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What is "time resolution"?
ChiGung
post Nov 15 2006, 17:53
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QUOTE (SebastianG @ Nov 15 2006, 16:30) *
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.

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.

QUOTE
However, 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. (I tested this and IMHO this is not surprising). By your definition of time resolition (spatial resolution for images) this would mean that the two images would have the same spatial resolution.

I dont fully agree with your case there, regard how you are locating nodes in a very ideal pattern (checkerboard). It will get complex to investigate fully, but the location of details when the source pattern is unpresumable (piano or violin, cymbal or triangle, square or saw or sine.. noise or not..) is a significant additional factor in recovering source material detail from pcm records.


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SebastianG
post Nov 15 2006, 17:59
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QUOTE (ChiGung @ Nov 15 2006, 17:53) *
It will get complex to investigate fully, but the location of details when the source pattern is unpresumable (piano or violin, cymbal or triangle, square or saw or sine.. noise or not..) is a significant additional factor in recovering source material detail from pcm records.

It seems nobody else than you interested in those "details" since it's very likely that our auditory system doesn't care about whether peaks have moved due to band limitation.
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2Bdecided
post Nov 15 2006, 18:06
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QUOTE (ChiGung @ Nov 15 2006, 17:01) *
QUOTE (2Bdecided @ Nov 15 2006, 15:18) *

It's a fair enough experiment to ask an undergrad to do in order to practice computer programming and audio processing, but in terms of what it actually tells you about anything, all I can do is just sit here slowly shaking my head!

Yet you cant explain what is pointless about generating the data described, without indestinct reference to some 'theory' which you believe I dont understand.


OK, you're starting with any audio, aren't you? A signal picked up by a microphone, synthetic pink or white noise, etc - correct?

You won't accept pre-filtering of the signal, correct?

And you will low pass filter the signal at varying frequencies, and see how the peaks in the "original" change, correct?

Well think about this: You can start with a 10MHz sampled signal. Given the lack of a filter, there will be something (mainly noise) up to 5MHz. If you filter the signal at 1MHz, some peaks will move a little.

Thus you have proven that a 1MHz low pass filter does something.

So what?!?!?!?!

Cheers,
David.
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ChiGung
post Nov 15 2006, 18:21
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QUOTE (SebastianG @ Nov 15 2006, 16:59) *
QUOTE (ChiGung @ Nov 15 2006, 17:53) *

It will get complex to investigate fully, but the location of details when the source pattern is unpresumable (piano or violin, cymbal or triangle, square or saw or sine.. noise or not..) is a significant additional factor in recovering source material detail from pcm records.

It seems nobody else than you interested in those "details" since it's very likely that our auditory system doesn't care about whether peaks have moved due to band limitation.

I dont care what they sound like, my interest in them is that they exist and cause real, measurable, examinable, innacuracy between waveform sources and pcm waveform records.

When there is negative interest in that practical circumstance here, in HAs Scientific/R&D Discussion forum, in a thread called "what is time resolution", and all my explainations of it are run around with... relentless indifference and absolutely no apparent solvent interest, does that make me the fool?

'who knows


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ChiGung
post Nov 15 2006, 18:31
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QUOTE (2Bdecided @ Nov 15 2006, 17:06) *
You won't accept pre-filtering of the signal, correct?

No, it is clear in the process described, that all records of source can be suitably prefiltered to fit their format.
ie. we can assume the cd audio will be suitably prefiltered at 22kHz
only to compare that records time resolution to lower sampling rates, it is insensible to prefilter the higher sampling rates to the enforced bandlimit of the lower rate.

QUOTE
Well think about this: You can start with a 10MHz sampled signal. Given the lack of a filter, there will be something (mainly noise) up to 5MHz. If you filter the signal at 1MHz, some peaks will move a little.
Thus you have proven that a 1MHz low pass filter does something.
So what?!?!?!?!

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.

This post has been edited by ChiGung: Nov 15 2006, 18:32


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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, 20:14
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QUOTE (Woodinville @ Nov 15 2006, 18:42) *
QUOTE (ChiGung @ Nov 15 2006, 05:45) *
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.

