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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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2Bdecided
post Nov 15 2006, 14:29
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So, in short, you want to run an experiment to see what effect a low pass filter has?
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ChiGung
post Nov 15 2006, 14:45
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QUOTE (2Bdecided @ Nov 15 2006, 13:29) *
So, in short, you want to run an experiment to see what effect a low pass filter has?

Yes.

As particular sample rates, do have implicit unavoidable lowpasses -the process of comparing the capabilites of different samplerates, refactors as comparing effects of different lowpasses. It is almost the same thing, although actualy doing the full downsample (as well its implied lowpass) investigates an attained quality of the full process, so would preferable for this charge for actual proof of subsample source/record ambiguity.


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Woodinville
post Nov 15 2006, 19:42
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QUOTE (ChiGung @ Nov 15 2006, 05:45) *
QUOTE (2Bdecided @ Nov 15 2006, 13:29) *

So, in short, you want to run an experiment to see what effect a low pass filter has?

Yes.

As particular sample rates, do have implicit unavoidable lowpasses -the process of comparing the capabilites of different samplerates, refactors as comparing effects of different lowpasses. It is almost the same thing, although actualy doing the full downsample (as well its implied lowpass) investigates an attained quality of the full process, so would preferable for this charge for actual proof of subsample source/record ambiguity.


So, if the lowpass filter is above the point where your ear captures information, then what have we found?

QUOTE (cabbagerat @ Nov 15 2006, 06:22) *
The second is that you seem to doubt whether lowpass->sample->reconstruct can be shown to have the same effect as just the lowpass. Without quantization, the theory says that the two processes are identical. If you wish to question this then a mathematical treatment will probably be necessary before your demonstration is accepted.



This mathematical treatment can be found in many places. I believe Taub and Shilling deal with it. Certainly Jayant and Noll address it, but not quite in a form a novice will recognize. Any good older book on modems will discuss it in great detail (PSK being exactly what would discover such differences, including quantization, noise, and distortion).

There is a lot of good mathematical treatment out there.

QUOTE (ChiGung @ Nov 15 2006, 08:53) *
Interesting, in this case however you know what the checkboard looks like, unexpected deviations from a clean checkboard appearance, would introduce innaccuracy. It is a selective example not fully similar to resolving details in waveforms - which we can have few presumptions about.


So, do you LOOK at your audio, or do you listen to it?

QUOTE (ChiGung @ Nov 15 2006, 09:31) *
So you will observe how the bandwidth limitations of samplerates damages timing and/or survival of time locatable conditions/events in waveform records vs waveform sources.


Once more, it is trivial to calculate this from first principles.

You DO understand that phase shift at a given frequency is a way of measuring time delay, yes?

Now, can you measure the phase shift (removing the ft, or pure delay, part) of your processing?

If you can't, it's not changing the in-band time resolution.

Now, a given level of quantization can be directly related to a given amount of phase uncertainty. Figure out for yourself what that equals at 16 bit quantization levels for a full-scale signal, now. Just go ahead and do it.


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ChiGung
post Nov 15 2006, 19:56
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QUOTE (Woodinville @ Nov 15 2006, 18:39) *
So, if the lowpass filter is above the point where your ear captures information, then what have we found?

I refer to previous replies on this matter such as:
QUOTE (chigung)
What is 'accurate enough' is a different matter id not like to confuse the main investigation with.


QUOTE
QUOTE (cabbagerat @ Nov 15 2006, 06:22) *
The second is that you seem to doubt whether lowpass->sample->reconstruct can be shown to have the same effect as just the lowpass. Without quantization, the theory says that the two processes are identical. If you wish to question this then a mathematical treatment will probably be necessary before your demonstration is accepted.

This mathematical treatment can be found in many places. I believe Taub and Shilling deal with it. Certainly Jayant and Noll address it, but not quite in a form a novice will recognize. Any good older book on modems will discuss it in great detail (PSK being exactly what would discover such differences, including quantization, noise, and distortion).

