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What is "time resolution"?
ChiGung
post Nov 19 2006, 03:23
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QUOTE (Woodinville @ Nov 19 2006, 01:18) *
QUOTE (ChiGung @ Nov 18 2006, 13:49) *
Im very interested to hear about other & better methods..............

Then how come you won't accept them when they are offered?

It depends partly on the manner of offering and partly on the excercises potential to distract, - because i am making cases here which you are opposing.
At this stage im trying to measure distortion in time done to various waveform types, due to simulated resampling with lowpasses. Once measured, the expected distortion for different simulated samplerates will define the uncertainty of temporal placement of events within the waveforms source.
A task which is synonymous to me as quantifying 'time resolution'

btw, i confirmed that the spike in the preceeding plots is a bug, throwing much uncertainty on the programs performance at the moment, but ill get it fixed (the toil is in the assembling). In the meantime i expect honest estimates to be made here of the temporal resolution of pcm records. Because the proof will follow wink.gif

QUOTE
Try it. Learn.
Thankyou for encouraging me to learn, may you also continue to learn tongue.gif

^I expect that you do know a better expression to use to locate the maxima and minima or other time pin-pointable conditions in waveforms, that i have used. If you could provide something i could use in this investigation - 'great

QUOTE
I have a suggestion, go load Cygwin, Xserver, and Octave.
Octave is a good processing suite? I havent had time to try it, thanks for the tip though.

QUOTE
It will save you lots of time and eventually you'll understand that phase shift and time delay are the same thing,
maybe if you didnt save time, and built your own codebase, you just might realise that "phase shift and time delay" are different....

Phase shift's 'dimension' is tightly cyclic, time's dimension is not normaly considered so, most commonly an infinite line. The geometry of phase differs from the geometry of time, phase has a finite distribution through its own 'time' (loop) and an infinite distribution throughout 'real' time. This makes phase detail imperfect for locating finite positions in 'real' time. If I could recall Euclid as well as others i could say it better -but basicaly time delay and phase shift are different.

Although i supposed they might be used synonymously in some professional contexts.

rgrds'
cg

This post has been edited by ChiGung: Nov 19 2006, 03:25


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Woodinville
post Nov 19 2006, 06:14
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QUOTE (ChiGung @ Nov 18 2006, 18:23) *
maybe if you didnt save time, and built your own codebase, you just might realise that "phase shift and time delay" are different....

I see you're resorting to insuts again.
QUOTE
Phase shift's 'dimension' is tightly cyclic,

No, it's not. 2 pi is not the same phase shift as 4 pi, although sometimes measuring which is which requires good understanding, or in some cases even the use of time delay to disambiguate between 2 pi and 4 pi.

The fact that they can be disambiguated in relevant contexts shows fully your mistake.

I would suggest, again, that you go back and learn the basic definitions for what you seek.


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cabbagerat
post Nov 19 2006, 10:20
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QUOTE (ChiGung @ Nov 18 2006, 18:23) *
Phase shift's 'dimension' is tightly cyclic, time's dimension is not normaly considered so, most commonly an infinite line. The geometry of phase differs from the geometry of time, phase has a finite distribution through its own 'time' (loop) and an infinite distribution throughout 'real' time. This makes phase detail imperfect for locating finite positions in 'real' time. If I could recall Euclid as well as others i could say it better -but basicaly time delay and phase shift are different.
Euclid? If you want to have a scientific discussion perhaps following the standard of scientific publications would be a good idea. Either put up a proof or a reference to a published document containing a proof.


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Garf
post Nov 19 2006, 10:54
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QUOTE (ChiGung @ Nov 19 2006, 03:23) *
btw, i confirmed that the spike in the preceeding plots is a bug, throwing much uncertainty on the programs performance at the moment, but ill get it fixed (the toil is in the assembling)


QUOTE
maybe if you didnt save time, and built your own codebase, you just might realise that "phase shift and time delay" are different....


One wonders how you can make these two statements and keep a straight face.

If you are going to try arguing based on the implication that results from Octave would somehow be flawed, compared to your own software, then I think there is absolutely no point in continuing this argument further.
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SebastianG
post Nov 19 2006, 14:17
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It looks like we're going in circles. I see you, ChiGung, posted some Java code that estimates the positions of peaks (quite badly I might add -- but since the signal you used is oversampled at least 4 times it doesn't hurt that much). But what was the point of doing it? You didn't have to "prove" that bandlimitation changes something. Nobody questioned it.

It's merely your notion of "time resolution", "timing detail" and your obsession about peaks. I mentioned a real practical example where one is interested in the location of a saddle point which is a center of a highly symmetric region (checkerboard corner) and that detectors exist which are reliable even when noise is present (I got an accuracy of +/- 0.05 pixels at an SNR of 20 dB). The theoretical limit of accuracy that can be achieved when no noise is present and aliasing didn't take place during the sampling is infinitely fine.

Why should we accept your definition of time resolution? Is there any practical reason for it? Who cares about how peaks may move on arbritrary signals due to band limitation? In all interesting cases those features don't move when band limiting due to symmetries (Try a smooth Gaussian pulse for example). Your "definition" (we've yet to see an good formulation) of time resolution is just a vague statement about how peaks may move. Your "time resolution" is what? An attribute to describe the accuracy of what? An instance of the PCM format? The way peaks may move certainly depends on the type of signal. So, is "time resolution" something you use to describe a type of signal? It's just vague nonsense. Again, nobody questions that peaks may move but you seem to be overly concerned about it. Regardless of how one should measure this and assign a number to describe the accuracy of something.... Why should we care?