The damage is trivial for you to calculate? Well, i wouldnt say that my method of actualy discerning it was trivial or too involved, but Im just the one who has pressed the issue to be acknowledged arent i?

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

I dont accept phase shifts can be directly interprated as a 'time delay' because they applies to long multisample sinusoidal patterns (frequencies), phase shifts never alone detail any isolatable instants. Phase shifts are time relateable attributes of frequencies, not instant isolateable positions or durations in linear time.

QUOTE
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.

Im not interested in performing your excercises.
The resulting flaw of your own excercising, is that you neither can acknowledge that timing resolution of locateable conditions in real waveforms has significant 'subsample' uncertainty regarding the unknown frequencies which are unrepresentable at any given samplerate.


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Garf
post Nov 15 2006, 20:18
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QUOTE (ChiGung @ Nov 15 2006, 20:14) *
The resulting flaw of your own excercising, is that you neither can acknowledge that timing resolution of locateable conditions in real waveforms has significant 'subsample' uncertainty regarding the unknown frequencies which are unrepresentable at any given samplerate.


I don't understand a word of what you are saying there.

"unknown frequencies which are unrepresentable at any given samplerate"

Uh?
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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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Woodinville
post Nov 15 2006, 23:35
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QUOTE (ChiGung @ Nov 15 2006, 11:14) *
Im not interested in performing your excercises.

Then you're not interested in the answer to your question.
QUOTE
The resulting flaw of your own excercising, is that you neither can acknowledge that timing resolution of locateable conditions in real waveforms has significant 'subsample' uncertainty regarding the unknown frequencies which are unrepresentable at any given samplerate.



The exercises I provided you allow you to do exactly what you want to do.

If you don't want to do them, you aren't going to get your answers.

QUOTE (ChiGung @ Nov 15 2006, 11:14) *
I dont accept phase shifts can be directly interprated as a 'time delay' because they applies to long multisample sinusoidal patterns (frequencies), phase shifts never alone detail any isolatable instants. Phase shifts are time relateable attributes of frequencies, not instant isolateable positions or durations in linear time.


Actually, given an amount of phase shift at any given frequency, you have precisely specified duration in time.

But this seems to suggest you're stuck in a larger problem. You do realize that all physically realizable waveforms (we're talking audio here, not cosmology, after all) can be represented by an integral of sine waves, do you not? You do realize that you can decompose any physically realized waveform into its sinusoidal components, yes?

Your failure to understand that phase shift and time delay are DEFINED to be related would suggest, as well, that you "don't accept" the language of the field. This is not a good place to start. Perhaps you could start by accepting the language, and then state what your problem is in terms of generally accepted language. Language, after all, is no good for communication if you use different meanings, and if you are using the same meaning as everyone else, a phase shift of x at a given frequency is exactly, precisely specifying a given amount of time.


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ChiGung
post Nov 16 2006, 01:20
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QUOTE (Woodinville @ Nov 15 2006, 22:35) *
The exercises I provided you allow you to do exactly what you want to do.
If you don't want to do them, you aren't going to get your answers.

i'm scheduled to dip my head in a clow clap and sprinkle ants in my pants just before i get your answers prof tongue.gif

The positions have been stated, time may clarify.....


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kwwong
post Nov 16 2006, 10:24
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QUOTE (kwwong @ Nov 15 2006, 03:50) *
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


Sorry I was wrong..

For a fixed frame size,

44kHz pcm 'frequency resolution' = 0.25*11kHz pcm 'frequency resolution',

44kHz pcm 'time resolution' = 4*11kHz pcm 'time resolution' ohmy.gif
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2Bdecided
post Nov 16 2006, 14:22
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QUOTE (ChiGung @ Nov 15 2006, 20:30) *
Im feeling a little distrurbed again, that no one seems to be understanding anything that I have made efforts to explain.


No, I think I get it perfectly.

When you low pass filter a signal, the positions of the peaks will move (and some peaks will vanish).

