Article: Digital Vinyl: Temporal Domain

[Don Hills]

Wow.

Well, from someone who has studied the math and knows as much about the subject as anyone alive (James Johnston, aka "JJ"):

 

The time resolution of a 16 bit, 44.1khz PCM channel is not limited to the 22.7µs time difference between samples. The actual minimum time resolution is equivalent to 1/(2pi * quantization levels * sample rate). For 16/44.1, that is 1/(2pi * 65536 * 44100), which is about 55 picoseconds. To put that in perspective, light travels less than an inch in that time.

 

Shannon and Nyquist stated that as long as you keep all components of the input signal below half the sampling frequency, you can reconstruct the original signal perfectly - not just in terms of amplitude, but in terms of temporal relationships too. They only addressed sampling, and assumed infinite resolution in amplitude. With a digital signal the precision is limited by the number of amplitude steps, leading to the above formula.

 

Edit; This is clearly illustrated in Monty's digital primer video, from about the 20 minute mark, and people still fail to understand it.

 

[Jud]

Well, from someone who has studied the math and knows as much about the subject as anyone alive (James Johnston, aka "JJ"):

 

The time resolution of a 16 bit, 44.1khz PCM channel is not limited to the 22.7µs time difference between samples. The actual minimum time resolution is equivalent to 1/(2pi * quantization levels * sample rate). For 16/44.1, that is 1/(2pi * 65536 * 44100), which is about 55 picoseconds. To put that in perspective, light travels less than an inch in that time.

 

 

 

 

Yes, but what about:

 

 

 

 

 

 

Edit - also:

 

 

 

[Archimago]

Yup. Good to see all the discussions on time domain and hopefully everyone becoming clear about the FACT that 16/44 is already capable of time domain resolution much lower than intersample spacing.

 

I wrote about this recently as well when having a peek at the MQA filter characteristics. Check out the Monty Show and Tell video starting at 17:20.

 

Obviously vinyl has poor time-domain fidelity. In fact, anyone who has any concerns about digital jitter should be absolutely freaked out about the limitations of vinyl playback!

[esldude]

Alright I made a sine wave at 4410 hz at 352 khz 24 bit. The right channel is delayed by 2 samples vs the left. This would be 1/4 of a sample at 44.1 khz sample rates. I then downsampled to 44.1 khz 16 bit. Igor has indicated 44.1 khz could not show a shift in time of less than 22.7 microseconds at the 44.1 khz sample rate.

 

I next up sampled the 44.1 khz file back to 352 khz. This is the second stereo file in the screenshot below. Notice at the marker point the two channels are offset at the zero crossing point by 2 samples just as originally. This indicates that 44.1 khz rates can show timing between channels of less than one sample period of 22.7 microseconds.

 

The 3rd file in the image shows the file at 44.1 khz before upsampling. You will see though both channels are sampling a 4410 hz sine wave the sample levels are different. They are different because with the wave shifted in time different portions of the wave get sampled to different values. If you don't believe both will reconstruct to a real sine wave watch the video in my signature. The reconstructed wave due to the different sample values will shift the wave in time as reconstructed to amounts much smaller than the time between samples.

 

Now I did all this in software. However, in the past I have done it with actual gear. I created a 192 khz file. Played that at 192 khz while recording at 44.1 khz. Each channel was offset by two samples. I took the recorded 44.1 khz file and played it back at 44.1 khz while recording at 192 khz. The result was the two channels were offset by 2 samples in the 192 khz recording. This is less than half a sample width at 44.1 khz. Showing that the theory works as declared.

 

This may not explain to you how it works, but it shows that indeed 44.1 khz sampling can reproduced timing differences smaller than one sample period. If the how is still foggy ask questions I'll try and make it clear or others will. This is an old bit of misinformation that should have died long ago.

 

[The Computer Audiophile]

Thanks to those who've helped educate and explain things to those of us who want to learn more.

 

I've reached out to a well respected third party for another opinion about this topic.