Lemme say that I think I know what situation you are in. I wouldn't be honest if I denied that I've never been in a similar situation (me being sure about something and thinking everybody was wrong). Hopefully one realizes what's going on and feels only a little embarressed -- instead of really ashamed because of name calling, arrogant behaviour or whatever...

This post has been edited by SebastianG: Nov 19 2006, 14:56
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ChiGung
post Nov 19 2006, 18:25
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QUOTE ('cabbagerat')
Euclid? If you want to have a scientific discussion perhaps following the standard of scientific publications would be a good idea. Either put up a proof or a reference to a published document containing a proof.
I roughly recall Euclid doing some early explorations into the 'geometry of space" You guys need references to remind you that "phase" and "delay" exist in different dimensions? perhaps compare "phase space" with "space time"
QUOTE ('sebastianG')
It looks like we're going in circles.
a bit like phase space -infinite cycles smile.gif

SebastianG:"I see you, ChiGung, posted some Java code that estimates the positions of peaks (quite badly I might add"
- Its just an approximation to get the ball running. Like i said im interested if you might describe a better method. We could also see how the methods compare. When ive tidied the code up a bit,it will be quite easy to modify.

SebastianG:"but since the signal you used is oversampled at least 4 times it doesn't hurt that much). But what was the point of doing it? You didn't have to "prove" that bandlimitation changes something. Nobody questioned it."
- Ive had to respond to a great deal of dismissals and missreports, but here are some quotes about youre claim that "nobody questioned it" :
QUOTE ('cabbagerat')
If you are saying that, in PCM, distortion is introduced by the impulse response of the system, then please demonstrate that this distortion is even plausibly audible.
Note the sly attempt to shift context from detectability to "audibility"

QUOTE ("KikeG")
Resolution refers about the smallest time event that can be resolved.
KikeG never questioned its existence, just dismissed its relevance. I am attempting resolve events and observe their timing differences throughout different bandwidths/samplerates, to inform claims about pcm time resolution.

@SebastianG
- you might have a better appreciation of my efforts if you were more familiar with the content of this thread:

QUOTE ('woodinville')
Chigung wrote: "Detail of any time localisable events, will be distorted by the implicit lowpass of conversion by an unknowable amount (post conversion) by upto a sample-period-width of difference."

This is completely incorrect. Please do not state it as a fact, and please do not reproduce this myth where it may confuse others.
(not just "incorrect" but completely incorrect - followed by an order to desist saying so(!)

Do people read HA to learn? How well is sense defended here?

QUOTE ("2bdecided")
So, we have two filters. If _both_ filters block everything above fs/2, then the sampling stage itself will be transparent - lossless, if you like. In other words, these two systems would be identical...
I have never disagreed with this, but this is the fact which has been repeatedly put forward to show the futility of examining timing differences between different samplerates/bandwidths of the same potential source. Because it only considers sources with the same bandwidth - it is an irrelevant, disruptive case -especialy when repeated often throughout this thread as something i 'dont get'

SebastianG:"Why should we accept your definition of time resolution? Is there any practical reason for it? Who cares about how peaks may move on arbritrary signals due to band limitation?"
- 'Arbitrary' is a dismissive term to use there, this an investigation of practical time resolution in pcm of various kinds of source including music tracks. Who cares? The thread is "what is time resolution", this is the R&D section of an audio forum. But hey it might be true,that no one but me really cares about the subject.

SebastianG:"Lemme say that I think I know what situation you are in. I wouldn't be honest if I denied that I've never been in a similar situation (me being sure about something and thinking everybody was wrong). Hopefully one realizes what's going on and feels only a little embarressed -- instead of really ashamed because of name calling, arrogant behaviour or whatever..."
- Sincerely thanks, but i dont think you have appreciated the thrust of this debate, or how my ultimately trivial situation in this thread might relate to my circumstances outside of it.

I am self critical and acknowledge my faults, i percieve that you all too should perform some critical introspection.

QUOTE ('Garf')
ChiGung:"btw, i confirmed that the spike in the preceeding plots is a bug, ....
maybe if you didnt save time, and built your own codebase, you just might realise that "phase shift and time delay" are different...."

One wonders how you can make these two statements and keep a straight face.
They arent related. If you develope your understanding from first principals you are more likely to spot fundamental differences between different entities like "phase shift" and "time delay" - than if you prematurely seek the meanings of the terms as reported by other peoples studies.

Garf: "If you are going to try arguing based on the implication that results from Octave would somehow be flawed, compared to your own software, then I think there is absolutely no point in continuing this argument further."
- Ive no idea why you suspect that. Please do present comparable results from Octave if you get the time.

---

Im not over the moon, that my program is not working completely yet, but it will when I get an hour or so to concentrate on fixing it. Its not complex compared to my other projects, just a quick throwing together of a couple of parts. I could just await more accurate data on the matter from you guys and your own tools, but suspect that might never materialise.

