Fine forget about the code and do try to provide mathematical proof of your statements instead of blabbering. I'm sure a person that names himself smart ass will be able to provide such proof.

FYI, java is NOT a low level language, it is actually FAR from being one. C is closer but it isn't considered low level either, the actual term to describe C is middle level.


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MedO
post Oct 9 2006, 09:35
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If I understand you right, you are saying that the time when the signal reaches a certain level in the recorded PCM waveform may be different from the time in reality.

This is equivalent to saying that the recorded waveform is different from the real one. Which is true if you are sampling with less than twice the highest frequency which will occur in the source.

The signal will be reconstructable to great accuracy if it is bandlimited to half the sampling frequency. It won't if it isn't. Why make it so complicated?
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ChiGung
post Nov 15 2006, 01:16
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Hello all, I left this discussion in a tizz and have only just checked again to find these constructive replies.

A 'thought' experiment occured to me which would illustrate my point about PCMs 'time resolution' -which could be performed computationaly to generate precise data... Ill set it out hopefully:

I assume 'resolution' can refer to the ability to resolve discrete details of source material in pcm records. And there must be a difference in the potential of detail resolution in 'the source' and that in 'the record'.
eg if the source was just a CD, and the target record was 11kHz pcm,
- then their potential to have detail resolved in them would differ.
Fundamentaly the 11kHz pcm's potential to resolve detail 'should' seem to be 1/4 of the CDs 44kHz record.

That would go,
44kHz pcm 'time resolution' = 4* 11kHz pcm 'time resolution'

oddly, here and elsewhere this formula is eclipsed with not insubstantial excursions into test pattern replications and counter intuitive textbook quotations.

If i needed exact data on the capability of 'time resolution' in PCM records, here is how I would go about generating it:
Write a small program to read in pcm, and locate exact time of specifiable conditions in it. Conditions such as (level=0) or level=p(test),
or gradient =0, or gradient =p.
To avoid porting in or trying to write my own bandlimited solution of the pcm record, id write the code for simple linear interpolation and feed it high quality upsamples in order to achieve near 'bandlimited accuracy' in discernment of 'time location' of 'conditions'.

So a program can read in a bandlimited upsample of source pcm, and generates a list of times of all matching conditions which are found/resolvable within the upsample.

eg. hq upsample of cd track at 44kHz to ~192kHz
>list of times of peaks and troughs (gradient=0) found in 192kHz pcm rendering.

Next, high quality downsample the cd track to 11kHz (1/4 sample rate)
Then upsample to 192 again (for hq interpolation), and generate its list of (gr=0) times.
//(the upsample to 192 is only to facilitate high quality bandlimited interpolation)

At this stage in the thought experiment, I would note, that although both list of timings look for the same condition, there may be considerably less occurences of the condition (peaks or troughs) found in the predownsampled record, which would depend on the nature of the source material.

The two lists plotted on a graph should illustrate an observable time correlation between conditions found in each record, as well as 'orphaned' conditions represented only in the higher pcm.

Disregarding the orphaned conditions, the detail of 'time resolution' rests on how closely correlated the pairable condition times turn out to be.
A plot could be made of their distribution of correlation, perhaps it would tend to be a bell curve? for pink noise only? What would the limits of correlation be?

Additional explores: Compare accuracy of correlation of surviving details, in CD to 11kHz, then CD to various other rates. White noise, to some rates, then pink noise..etc.. Also do some comparisons in using different upsample rates, to discern the programs simpler linear discernments inherent innacuracy.

If we can spot a condition occuring at a time in a pcm record, with correlation data, we could indicate probabilities of that condition occuring within temporal distances in higher sampled records of the same kind of source material

It would be interesting to look at.

If I ever spend my sparse powers of collected concentration to generate the info myself, Ill post it here for all your troubles'

best'
cg

This post has been edited by ChiGung: Nov 16 2006, 18:20


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kwwong
post Nov 15 2006, 09:50
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QUOTE (ChiGung @ Nov 14 2006, 19:16) *
44kHz pcm 'time resolution' = 4* 11kHz pcm 'time resolution'


For a fixed frame size,

44kHz pcm 'frequency resolution' = 4*11kHz pcm 'frequency resolution',

44kHz pcm 'time resolution' = 0.25*11kHz pcm 'time resolution' biggrin.gif

This post has been edited by kwwong: Nov 15 2006, 09:51
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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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