 

More to follow ...

[Jud]

Yup. Good to see all the discussions on time domain and hopefully everyone becoming clear about the FACT that 16/44 is already capable of time domain resolution much lower than intersample spacing.

 

I wrote about this recently as well when having a peek at the MQA filter characteristics. Check out the Monty Show and Tell video starting at 17:20.

 

Obviously vinyl has poor time-domain fidelity. In fact, anyone who has any concerns about digital jitter should be absolutely freaked out about the limitations of vinyl playback!

 

IIRC, the time domain stuff (wow, flutter) and surface noise were the big bugaboos leading to development of CDs.

 

Let's not liken wow and flutter to the audible effects of jitter, though. That's another form of "analog thinking" we should leave behind.

 

 

Sent from my iPhone using Computer Audiophile

[The Computer Audiophile]

IIRC, the time domain stuff (wow, flutter) and surface noise were the big bugaboos leading to development of CDs.

 

Let's not liken wow and flutter to the audible effects of jitter, though. That's another form of "analog thinking" we should leave behind.

 

 

Sent from my iPhone using Computer Audiophile

 

Are you saying that sound quality was a leading factor in the creation of the CD?

[esldude]

Perhaps this will help someone. Upper samples are 44.1 khz for a 11,025 hz sine wave that starts exactly on a sample time. The lower samples are for the same 11,025 hz sine wave that started exactly halfway between sample times. Remember the straight lines drawn between samples aren't how the wave reconstructs. Adobe Audition will show the correct wave, but I don't have that available. Both of these waves would playback identical 11,025 hz tones. One is shifted by roughly 11.35 microseconds vs the other.

 

It is possible with some very simple trig and a hand calculator to show 44/16 can sample differently between timing of waves at 56 picoseconds though a bit laborious to work thru that way.

 

[esldude]

Maybe this will help someone. Upper samples are for 11,025 hz wave that started exactly during a sample. The lower is 11,025 hz wave that started exactly halfway between samples. Please note that straight lines drawn between samples are not the actual wave shape. Adobe Audition will show the correct shape, but other software does not.

 

As odd as these look, both will reconstruct identical sine waves that differ only by a timing shift of about 11.35 microseconds. The fact they were differently timed meant sample values were different. As Jud and others have pointed out there is one and only one wave that will fit sample values if the wave is below the Nyquist frequency. So a wave offset by a tiny time amount causes different sample values. This causes the wave to differ by a tiny time amount when reconstructed upon playback from such a sampled and reconstructed digital system.

 

It is possible with simple trig and a scientific calculator to show how timing shifts of 56 picoseconds cause different sample values. Doing so is a bit tedious. It does mean you can get some handle on how this works without extremely advanced math. It still might not explain in your mind how reconstruction works. It is easy enough to demonstrate it works so you don't have to take it on faith even if you don't know how in your mind's eye.

 

[Archimago]

Oh yeah, I just remembered another example of vinyl's inferior time domain performance.

 

Notice why we never talk about "wow & flutter" in the digital world? Simply because speed fluctuations (ie. timing) is not an issue...

PlatterSpeed Technics SL-1200M3D

PlatterSpeed Roksan TMS

PlatterSpeed digital :-)

 

Compare those PlatterSpeed results with 5-figure turntables if you like such as from Mike Fremer.

 

Just to be clear. I do like my vinyl setup and LPs. As collectable items, nostalgia and for nice artwork. They sound good when the mastering is better than highly dynamically compressed CD or hi-res. For example, I know our host likes his Pearl Jam - Vitalogy remastered LP blows away the crappy HDtracks 24/96 version.

 

Sure, there can be >22kHz high frequency signal in those grooves as well. But in every other way, the technical abilities of LPs are clearly inferior. Including temporal domain performance of course.