If i dont bother finishing the program, who has contributed less? Me, or those who simply refered the great job their own favourite tools could do?

QUOTE ('woodinville')
chigung: "maybe if you didnt save time, and built your own codebase, you just might realise that "phase shift and time delay" are different...."

I see you're resorting to insuts again.
I didnt mean for that to be insulting to you.
Please examine your own manners of expression.
(I attempt to fairly return the respect i recieve)

QUOTE ('woodinville')
chigung:Phase shift's 'dimension' is tightly cyclic,

No, it's not. 2 pi is not the same phase shift as 4 pi, although sometimes measuring which is which requires good understanding, or in some cases even the use of time delay to disambiguate between 2 pi and 4 pi.
This reported subtlety does not make phase shifts dimension equivalent to realtime's. However you arrange it, you cant show these things are equal. But you do often half report a theoretical contention, before handwaving towards further neccessary 'studies'

Woodinville:"I would suggest, again, that you go back and learn the basic definitions for what you seek."
- I gather if i suggested that to you, you would report insult.

--
'fair regards to you all,
cg


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MoSPDude
post Nov 19 2006, 21:03
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@ChiGung, A phase shift at a given frequency is equal to a time shift. As you said, a phase shift on its own doesn't really have any meaning. The time shift in seconds for a frequency 'f' in Hz, and phase shift 'p' in radians is equal to p/(2*pi*f) for a straight sinusoid. This can be extended and applied to any form of signal, for any duration, by realising that any waveform is a composite sum of sines and cosines - hence why the fourier transform returns both magnitude and phase plots.

When you perform the up-sampling, perhaps adding a small sample shift manually and taking the FFT would help to illustrate the phase-time relationship.

This post has been edited by MoSPDude: Nov 19 2006, 21:11
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MedO
post Nov 19 2006, 21:22
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QUOTE (ChiGung @ Nov 19 2006, 18:25) *
Woodinville:"I would suggest, again, that you go back and learn the basic definitions for what you seek."
- I gather if i suggested that to you, you would report insult.


Well, you have to admit that this quote of you kind of suggests that you didn't read up on the definitions of the terms used in the textbooks:

QUOTE
Untrue. I limit my research to protect my originality. Education is to Innovation what Masterbation is to Procreation. I have learned adequate tools at home, school and university and beyond to suit my own designs.


A main problem through this discussion is that there is a lot of misunderstanding going on. Most notably, the term "time resolution" is used a lot, and interpreted as a different concept by different people here.

As far as I understand it, what you're trying to show is that certain conditions (like "level=x" or peak positions) shift in time when the signal is lowpassed. Big deal. This is completely equivalent to saying that the waveform has changed. Why? Because if the waveform was different in one place, you could construct a condition that was fulfilled in this place in the source signal but not in the result.

Conclusion: Lowpassing changes the waveform, so some or all of your conditions might not be fulfilled anymore (or will be fulfilled in different positions) in the result. Please note that this is probably not what most other people here understand as "time resolution".

The question now asked is, how much will those conditions move. I (and other people following this thread) fail to see the point in this question. Maybe you could give an example where this information would be relevant?
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ChiGung
post Nov 19 2006, 21:30
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QUOTE (MoSPDude @ Nov 19 2006, 20:03) *
As you said, a phase shift on its own doesn't really have any meaning.

Yes, i would say an individual 'phase shift' is an incomplete value, without refering to a (potential) period which resides within a phase space. A 'time delay' is an incomplete value without refering a (potential) instant within 'time'.
When phase space is mapped onto time, it fills time with unending repetitions of its periodic content (ie frequencies are theoreticaly infinite in duration). So a value which is interprated as a phase shift, cannot locate any finite point in time, only a theoreticaly infinite amount of finite points described with reference to the 'phase shifts' accompaning period.

QUOTE
- hence why the fourier transform returns both magnitude and phase plots.

I'm normaly interested in discussing such, but am weary from the previous reactions and charges made against my outlooks and character here.

may you fair better here'

cg


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ChiGung
post Nov 19 2006, 21:45
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QUOTE (MedO @ Nov 19 2006, 20:22) *
Maybe you could give an example where this information would be relevant?

It would be relevant to knowing how accurately times of conditions which are indicatable in PCM records can predict the conditions true time of occurence in source material.

Such as this simple example brought up pages ago:
QUOTE
techie: "captain we have located a 'spike' event on the PCM sensor"
captain:"what is the position of the spikes peak teki?"
techie:"324.37643 sampling intervals exactly captain"
captain:"how can you be so precise?"
techie:"because time delays are quite precisely encodable in PCM"

But a natural spike, will have an unknown frequency spectrum, the tools (information) to locate the true peak with certainty had to be removed before the downsample, so we can make the best guess by assuming the 'subsample deviators' (frequencies beyond nyquist) were all flat anyway but thats just a guess, the true peak could have been anywhere in the sample interval. If it was actualy somewhere other than the record suggests most likely, that information was contained in the lowpassed higher frequencies which now manifest as the unrecorded gaps between samples.