You seem to think this is important, and want to perform an experiment to determine how far the peaks move, and then relate this quantity to the low pass filter cut-off frequency. You believe the peak location is related to time resolution, and thus hope to show the relationship between low pass filter cut-off frequency (or bandwidth, or sample rate, etc) and time resolution.

That's your position, isn't it?


No one is doubting that the peaks will move and/or vanish with most signals.

I personally am doubting you can perform the experiment on arbitrary samples, because you won't be able to track the peaks.

More generally, I think everyone (including me) is failing to see the point of the experiment.


I tried, intuitively, so show why I think it's pointless with the 10MHz example...

QUOTE (ChiGung @ Nov 15 2006, 18:31) *
QUOTE (2Bdecided @ Nov 15 2006, 17:06) *
Well think about this: You can start with a 10MHz sampled signal. Given the lack of a filter, there will be something (mainly noise) up to 5MHz. If you filter the signal at 1MHz, some peaks will move a little.
Thus you have proven that a 1MHz low pass filter does something.
So what?!?!?!?!

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.


...but you just re-iterated that the peaks would move/vanish, and the amount may be related to bandwidth. I know. I said that too!

My "So what?!?!?!" wasn't facetious - it was a serious (albeit exasperated smile.gif ) question. Having done your experiment, what have you proven? What conclusion can you draw? What relevance does this conclusion have to anything?


The thing is, I think your experiment is impossible, so we're never going to get trustworthy results from it. That is why I am trying to move things on; Since the fact that the peaks move isn't disputed by anyone, what we want to know is: what conclusion do you draw from that?

(because I suspect its a vastly different conclusion from the one drawn by everyone else!!!)

Cheers,
David.
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ChiGung
post Nov 16 2006, 17:10
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QUOTE (2Bdecided @ Nov 16 2006, 13:22) *
My "So what?!?!?!" wasn't facetious - it was a serious (albeit exasperated smile.gif ) question. Having done your experiment, what have you proven? What conclusion can you draw? What relevance does this conclusion have to anything?

Hi 2B, thanks for going through what you understand of the investigation I presented. I think we have similar expectations of the outcome of the investigation, although I find the 'best matching' stage (of nodes) less troublesome, because the innacuracy introduced by missed and imaginary matches only tends to increase the appearance of accuracy and i am satisfied to look at flatteringly skewed best case data from practice, rather than isolated formulations or none at all.

The investigation was designed to give us a most optimistic reckoning, of our ability to match the location of instantaneous features apparent in PCM records, to their potential position in their original source material.
The findings could apply to eg, estimating the location of percussive attacks in human audio from audio pcm, or (perhaps fancifully) estimating the edges of a region of different luminousity and/or spectroscopy in an image of space.
As a thought experiment, we are reminded that timings (or positions) derived from pcm, are often/normaly unknowable estimations of the timings occuring in the recordings source.
I believe this relationship of uncertainty and innacuracy between PCM and its potential source is central to the issue of achieved time resolution @ sample rate, and makes claims of confident subsample time resolution highly misleading -misreadings of the fundamental algebraic systems useable to most consistently process PCM.

I appreciate you taking my position head on. I am satisfied that my point is explicit enough now for readers to draw their own conclusions.

cheers'
cg

QUOTE (kwwong @ Nov 16 2006, 09:24) *
Sorry I was wrong..

For a fixed frame size,
44kHz pcm 'frequency resolution' = 0.25*11kHz pcm 'frequency resolution',
44kHz pcm 'time resolution' = 4*11kHz pcm 'time resolution' ohmy.gif

Thanks kwwong, I should try and make less typos really emot-eng101.gif

This post has been edited by ChiGung: Nov 16 2006, 17:03


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SebastianG
post Nov 16 2006, 18:22
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QUOTE (ChiGung @ Nov 16 2006, 17:10) *
The findings could apply to eg, [...] or (perhaps fancifully) estimating the edges of a region of different luminousity and/or spectroscopy in an image of space.

See? You usually have a model for the kind of thing you search for. For example: Edge = curve that joins dark and bright areas in an image. Usually the signal you recorded is distorted in some ways (noise, nonlinear transfer, ...), so you have to account for that via preprocessing and stuff (oftentimes even a lowpass with Gaussian-like response is used for that, actually).

