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[maxdimario]

recently in the endless digital thread on the GM forum there was a point brought out about the timing resolution if a a sampling system.

I don't want to digress into musical arguments on this thread, nor am I interested in the probability of it's effect on the sound etc.

I need a clarification on the following technical issue.

if some short bursts are digitized with the bursts occurring between samples, and we need to be aware with *absolute* precision exactly when the short burst begins in time, would the sampling rate not influence the resolution in time regarding the beginning of these bursts, when recorded and played back?

I would appreciate a technical clarification.

[danlavry]

maxdimario wrote on Fri, 30 September 2005 13:49

recently in the endless digital thread on the GM forum there was a point brought out about the timing resolution if a a sampling system. I don't want to digress into musical arguments on this thread, nor am I interested in the probability of it's effect on the sound etc. I need a clarification on the following technical issue. if some short bursts are digitized with the bursts occurring between samples, and we need to be aware with *absolute* precision exactly when the short burst begins in time, would the sampling rate not influence the resolution in time regarding the beginning of these bursts, when recorded and played back? I would appreciate a technical clarification.

I have answered much of it in my paper "Sampling Theory".
The "short answer" is:

Many people do not understand it yet a system bandwidth and a system impulse response (impulse width), is THE SAME THING. One is viewed in the time domain (such as with a scope), and the other is viewed in the frequency domain (such as with a spectrum analyzer). You CAN NOT have a low bandwidth element with narrow pulse, as is suggested by those that do not understand signal theory and system theory. The relationship between the impulse width ("time definition") and frequency response (bandwidth) is true for mechanical devices, as well as electronics, thus mics and speakers DO enter the picture. The lowest bandwidth device in the system will define the system bandwidth, and also the impulse width. Defining one is equal to defining the other.

Add to it a couple of more facts: At 96KHz sampling, the impulse is so narrow that few people can tell it in a sudden AB test if their head is in a vice. Remember that 10usec time delay is like moving your head or the speaker by .12 inch. I wonder, does not the speaker membrane moves by more than that while playing?

10usec or less can be a serious problem when mixing channels electricaly, but that is not an acoustic issue nor is it a sample rate issue what so ever. It is the the same problem at 44.1KHz or 10MHz sampling. It is not about the sampling, it is about adding the same audio signal (sampled or not) out of phase that causes phasing. But while the the 10usec represents 180 degree shift of a 50KHz signal, or 90 degree shift of a 25KHz signal... the same 10usec represents negligable shift acousticaly (sound in air). 10usec is about 1/4 degree at 50KHz...

The last comment, a word of caution: Playing with "bursts" may be done correctly or incorrectly. A burst that is done "too simplistically" is the wrong way to go. By too simple, I mean a gated sine wave where you start a cycle suddenly (and/or end it suddenly). The burst "envelope" should not be a square wave, because such a burst contains very high frequencies which may alias into the audio band. A burst must be filtered (low pass) to accommodate the appropriate Nyquist frequency. Of course one can "manufacture" a burst with a proper envelope, or one can take a "square wave gated" burst and pass it through a low pass filter to eliminate aliasing. I have seen experiments with bursts where one ended up with aliasing, inter modulations thus wrong conclusions...

Regards
Dan Lavry
www,lavryenineering.com

[maxdimario]

Ok,

is your reply related to a very short pulse?

I meant a 5Kz pulse of say 20 ms.

would the digital system be able to reproduce with *absolute* precision exactly when the short burst begins in time, in relationship to an absolute timeline?

I am not worried about a constant shift in time due to lag etc. just absolute precision in time between the bursts.

in other words, if the bursts were *exactly* 60 ms apart, would there not be a minute shifting of the 'attack', due to digitization, regarding the point in which the burst begins in time?

whether it can be heard or not isn't what I'm asking.

[danlavry]

maxdimario wrote on Sat, 01 October 2005 14:18

Ok, is your reply related to a very short pulse? I meant a 5Kz pulse of say 20 ms. would the digital system be able to reproduce with *absolute* precision exactly when the short burst begins in time, in relationship to an absolute timeline? I am not worried about a constant shift in time due to lag etc. just absolute precision in time between the bursts. in other words, if the bursts were *exactly* 60 ms apart, would there not be a minute shifting of the 'attack', due to digitization, regarding the point in which the burst begins in time? whether it can be heard or not isn't what I'm asking.

There are numerous mechanisms to give you a "minute" shifting in signal delay. You have to define "minute". A digital audio receiver, or transmitter will yield some delay. A cable does too though it is really "minute". If matching is what you are after, match all the devices, the cables the amps, speakers. Pay attention to the clocking of the AD, as a rule, stay away from SRC's...