Responses to this example included, refutations that the true spikes subsample position was insecure at all. The case can also be applied to any use of pcm, where the source is not known to be suitably bandlimited to the bandwidth of the employed samplerate. Such as master audio > CD audio, CD audio> less, seismology, radio astronomy... astrology...nope not quite astrology wink.gif

Imagine it was an examine question: what applications of pcm records do you think are susceptable to timing uncertainties caused by samplerate enforced bandlimitation ? How does the concept and common usage of the term 'time resolution' contrast with practicaly introduced distortions?

cheers,
cg

edit: added clarifications to over saturated language used in the quote

This post has been edited by ChiGung: Nov 19 2006, 21:52


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MoSPDude
post Nov 19 2006, 22:09
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I agree a reference point is needed, a phase shift at a specified frequency does not specify an exact time, as does a time delay not specify an exact time - but both a phase shift at a specified frequency and a time delay are equivalent in these terms, and it's possible to have a phase shift of greater than 2*pi allowing any duration to be specified. Phase shifts tend to be measured relative to the input to a transfer function - so could be used to locate exact positions if you know those of the input. Again, comparing input mag/phase plots to output mag/phase plots would help to illustrate this.

Perhaps looking at it from a different angle is needed, I think in the end we're interested in if PCM can follow its analogue band-limited source counterpart exactly. Quantization will add a noise error signal so 'exact' won't be fully achievable. At the moment, the movement of peaks haven't be attributed to anything other than removal of frequencies. Just a thought.

QUOTE
Imagine it was an examine question: what applications of pcm records do you think are susceptable to timing uncertainties caused by samplerate enforced bandlimitation ? How does the concept and common usage of the term 'time resolution' contrast with practicaly introduced distortions?


These questions are only valid to the extent that they question the use of ANY form of sampling, not only PCM. Again, all the ideal theoretical mathematical explainations of sampling I've read don't indicate any such timing uncertainties - only problems caused by causality and the knowledge of all samples and the like. Practically I've not tested this but again, in the physical world things are a bit different!
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ChiGung
post Nov 19 2006, 22:21
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QUOTE (MoSPDude @ Nov 19 2006, 20:59) *
I agree a reference point is needed, a phase shift at a specified frequency does not specify an exact time, as does a time delay not specify an exact time - but both a phase shift at a specified frequency and a time delay are equivalent in these terms,

I dont think so -
A phase shift is an 'orphaned' value without reference to a period and a mapping onto time (reference point to)
A time delay, just needs a reference point in time, as a time value just needs a reference point to time=0

The difference is, with knowledge only of time, a time value is complete.
With knowledge only of time, a phase-shift value is incomplete (until we have reference to its period)
Then, when a phase shift value is employed as a phase shift value, it details the location of an infinite periodic conditions throughout realtime. It cant detail a finite condition without meaning something other than "phase shift"

QUOTE
and it's possible to have a phase shift of greater than 2*pi allowing any duration to be specified.

I admit i dont know how the particulars of that are theoreticaly employed, though i could make guesses at options. In practice i interprate things circumspectly for the task at hand.

Its not absolutely clear to me how his subject applies to showing that my investigation of how lowpass distortion affects timing is uninformative,
besides it being arguement presented for me to answer - "time delays and phaseshifts are exactly the samething"

rgrds'
cg

QUOTE (MoSPDude @ Nov 19 2006, 21:09) *
Perhaps looking at it from a different angle is needed, I think in the end we're interested in if PCM can follow its analogue band-limited source counterpart exactly. Quantization will add a noise error signal so 'exact' won't be fully achievable. At the moment, the movement of peaks haven't be attributed to anything other than removal of frequencies. Just a thought.

Its a good point about the situation in practice which i wondered about while putting together my 'great unfinished' program.

QUOTE
These questions are only valid to the extent that they question the use of ANY form of sampling, not only PCM.

I dont know, question get asked about particular things all the time, without needing to encompass all of creation rolleyes.gif

QUOTE
Again, all the ideal theoretical mathematical explainations of sampling I've read don't indicate any such timing uncertainties - only problems caused by causality and the knowledge of all samples and the like. Practically I've not tested this but again, in the physical world things are a bit different!

I will try to generate data about it unhurredly over the next while... (read >days)

cheers'
cg

This post has been edited by ChiGung: Nov 19 2006, 22:35


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MoSPDude
post Nov 19 2006, 22:26
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I think we are deviating from the point, but totally disagree with the phase shift requiring a mapping onto an exact period in time, the period is found from the frequency which is given and as we mentioned before a reference point in time is needed - which is usually given by the input to the transfer function.

In terms of your exact study, of how low pass filtering affects timing, what kind of lowpass filter are you studying? I'd be interested in this filters transfer function. Is this filter being applied in the digital domain or analogue before sampling?

I don't disagree with anyone who performs any study or investigation, as I find it helps to perform these things to allow a clear view of why things work.
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ChiGung
post Nov 19 2006, 22:34
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QUOTE (MoSPDude @ Nov 19 2006, 21:26) *
I think we are deviating from the point, but totally disagree with the phase shift requiring a mapping onto an exact period in time,

That wasnt quite what i meant to describe, but can put it on hold.

QUOTE
In terms of your exact study, of how low pass filtering affects timing, what kind of lowpass filter are you studying? I'd be interested in this filters transfer function. Is this filter being applied in the digital domain or analogue before sampling?
I would be studying relevant available lowpasses to simulate the effect on event timing of high quality downsampling.