What you can determine through simulation is that detector algorithm A locates feature type B (eg. edges) with accuracy C (eg. +/-0.2 pixels) when given a signal with distortion D (eg. SNR of 20 dB).

In these cases where the location of features is interesting (like the position of an x-corner for camera calibration or peaks of a cross-correlation to detect movements and stuff) zero-phase-lowpassing (to some extent) hardly affects the accuracy that can be achieved. Most changes you encounter after lowpassing is due to the noise that has been filtered out so it can't disturb the estimated location anymore. Usually the parameter that is directly related to the accuracy that can be achieved is a combination of noise power and sampling rate. But increasing the sampling rate doesn't necessarily imply that the accuray you get with "detector A" will improve because you also collect more high frequency noise that isn't filtered out anymore ...

Anyhow ... I guess I can say that most of us don't agree with you that a definition of "time resolution" based on how peaks will move around, vanish or appear due to band-limitation makes much sense/is any practical.

This post has been edited by SebastianG: Nov 16 2006, 18:37
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ChiGung
post Nov 16 2006, 18:51
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QUOTE (SebastianG @ Nov 16 2006, 17:22) *
QUOTE (ChiGung @ Nov 16 2006, 17:10) *

The findings could apply to eg, [...] or (perhaps fancifully) estimating the edges of a region of different luminousity and/or spectroscopy in an image of space.

See? You usually have a model for the kind of thing you search for. For example: Edge = curve that joins dark and bright areas in an image. Usually the signal you recorded is distorted in some ways (noise, nonlinear transfer, ...), so you have to account for that via preprocessing and stuff (oftentimes even a lowpass with Gaussian-like response is used for that, actually).

I understand you are talking about knowledge of the artifacts/condtions searched for - and I recognise if the artifact is known to span several samples and has its own consistent reliable form through a period or periods of time, its form can be traced throughout multiple samples, allowing increased accuracy of placement. This is the case i see with calculating phase delays, or checkerboard positioning - not so much with uncertain appearances in space, where we cant be sure of eg. a nebulas form or objects' edge consistency.

QUOTE
What you can determine through simulation is that detector algorithm A locates feature type B (eg. edgex) with accuracy C (eg. +/-0.2 pixels) when given a signal with distortion D (eg. SNR of 20 dB).

In these cases where the location of features is interesting (like the position of an x-corner for camera calibration or peaks of a cross-correlation to detect movements and stuff) zero-phase-lowpassing (to some extent) hardly affects the accuracy that can be achieved. Most changes you encounter after lowpassing is due to the noise that has been filtered out so it can't disturb the estimated location anymore. Usually the parameter that is directly related to the accuracy that can be achieved is a combination of noise power and sampling rate (something like the ratio of sampling rate to the square root of the noise power). But increasing the sampling rate doesn't necessarily imply that the accuray you get with "detector A" will improve because you also collect more high frequency noise that isn't filtered out anymore ...

This is an informative account of a practical situation but it should not detract from the case presented that in many applications, most relevantly -the selection of sample rates for human audio, the practical rates selected 44,32,24 etc.. do differ in bandwidth from potential sources, and that reduction in bandwidth does affect accurate recording of timeable events/conditions/features, which within audio are not usualy suitable for extra interpolations for locating knowable formations (some instruments might be predictable enough to try experimentaly, but in practice this isnt done).

QUOTE
Anyhow ... I guess I can say that most of us don't agree with you that a definition of "time resolution" based on how peaks will move around, vanish or appear due to band-limitation makes much sense/is any practical.

I believe if that is so, you are all kidding yourselves, because the situation that "peaks will move around, vanish or appear due to band-limitation" is unavoidably present at such audio ranges considered, and when you accept 'subsample accurate' reproduction at those ranges, you are simply deciding to dismiss the highlighted matter - that the pcm record cannot indicate any instantaneous condition's presence in their potential sources with 'subsample accuracy'.