A faster sampling will enable passing a signal with faster rise, assuming that the mics and speakers can handle it, and BTW a 96KHz rate is sufficient to acomodate over 40KHz of audio. But upping the sample rate will not yield better matching in time. Matching the signal chains is the way to go.

Regards
Dan Lavry
www.lavryengineering.com    

[Andy Simpson]

I think we ought to be asking about micro-timing in low BIT-RATES, rather than sampling rates, since the bit-rate is the more significant factor for timing (as established in 'the other thread'). This is just a rephrasing of Max's question though.

Just why do we prefer 24bit to 16?

144dB appears to be quite a fine resolution, but when this is expected to represent the dynamics of time AND amplitude, perhaps it's not fine enough.

Andy

[David Satz]

Max, I'd like to try giving you a simpler answer, if I can. Intentionally or not, you've asked a "trick question"--a little like asking whether God can make a rock so heavy that He can't lift it.

As you know, the sampling frequency of any digital recording system limits its frequency range. To avoid aliasing, the recording system must use a cutoff filter so that no significant energy in the incoming signal will reach or exceed one-half the sampling frequency.

That filter won't permit a signal such as you described ("short bursts" "occurring between samples") to pass through unchanged. The energy of any "short burst" narrow enough to fit "between samples" would include frequencies far higher than the filter's cutoff point. So the system would preserve the part which was in the filter's passband, and if it's a good system, all the "delicate timing information" in that part of the signal would be preserved intact. But the great majority of the signal energy would be gone, simply because the signal waveform that you've described is one which--by your definition of it--will sit mainly above the passband.

Please note that in a system with a high enough cutoff frequency, all the "missing" signal energy would have been completely inaudible even if you could have reproduced it with perfect analog fidelity somehow--except that it might have caused overload and distortion in the playback equipment. In practice it isn't generally useful for an audio system to reproduce "perfectly" a signal such as you have described; it would more likely be harmful.

Your question embodies this contradiction. You (and many other audio people) seem to assume that if you can visualize a signal, then an audio system should be able to reproduce it so that it looks the same as the original on an oscilloscope. My question is, why isn't it good enough for the result to sound the same? And why do so many people who believe that "our ears are more sensitive than the most advanced scientific tools" get so incredibly hung up on the way they imagine that audio signals would look on a 'scope?

--best regards

[maxdimario]

Ok,

you've talked about various sampling issues, but I am not talking about a pulse that is so short that it occurs between samples, I realize that this is necessarily filtered out.

as I wrote above I am talking about a relatively short burst, to keep things in context of about 20 or 30 ms length but we could also say 100 ms.

the burst could be a 5 KHz sine wave burst 100 ms long, which is well under the nyquist frequency.

if the burts were occurring precisely every 60.0000 ms (60 ms with four decimal accuracy, as a theoretical example) when digitized, would there be an error regarding the absolute exact moment when the bursts begin in playback?

If the bursts don't begin exactly in the moment that sampling occurs, but slightly after... and before the next sample, then the digitizer has no way of 'knowing' exactly at what point in time the burst actually begins...right or wrong?

[Gunnar Hellquist]

maxdimario wrote on Sun, 02 October 2005 18:22

If the bursts don't begin exactly in the moment that sampling occurs, but slightly after... and before the next sample, then the digitizer has no way of 'knowing' exactly at what point in time the burst actually begins...right or wrong?

Let me venture a very simple explanation here:

Right.

The reason is that the information is contained in the higher frequencys that are filtered away before they reach the converter. Exact timing of things is information. A sampled signal has a limited amount of information.

The beauty of it though, is that the ear does not care.

Gunnar

[maxdimario]

that does not make sense.

timing is information, yes, but it has nothing to do with the aliasing filters other than lag..

with the same identical burst the filters will always have the same identical phase shift.

frequency content has nothing to do with when the 5 KHz burst BEGINS.

if you like we can make it a 1 KHz burst, with a definite 'on' time between bursts, of say 500 ms correct to the fraction of a picosecond.

if it is digitized and then converted to analog once again will the beginning of the bursts be exactly every 500 ms correct to the fraction of a picosecond or not, and why.

as to whether it's audible or not, that's another issue.

[Phillip Graham]

maxdimario wrote on Sun, 02 October 2005 17:15

frequency content has nothing to do with when the 5 KHz burst BEGINS. if you like we can make it a 1 KHz burst, with a definite 'on' time between bursts, of say 500 ms correct to the fraction of a picosecond. if it is digitized and then converted to analog once again will the beginning of the bursts be exactly every 500 ms correct to the fraction of a picosecond or not, and why.

Hey max,

I think I see what your question is, and I have to say that Dan Lavry has already answered it, whether you realize it or not.

The beginning and end of your burst tones has substantial high frequency content, in order to define the rapid rise/fall rates.  Frequency content has EVERYTHING to do with when the pulse begins!