QUOTE
I don't disagree with anyone who performs any study or investigation, as I find it helps to perform these things to allow a clear view of why things work.
I bow to your standards of intrest emot-science.gif

cheers'
cg


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SebastianG
post Nov 20 2006, 00:20
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QUOTE (ChiGung @ Nov 19 2006, 18:25) *
QUOTE

...You didn't have to "prove" that bandlimitation changes something. Nobody questioned it."

Ive had to respond to a great deal of dismissals and missreports, but here are some quotes about youre claim that "nobody questioned it":
cabbagerat> If you are saying that, in PCM, distortion is introduced by the impulse response of the system, then please demonstrate that this distortion is even plausibly audible.
Note the sly attempt to shift context from detectability to "audibility"

Actually band limitation is generally not considered distortion (as in "non-linear" distortions). You both were just talking about different kinds of distortion.

QUOTE (ChiGung @ Nov 19 2006, 18:25) *
QUOTE ("KikeG")
Resolution refers about the smallest time event that can be resolved.
KikeG never questioned its existence, just dismissed its relevance. I am attempting resolve events and observe their timing differences throughout different bandwidths/samplerates, to inform claims about pcm time resolution.

Then what are "timing events"? This discussion seems pointless because we don't seem to have a common ground concerning many (pseudo-) technical terms. Everybody knows what a peak is. <rethorical>But what is "timing event"?</rethorical>

QUOTE (ChiGung @ Nov 19 2006, 18:25) *
QUOTE ('woodinville')
Chigung wrote: "Detail of any time localisable events, will be distorted by the implicit lowpass of conversion by an unknowable amount (post conversion) by upto a sample-period-width of difference."
This is completely incorrect. Please do not state it as a fact, and please do not reproduce this myth where it may confuse others.
(not just "incorrect" but completely incorrect - followed by an order to desist saying so(!)

That's probably because Woodinville interprets "timing event" differently. This only shows the need for a common vocabulary with precisly defined terms. ("timing event" is not part of it!)
Note that I was talking about peaks. Nobody claimed that peaks remain at the exact same position in general when you lowpass a signal (even with a zerophase lowpass). This is only the case when the filter's impulse response and the signal (locally) have certain properties. But of course we all know that already.
However, if you talk about "time events" this is a different story. Then it's up to interpretation. Or perhaps you should have just included the word "may" in there. Quote:"Any time localisable event" is pretty much anything and also includes the "events" whose location won't be altered during bandlimiting. <splitting hairs>These exist. So you're wrong.</splitting hairs>

One could also think of "time event" as a specific energy distribution in time (Woodinville's example: gaussian pulse). This (or the lower spectrum part that's left after lowpassing/sampling) can be located perfectly if the signal has been properly sampled. The only thing that'll mess things up here is noise (eg quantization noise).

QUOTE (ChiGung @ Nov 19 2006, 18:25) *
...Who cares? The thread is "what is time resolution", this is the R&D section of an audio forum. But hey it might be true,that no one but me really cares about the subject.

Again: I was talking about peaks and their possible movement. It's you not me nor 2B nor Woodinville that connects peaks and their possible movement to "time resolution" -- a term whose notion we havn't agreed upon. After all the "who cares"/"so what"-talk I was kind of expecting you to mention a case where a possible movement of peaks poses an actual problem. I still can not understand your obsession about those things on arbitrary signals ("arbitrary" = those that may show different locations of those points you look for after bandlimiting).

Cheers!
SG

This post has been edited by SebastianG: Nov 20 2006, 00:20
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ChiGung
post Nov 20 2006, 01:46
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QUOTE (SebastianG @ Nov 19 2006, 23:20) *
cabbagerat> "If you are saying that, in PCM, distortion is introduced by the impulse response of the system, then please demonstrate that this distortion is even plausibly audible."
chigung: Note the sly attempt to shift context from detectability to "audibility"

Actually band limitation is generally not considered distortion (as in "non-linear" distortions). You both were just talking about different kinds of distortion.

The type of distortion i was talking about, was already described (ie that which occurs in the "tekkie's spike" example which preceeded it and elsewhere besides).
It is also possible to be over pedantic about terminology.

QUOTE ('SebastianG')
chigung:"KikeG never questioned its existence, just dismissed its relevance. I am attempting resolve events and observe their timing differences throughout different bandwidths/samplerates, to inform claims about pcm time resolution."

Then what are "timing events"? This discussion seems pointless because we don't seem to have a common ground concerning many (pseudo-) technical terms. Everybody knows what a peak is. <rethorical>But what is "timing event"?</rethorical>


Firstly, I did not use the term "timing event" there, though i may have used loose phrases elsewhere. I apologise for my over occasional errors in spelling grammar and terminology, but i shouldnt apologise for the diversity or ambitiousness of my expression, which may also challenge those not especialy fluent in my dialect of english.
Regarding 'timeable events' I use such terms as a broad set of which 'peaks' are a member.
I simply wished to refer to any kind of detail which might be identified and pinpointed in time within waveforms. Basicaly anything you might think of which might be precisely locateable in time (in a prcm record) -( which peak of level is an example of).