Why people should wish to ignore such practical uncertainty of source timing (in R&D discussion) -i do not know.

regards'

edit: tpyos & phrasing

This post has been edited by ChiGung: Nov 16 2006, 21:22


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Woodinville
post Nov 16 2006, 22:48
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QUOTE (ChiGung @ Nov 16 2006, 09:51) *
I believe if that is so, you are all kidding yourselves, because the situation that "peaks will move around, vanish or appear due to band-limitation" is unavoidably present at such audio ranges considered, and when you accept 'subsample accurate' reproduction at those ranges, you are simply deciding to dismiss the highlighted matter - that the pcm record cannot indicate any instantaneous condition's presence in their potential sources with 'subsample accuracy'.

Once again, a simple test using a gaussian pulse will show that you can trivially resolve subsample intervals. Ergo, your assertion is defeated directly.
QUOTE
Why people should wish to ignore such practical uncertainty of source timing (in R&D discussion) -i do not know.

regards'

edit: tpyos & phrasing


Allow me to point something else out, since you said "record". Peaks in the record (vinyl) playback will move around and vanish with record wear, stylus pressure, the difference in phase between the turntable rumble and the "peak", and furthermore, distortion mechanisms will create peaks (very sharp ones) here and there.

Of course, said peaks have no frequency content inside the range of hearing, but that's a separate issue.

The position of such error peaks can be distinquished easily to sub-sample accuracy in PCM, as well. Been there, done that.

The thing, and the only thing, you can't see in the PCM representation, is the part of the peak that has frequency content OUTSIDE the pcm range.

Now, I notice that you've refused to try the basic experiments I've suggested earlier, and instead engaged in personal abuse. Don't engage in abuse again.

If you ever do finally try a few real-life experiments you will discover immediately that a phase shift at a given frequency precisely specifies a time delay. I'll await your admission of that.


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ChiGung
post Nov 16 2006, 23:32
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QUOTE (Woodinville @ Nov 16 2006, 21:48) *
QUOTE (ChiGung @ Nov 16 2006, 09:51) *
....the situation that "peaks will move around, vanish or appear due to band-limitation" is unavoidably present...

Once again, a simple test using a gaussian pulse will show that you can trivially resolve subsample intervals. Ergo, your assertion is defeated directly.

"woosh", (thats the sound of the practical matters which ive brought brought up and Seb and 2B have finaly acknowledged as real (though not yet central)

- flying over over your head.

QUOTE
Allow me to point something else out, since you said "record".

As in pcm "record" - 'nice smoke screen.

QUOTE
Now, I notice that you've refused to try the basic experiments I've suggested earlier, and instead engaged in personal abuse.

Which person?
I said i'd abuse myself before taking you seriously again Woody.
QUOTE
Don't engage in abuse again.

Aww i thought you liked it - stop scratching my back, and i wont scratch yours then.

always'
cg


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Woodinville
post Nov 16 2006, 23:44
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QUOTE (ChiGung @ Nov 16 2006, 14:32) *
"woosh", (thats the sound of the practical matters which ive brought brought up and Seb and 2B have finaly acknowledged as real (though not yet central)

- flying over over your head.


Since I've said the same thing they have, in different words, I think that perhaps you're just handing out abuse again.

Ciao.


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ChiGung
post Nov 17 2006, 00:15
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QUOTE (Woodinville @ Nov 16 2006, 22:44) *
Since I've said the same thing they have, in different words, I think that perhaps you're just handing out abuse again.

You are very sensitive for someone who posts in such a critical manner.

2B confirmed:
QUOTE (2bdecided)
When you low pass filter a signal, the positions of the peaks will move (and some peaks will vanish).

Seb stated:
QUOTE
Anyhow ... I guess I can say that most of us don't agree with you that a definition of "time resolution" based on how peaks will move around, vanish or appear due to band-limitation makes much sense/is any practical.