Your abstraction presumes a tone generator of infinite bandwith (instant on), even if this existed, the faithfulness of the recapture would be directly related to the bandwidth of the capturing system.

BTW, this is not a merely an abstraction, it has many practical applications in physics.  The most famous is Heisenberg's uncertainty principle.

The momentum of an electron is defined by its wavelength, but a single sine wave has no beginning or end, and therefore it's position is unknown.  To define spatially/temporally the electrons position requires a wave PACKET composed of many different frequencies.  Therefore you must trade knowledge of an electron's position for information about it's momentum (energy).  This is limited by the value of planck's constant, which in some ways may be thought of as the nyquist limit of the physical universe.

In many ways the electron wave packet is analagous to your tone burst pattern, as each burst represents a wave packet.  The rise and fall section of your packet contain all the high frequency content.  For the packet to be finite in time requires it to be infinite in frequency, per fourier.

Food for thought!

[David Satz]

Max, Gunnar is right. If you start from a standstill and suddenly begin generating a 5 kHz sine wave from out of nowhere, that will NOT (contrary to intuition, perhaps) create a signal with its sole energy at 5 kHz. It would in fact have a very large proportion of its energy at higher frequencies.

If you apply a low-pass filter to that test signal at 20 kHz or higher, it will still sound the same, assuming that it could be reproduced in its original form without audible distortion. But it will look different on a scope; it will have a more gradual build-up and decay. To get perfect visual fidelity for all imaginable audio waveforms, you'd need perfect minimum phase processing and infinite bandwidth.

Fortunately, audible fidelity doesn't require anything like that, or this industry would never have gotten off the ground! The whole analog era would be regarded as a horrible period of time that we all suffered through somehow.

Again, discrete-time sampling isn't the issue here. You really need to consider the frequency domain, too, or else you'll probably just keep on proposing test signals that don't exist and can't exist within the audio band. That whole amateur approach of visually imagining test signals in the time domain isn't part of the solution--it's part of the problem.

--best regards

[maxdimario]

Quote:

The beginning and end of your burst tones has substantial high frequency content, in order to define the rapid rise/fall rates. Frequency content has EVERYTHING to do with when the pulse begins!

Ok,

I don't think we are talking about the same thing yet.

Let's stick to the burst. This is strictly technical.

how about if the burst begins at O volts (rest)...let's make it 1KHz, so that we have a low enough slew rate.  

the burst is a perfect, sampled burst played back into the AD converter, with absolutely no imprecision, so that the timing between bursts is identical to unmeasureable limits..

The wave begins to rise above 0V at the moment the burst begins(let's make it that the burst begins with the positive half of the sine wave) to a value greater than 0V.

let's make it that on a 1Volt peak to peak 1 KHz sine wave, we consider the burst to begin, when it rises above 0Volts to .1 mV.

we now have a sine wave that begins at a specific point in time and lasts let's say 100 ms, well over the length of a sample .

if the filters eliminate any initial transients that occur over the Nyquist frequency, or create phase shift of elements of the burst, this does not change the fact that the burst has to begin at a specific time, and that every identical burst (read my posts above) will be digitized under identical conditions.

it seems that I am getting explanations that have more to do with sound, and not my original technical question of a sine burst.

The fact that sudden transitions from rest to modulation are frequency-bandwidth limited, does not have anything to do with the timing between identical bursts *precisely* every 500 mS.

do you not agree and why?

[Spock]

To me what you are describing is 1K or 5K sine wave AM modulated by perfect square wave with a period of 500ms.  If you AM modulate a since wave, then you get sidebands around that 5K carrier.  These sidebands depend on the frequency content of the modulating signal, the square wave.  This perfect square wave has an infinite frequency content.  

Very short times, such as this square wave require very high frequencies.

If you were to try to make this signal in the analog world and pass it thru a filter at 22K, then looked at it on a scope, this is what you would see.

The 5K sine wave would not just turn on, you would see it follow a slope the same as 22K band limited square wave.

[Yannick Willox]

I think we still misunderstand the basic question:

I think it is more like this:

if we record eg a 11.05K sine wave in a 44.1K system, will the peaks of the sine be SHIFTED to the sampling intervals ?

Answer : of course not, so the 44.1K sample DOES contain timing info - in between - the samples.
The sine wave will be exactly restored during the DA conversion, with its timing intact.

[crm0922]

Max, I think I explained this in the "other thread" too.

If your pulse rises within a certain time that creates a frequency within the passband, it will be reconstructed perfectly.  Exactly where it began, as it is essentially deduced by process of elimination (to make it very simple).

The only remaining information after removing frequencies above Nyquist will result in the output beginning at the only possible time that is mathematically resolved.

And that time is precisely when the wave began, given the limit of the frequency response, and thus the timing response.

Frequency and time are not separable.  f=1/T.

Chris