QUOTE ('SebastianG')
That's probably because Woodinville interprets "timing event" differently. This only shows the need for a common vocabulary with precisly defined terms.

Again, I did not use the term 'timing event' in the statement which woodinville expressed great objection to.

This statement i used:
"Detail of any time localisable events, will be distorted by the implicit lowpass of conversion by an unknowable amount (post conversion) by upto a sample-period-width of difference."

-Is very explicit english. "time localisable events" are> [events] [which are possible to locate in] [time].

I do use complex and varied english (in order to be as descriptive as possible) Some of my posts contain more grammatical errors than others, but most are not too bad, and some are carefuly composed. I think you suspect my english is worse than it actualy is, because it is not your own first language and i attempt to describe concepts in complex english, rather than employing the terminology which you are familiar with.

There is a similar problem with the phrase "time resolution" here. "Resolution" has a common meaning, and "time" does to. If a technical usage of the term 'time resolution' conflicts with the plain english translation, that can certainly cause confusion.

QUOTE
"Any time localisable event" is pretty much anything and also includes the "events" whose location won't be altered during bandlimiting.

Yes that term is meant to mean anything time-locatable. I am interested to hear any event-types (conditions) which are not susceptable to being altered by bandlimitation - or other types which are.

QUOTE
One could also think of "time event" as a specific energy distribution in time (Woodinville's example: gaussian pulse). This (or the lower spectrum part that's left after lowpassing/sampling) can be located perfectly if the signal has been properly sampled. The only thing that'll mess things up here is noise (eg quantization noise).
Yes as i wrote before, when patterns spanning multiple samples are known to be present, their solution in time can be refined by involving all the samples they affect.

QUOTE
It's you not me nor 2B nor Woodinville that connects peaks and their possible movement to "time resolution" -- a term whose notion we havn't agreed upon.

I think you eventualy will understand how the movement of measureable occurences in time which might result from lowpassing, informs 'time resolution' @ pcm samplerates.

QUOTE
After all the "who cares"/"so what"-talk I was kind of expecting you to mention a case where a possible movement of peaks poses an actual problem. I still can not understand your obsession about those things on arbitrary signals ("arbitrary" = those that may show different locations of those points you look for after bandlimiting).


My obsession here, has simply been to defend my reputed understanding of the topic.
The quote which started it all, was in the otherwise great "vinyl myths" article in the HA wiki.

cheers'
andy


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Canar
post Nov 20 2006, 02:38
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The common definition of "time resolution" is not sufficient. Mathematical and common definitions are usually quite different. If mathematical language is too much for you, give an example in which "time resolution" is defined. We may be able to do something with that.

If you use the Techie example, it is obvious that the a spectral component of the measured peak is significantly below the sampling frequency. However, where is this "spike" defined? Any similar definition I've seen tends to be the length of time a signal is above a certain value. The "Techie"'s language is woefully inadequate and is not at all descriptive. "The signal was 20dB above the noise floor for 324.37643 sampling frequencies with the rising edge located at a system time stamp of X." That would be a more scientific statement. Noise is interfering with precise temporal placement. The precise location of the rising edge is lost in the noise. Statistics can then give you an idea of the location and a level of certainty that you can apply to the measurement.

QUOTE
"Detail of any time localisable(sic) events, will be distorted by the implicit lowpass of conversion by an unknowable amount (post conversion) by upto(sic) a sample-period-width of difference."

-Is very explicit english. "time localisable(sic) events" are> [events] [which are possible to locate in] [time].


Very explicit English, sure. It is not, however, very precisely defined English. What is an event? Likewise what is a detail? A peak? A zero-crossing? Both are affected by low-pass and are therefore unsuited for defining time resolution. What does this leave? Not a lot, I'm afraid. Until you can pick out some detail that actually withstands low-passing and allows for some measurement before and after, you're going to be in trouble.

The single detail I could think of for experimental use would be for a signal to go from 0 to 1 in some set time. Then the detail becomes your zero-crossing, and it should resist low-pass. "Time resolution" as I understand it is very well defined in this context.

This post has been edited by Canar: Nov 20 2006, 02:42


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SebastianG
post Nov 20 2006, 02:57
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QUOTE (ChiGung @ Nov 20 2006, 01:46) *
The type of distortion i was talking about, was already described

Yeah, I was aware of that. I just pointed out that there was a possible misunderstanding between you and him.

QUOTE (ChiGung @ Nov 20 2006, 01:46) *
Regarding 'timeable events' I use such terms as a broad set of which 'peaks' are a member.
I simply wished to refer to any kind of detail which might be identified and pinpointed in time within waveforms. Basicaly anything you might think of which might be precisely locateable in time (in a prcm record) -( which peak of level is an example of).

Yeah, I was aware of that. I just tried to point out a possible misunderstanding between you and him.

QUOTE (ChiGung @ Nov 20 2006, 01:46) *
I think you eventualy will understand how the movement of measureable occurences in time which might result from lowpassing, informs 'time resolution' @ pcm samplerates.

We can agree so far that lowpassing can move those things you mean (this is nothing new. we've been there already). However, I refuse to use the term "time resolution" for that. This is something you just made up and serves no purpose.

QUOTE (ChiGung @ Nov 20 2006, 01:46) *
My obsession here, has simply been to defend my reputed understanding of the topic.