There is a lot of good mathematical treatment out there.

Nice, it still doesnt make comparing waveforms encoded at different samplerates but bandlimited identicaly, any more informative of the realworld situation, where records usualy can utilise their samplerates implied full bandwidths.

QUOTE
So, do you LOOK at your audio, or do you listen to it?

I do all sorts of things with audio, but generaly pcm encoding and its limitations apply to much more material than just human audio.


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Woodinville
post Nov 15 2006, 20:01
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QUOTE (ChiGung @ Nov 15 2006, 10:56) *
Nice, it still doesnt make comparing waveforms encoded at different samplerates but bandlimited identicaly, any more informative of the realworld situation, where records usualy can utilise their samplerates implied full bandwidths.

Of course it does. Try it some time.
QUOTE
QUOTE
So, do you LOOK at your audio, or do you listen to it?

I do all sorts of things with audio, but generaly pcm encoding and its limitations apply to much more material than just human audio.


So, if you're dealing with other issues, why not state those issues? It seems to me that you have an investigation in search of a problem.


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ChiGung
post Nov 15 2006, 20:30
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QUOTE (Woodinville @ Nov 15 2006, 19:01) *
QUOTE (ChiGung @ Nov 15 2006, 10:56) *
Nice, it still doesnt make comparing waveforms encoded at different samplerates but bandlimited identicaly, any more informative of the realworld situation, where records usualy can utilise their samplerates implied full bandwidths.

Of course it does. Try it some time.

I dont need to 'try' what you are saying. I know the difference between comparing two records with the same utilised bandwidth, and two records with different spectrums.

QUOTE
So, if you're dealing with other issues, why not state those issues? It seems to me that you have an investigation in search of a problem.

Why not read my contributions to the thread? The issue i am dealing with is the sensible value we can give for the ability of pcm records to record events in time accurately. "inaudible" is not such a value.




QUOTE (Garf @ Nov 15 2006, 19:18) *
I don't understand a word of what you are saying there.
"unknown frequencies which are unrepresentable at any given samplerate"

Uh?

It is a tired rephrasing of an over repeated explaination:
The frequencies which are unrepresentable at any given samplerate, are of course, those above the nyquist for that samplerate, and being unrepresentable, they are usualy unknowable. Certainly in a downsample of cd audio to 22kHz, the frequency content of the origional CD track above 11kHz -is unknowable. Ok , in some cases we might know the source tracks frequency spectrum, generaly we shouldnt assume so should we?

Im feeling a little distrurbed again, that no one seems to be understanding anything that I have made efforts to explain.

edit: removed extraneous un, from "unusualy uknowable"

This post has been edited by ChiGung: Nov 16 2006, 01:27


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AstralStorm
post Nov 15 2006, 22:43
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QUOTE (ChiGung @ Nov 15 2006, 20:30) *
It is a tired rephrasing of an over repeated explaination:
The frequencies which are unrepresentable at any given samplerate, are of course, those above the nyquist for that samplerate, and being unrepresentable, they are unusualy unknowable. Certainly in a downsample of cd audio to 22kHz, the frequency content of the origional CD track above 11kHz -is unknowable. Ok , in some cases we might know the source tracks frequency spectrum, generaly we shouldnt assume so should we?

Im feeling a little distrurbed again, that no one seems to be understanding anything that I have made efforts to explain.


You know... air is a good lowpass filter too and there's a good deal of dither in it. (thermal noise, ~-20 bits, that is ~-120 dB)
Not to count interference from other sound waves.

Other than that, the eardrum/microphone has some known temporal resolution. Then, the neural analysis system has to react (much slower). Also mostly known.
What's more: those "errors" stack.

Nothing is perfect. So you can't even notice such a tiny temporal change, unless you're a robot. Then, it goes back to square one: the microphone and electrical noise.

Go figure.
If you ever build an infinite precision machine, go for the Nobel prize.

This post has been edited by AstralStorm: Nov 15 2006, 22:48


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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
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|- - 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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