-he does seem to confirm here that "peaks will move around, vanish or appear due to band-limitation" - only for some reasons denies relevance to 'time resolution'

But i think Seb understands that the investigation I described would confirm that "peaks* will move around, vanish or appear due to band-limitation" It would at least measure, with a flattering bias, the shifts in temporal position we can expect to result from a given downsample and source track type.
(not only "peaks" but troughs, zero crossings, slopes, every shape and form in the record can be distorted by the necessary lowpassing involved in hq downsampling) Because that point seem to be accepted and partly because Im a lazy so, I stopped writing the program to do the investigation.

Although ive had no encouragement, when i get round to finishing it, ill post the results here.

So Woody, your prediction is on record that no differences in timing (especialy in hand crafted gaussian pulses etc) will be observed.


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MoSPDude
post Nov 17 2006, 00:21
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I've been trying to follow this as well, and especially reading 2Bdecided post which I think summarises primarily what ChiGung wants to test, this is how I understand the issue.

A lot of this seems to not have much to do with PCM but more sampling theorem in general, as a quick reference I've been using my books and notes, for an online reference - wikipedia (Nyquist–Shannon sampling theorem) as it provides the mathematic descriptions accordingly. Theoretically, a band-limited signal sampled at greater than twice the highest frequency component when reproduced through the sinc interpolation, which requires knowledge of all samples over all time, is a perfect representation. Practically, we don't know all samples across all time and DACs use various methods to reproduce the signal, but not perfectly.

If we do these tests digitally, and the real-world source is band limited below the Nyquist frequency, then the Nyquist–Shannon sampling theorem will hold and values representing that signal will theoretically reproduce an exact perfect signal, including any sub sample shifts in peaks due to filtering. Quantisation will have an effect in terms of increasing noise. If the source signal was not band-limited, aliasing will occur - and the sampled signal will certainly not represent the original signal.

In terms of the peaks moving after a low pass filter etc, I was taught these such things were due to the phase characteristic of the filter where indeed the phase change specified at a specific frequency will give an exact definable time shift. As 2Bdecided said, it would be difficult to track EXACT peaks, but I imagine you could compare magnitude/phase plots of a set period of time with an arbitrary signal before and after an LPF or whatever filter, along with the magnitude/phase plot of the transfer function of the filter. What people are saying when they mention 'records' etc. is that a communication medium also has a transfer function and an appropriate magnitude/phase response - eg age/wear changes these responses.
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Woodinville
post Nov 17 2006, 00:40
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QUOTE (MoSPDude @ Nov 16 2006, 15:21) *
If the source signal was not band-limited, aliasing will occur - and the sampled signal will certainly not represent the original signal.

Very, very true.

And, as a dual, a signal that is reconstructed without a reconstruction filter will also mean that the resulting nonlinear system has worse time resolution than the system with the reconstruction filter.
QUOTE
In terms of the peaks moving after a low pass filter etc, I was taught these such things were due to the phase characteristic of the filter where indeed the phase change specified at a specific frequency will give an exact definable time shift.

That entirely depends on the signal. Suppose we have a gaussian pulse centered at time t1 whose substantial frequency components are above the cutoff, and another much smaller one at time t2 that is entirely in-band as far as the filter is concerned..

Doesn't matter what kind of filter you use there.
QUOTE
As 2Bdecided said, it would be difficult to track EXACT peaks,

Or, even define what an "exact peak" means, really, in the presence of noise, which is something that we always have, all the time, in the real workd.
QUOTE
but I imagine you could compare magnitude/phase plots of a set period of time with an arbitrary signal before and after an LPF or whatever filter, along with the magnitude/phase plot of the transfer function of the filter. What people are saying when they mention 'records' etc. is that a communication medium also has a transfer function and an appropriate magnitude/phase response - eg age/wear changes these responses.


You could go beyond that, and simply plot the Hilbert envelope of the signal at different bandwidths. I think you'd find that extraordinarily useful in this discussion.


QUOTE (ChiGung @ Nov 16 2006, 15:15) *
So Woody, your prediction is on record that no differences in timing (especialy in hand crafted gaussian pulses etc) will be observed.


No, that's not my prediction. You can abuse this, as I have already explained.

This post has been edited by Woodinville: Nov 17 2006, 00:41


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