So, you bring up possible peak movement just to tell us about your notion of "time resolution"?
I would have loved to hear from you about application examples where this does matter.
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2Bdecided
post Nov 20 2006, 13:17
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QUOTE (ChiGung @ Nov 18 2006, 19:04) *
Im not your student.


Ah, that's where you're going wrong!

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You're doing nobody any good by failing to read up on the field you're talking about before you work.
Untrue. I limit my research to protect my originality. Education is to Innovation what Masterbation is to Procreation


Einstein stood on the shoulders of giants, and you're standing on quicksand?

I wonder who will see further!

Cheers,
David.


QUOTE (Canar @ Nov 18 2006, 21:15) *
The time and frequency domains are mathematically identical, but are very different to conceptualize. If you wish to discover the ways in which a frequency domain transform affects audio, you must look at it from a frequency domain perspective if you wish to understand well. What you are doing is looking at a frequency domain transformation from a time domain perspective, and are getting complex results that you don't really understand. Because you don't understand them, you assume there's something weird happening there. There isn't. You're just not looking at it correctly.


You put that very well.

I tried to give an example that was so "simple" this became obvious, but CG felt that I was trying to hide something or use specific examples to back my view point.

The problem is that CG doesn't believe that some of us have both an intuitive and mathematical understanding of the relationship between time and frequency, and so actually understand what's happening to his peaks. (And it's not very interesting!(.

He is mistaking our disinterest in the "answers" he's generating with this program for a lack of understanding of his "big question". The problem is that we do understand it - that's why it's not very interesting!

Never mind the fact that there isn't an algorithm that will "work" even for what he's trying to prove.

Cheers,
David.
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2Bdecided
post Nov 20 2006, 13:35
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QUOTE (ChiGung @ Nov 19 2006, 03:23) *
In the meantime i expect honest estimates to be made here of the temporal resolution of pcm records. Because the proof will follow wink.gif


I already did that, and provided a worked example.

With your completely bizarre definition of "time resolution", which in fact means "how far will the peaks move" - it's up to + or - 1/2 the wavelength of the low pass filter cut-off.

WRT resampling to a lower sample rate, that's up to +/- 1 sample at the new sample rate.

I could be wrong. It's such a pointless question that I doubt anyone will bother to point it out if I am!


The distribution is the sum of some random process, but I'm not entirely sure what.

The actual results are confounded by the impossibility of "identifying and tracking the same peak". You're trying to see how far the peaks moves, but you have to make some assumption about how far they could move in order to track them!

Cheers,
David.
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2Bdecided
post Nov 20 2006, 13:59
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QUOTE (ChiGung @ Nov 17 2006, 19:02) *
QUOTE (2Bdecided @ Nov 17 2006, 12:25) *
All you have shown is that frequency components in signal A contributed to the position of peak A, and these have been removed, thus moving the peak. However, there is no limit to where peaks can occur. It is not like the quantisation amplitude resolution limit at all! It is not a time resolution limit, just a predictable effect of low pass filtering a signal.

If there is no limit to where the peaks can occur, how come they cant be arranged to occur in the correct place between records of differing sample rates? Why must they be susceptible to unknown distortions during downsamples with your "no limitations" argument? Because their precise subsample positions are limited - by every other sample in the record which they are a part of. Thats why you cant normally use the "unlimited" resolution which you can infer - without distorting all other samples to create the subsample details. (done to provide some limited demonstrations in this thread, but not possible in practice where all samples must be treated equally)


So (presumably) it's OK to look at multiple samples when discussing the position of a peak in the frequency domain, it's acceptable to talk about the time and frequency domains being linked, but its suddenly voodoo and/or cheating to look at multiple samples when discussing the position of a peak in the time domain?

Glad we got that cleared up!


I still don't get the obsession or difficulty. If a peak moves when low pass filtering, it's because you are deleting the part of the signal that put the peak there - how could it not move? It's not a limit in resolution because, if the peak was supposed to be there ("there" being absolutely anywhere), it could and would be. Nothing fake, clever or contrived. PCM audio allows a peak to exist absolutely anywhere - on samples, and anywhere between samples. What it doesn't allow is audio above fs/2. It's a frequency domain phenomena, not a time domain phenomena.


Let me draw a parallel. Try performing a time domain analysis on a nice linear-phase graphic equaliser with the bass at +6dB and the treble at -6dB. Would it change the time domain signal? Of course! It must change the time domain - you can't change one domain without affecting the other! But what we have is very much a frequency domain phenomena, any anyone who tries to analyse solely in the time domain is going to look very stupid - especially if they say they're going to do it for a random set of audio signals. Think about it - what on earth would it tell you?

Cheers,
David.
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ChiGung
post Nov 20 2006, 18:07
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QUOTE (2Bdecided @ Nov 20 2006, 12:59) *
I still don't get the obsession or difficulty. If a peak moves when low pass filtering, it's because you are deleting the part of the signal that put the peak there - how could it not move? It's not a limit in resolution because, if the peak was supposed to be there ("there" being absolutely anywhere), it could and would be.

Imagine sampling something at a very high sampling rate, so all the peaks are nearly exactly where they should be. Then downsample; if the peaks move are they where they 'should' be anymore? When we read a pcm record, how close can we say the peaks are to where they could/should be in the source material?
If we have knowledge of the source materials frequency distribution we can estimate the discrepancies we are likely to find.
(Peaks are just examined here as one example of waveform conditions which can be detected and precisely located in time.)

The statement i made earlier that ~"all peaks are susceptable to moving up to a samplewidth..." was speculative, it may be close to the exact situation, it may not be. There is only a question of detail to resolve -"how far are peaks susceptable to move?"

QUOTE
Nothing fake, clever or contrived. PCM audio allows a peak to exist absolutely anywhere - on samples, and anywhere between samples. What it doesn't allow is audio above fs/2. It's a frequency domain phenomena, not a time domain phenomena.

This is a commonly overread situation. - Just because a peak level created by any combination of frequencies can occur at any subsample location in time, does not imply that a peak represented in pcm as a neccessarily bandlimited frequency spread (limited by the nyquist f), can have its temporal position in the source predicted absolutely precisely.

When you suppose 'resolution' is dependant on the smallest values with which a record can confidently resolve itself Then with pcm, resolution of time and level is effectively infinite because the 'resolution' of algebra is effectively infinite. With such a flattering use of the term 'resolution' (which has been relied on here) the amount of information in a record has almost no contribution at all to its reportable resolution - all you really need are 2 samples in order to have a record which you can say you can resolve with infinite resolution.

Put another way, there have been great objections put forward to my report that unless we have secure knowledge of the frequency distribution of the source, time resolution is practicaly around 1/2 the sample interval.
What is "level resolution" then? Doesn't a pcm record of 8bit words differ in 'level resolution' from one of 16bit words? Or do you all contend that to a properly educated engineer, both records resolution of level are effectively infinite as well?


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2Bdecided
post Nov 20 2006, 18:15
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QUOTE (ChiGung @ Nov 20 2006, 18:07) *
Put another way, there have been great objections put forward to my report that unless we have secure knowledge of the frequency distribution of the source, time resolution is practicaly around 1/2 the sample interval.
What is "level resolution" then? Doesn't a pcm record of 8bit words differ in 'level resolution' from one of 16bit words? Or do you all contend that to a properly educated engineer, both records resolution of level are effectively infinite as well?


So you didn't even bother to read, never mind understand, that part where I contrasted quantisation (which does limit amplitude resolution) to sampling (which does not limit time resolution)?


Or comment on the part where I ask just how stupid it would be to perform time domain analysis on the output of a graphic equaliser?

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David.
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ChiGung
post Nov 20 2006, 18:26
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QUOTE (2Bdecided @ Nov 20 2006, 17:15) *
So you didn't even bother to read, never mind understand, that part where I contrasted quantisation (which does limit amplitude resolution) to sampling (which does not limit time resolution)?

Or comment on the part where I ask just how stupid it would be to perform time domain analysis on the output of a graphic equaliser?

Of course I read those parts, but choose other parts to attach clear comments to.
You decided to complain about 'the parts' i commented on rather than make any response to any of the answers put to you.

Ok then, ill take another look at the parts you would most like me to respond to,
maybe then you will honour me with a response to any of my points.....


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ChiGung
post Nov 20 2006, 18:41
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QUOTE (2Bdecided @ Nov 20 2006, 12:59) *
Let me draw a parallel. Try performing a time domain analysis on a nice linear-phase graphic equaliser with the bass at +6dB and the treble at -6dB. Would it change the time domain signal? Of course! It must change the time domain - you can't change one domain without affecting the other!
But what we have is very much a frequency domain phenomena,
any anyone who tries to analyse solely in the time domain is going to look very stupid - especially if they say they're going to do it for a random set of audio signals. Think about it - what on earth would it tell you?

Check the veracity of your focus here, you confirm "you can't change one domain without affecting the other" but then anounce that "we have a frequency domain phenomenon" (only modified conviently with the words "very much")
This is like bending a piece of steel, and anouncing "what we have is 'very much' a structural phenomenon" - therefore, anyone who wishes to observe how the structural phenomenon affects temperature is going to look very stupid.

I admit, i cant locate the comments on quantisation which you asked me to respond to. Generaly i would expect issues regarding quantisation will only reinforce limits on resolution of time & level detail within pcm records.....

@SebastianG
QUOTE (SebastianG @ Nov 20 2006, 01:57) *
I would have loved to hear from you about application examples where this does matter.

An example application where real-world 'time resolution' would matter would be in rangefinding. Imagine a very accurate visual sensor records a flash, and a sound sensor records a shock wave following it. Employing knowledge of the speed of light, and the speed of sound, we can estimate the distance of the cause of the flash and the shockwave (assuming the same event produced both).

[speed of sound] * [time interval] (between the flash and the shockwave)
=[distance of sensor] (from the cause)

or more accurately,
distance from event =observed time between sight and sound/(1/soundspeed-1/lightspeed)

This example is basicaly a filling out of the 'tekkie's spike' example.
If rangefinding processing used pcm, wouldnt 'time resolution' be one factor that limits its maximum "range resolution"?

It surely is an odd thing to hear engineers report that they cant think of any applications where practical 'time resolution' of an employed encoding format, might matter.

This post has been edited by ChiGung: Nov 20 2006, 22:17


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