 

No need to be romantically idealistic about analogue or LPs IMO. As much as there are great pressings, there are just as many crappy sounding ones out there... Not to mention the essential meticulous cleaning, turntable set-up, cartridge minutiae, impedance matching, RIAA phono pre-amp quality, inner groove distortion, and a ton of other details to obsess about (good or bad would also be subjective based on one's personality :-).

[The Computer Audiophile]

Oh yeah, I just remembered another example of vinyl's inferior time domain performance.

 

Notice why we never talk about "wow & flutter" in the digital world? Simply because speed fluctuations (ie. timing) is not an issue...

PlatterSpeed Technics SL-1200M3D

PlatterSpeed Roksan TMS

PlatterSpeed digital :-)

 

Compare those PlatterSpeed results with 5-figure turntables if you like such as from Mike Fremer.

 

Just to be clear. I do like my vinyl setup and LPs. As collectable items, nostalgia and for nice artwork. They sound good when the mastering is better than highly dynamically compressed CD or hi-res. For example, I know our host likes his Pearl Jam - Vitalogy remastered LP blows away the crappy HDtracks 24/96 version.

 

Sure, there can be >22kHz high frequency signal in those grooves as well. But in every other way, the technical abilities of LPs are clearly inferior. Including temporal domain performance of course.

 

No need to be romantically idealistic about analogue or LPs IMO. As much as there are great pressings, there are just as many crappy sounding ones out there... Not to mention the essential meticulous cleaning, turntable set-up, cartridge minutiae, impedance matching, RIAA phono pre-amp quality, inner groove distortion, and a ton of other details to obsess about (good or bad would also be subjective based on one's personality :-).

 

I have that album, but have never listened to it because I don't have a turntable :~(

 

I'm so bummed!

[Fokus]

but where within the width of the sampling pulse the transient starts.

 

Yes, it can and it does. End of.

[semente]

I see no mention of "wow" or "flutter"...does this affect "temporal" accuracy?

[mansr]

I see no mention of "wow" or "flutter"...does this affect "temporal" accuracy?

 

Wow and flutter are by definition temporal inaccuracies.

[Jud]

Are you saying that sound quality was a leading factor in the creation of the CD?

 

Certainly the desire to be free of audible wow, flutter and surface noise were leading motivating factors in the development of digital audio media. This is not to say compromises weren't made, or that making money wasn't (as always) the single most important thing to the companies involved.

 

 

Sent from my iPhone using Computer Audiophile

[Jud]

I have that album, but have never listened to it because I don't have a turntable :~(

 

I'm so bummed!

 

You're certainly invited to bring it with you if you're ever in the neighborhood.

 

 

Sent from my iPhone using Computer Audiophile

[Rexp]

Oh yeah, I just remembered another example of vinyl's inferior time domain performance.

 

Notice why we never talk about "wow & flutter" in the digital world? Simply because speed fluctuations (ie. timing) is not an issue...

PlatterSpeed Technics SL-1200M3D

PlatterSpeed Roksan TMS

PlatterSpeed digital :-)

 

Compare those PlatterSpeed results with 5-figure turntables if you like such as from Mike Fremer.

 

Just to be clear. I do like my vinyl setup and LPs. As collectable items, nostalgia and for nice artwork. They sound good when the mastering is better than highly dynamically compressed CD or hi-res. For example, I know our host likes his Pearl Jam - Vitalogy remastered LP blows away the crappy HDtracks 24/96 version.

 

Sure, there can be >22kHz high frequency signal in those grooves as well. But in every other way, the technical abilities of LPs are clearly inferior. Including temporal domain performance of course.

 

No need to be romantically idealistic about analogue or LPs IMO. As much as there are great pressings, there are just as many crappy sounding ones out there... Not to mention the essential meticulous cleaning, turntable set-up, cartridge minutiae, impedance matching, RIAA phono pre-amp quality, inner groove distortion, and a ton of other details to obsess about (good or bad would also be subjective based on one's personality :-).

There is nothing romantically idealist about liking analogue, it sounds better than the majority of CD's, getting over excited about some irrelevant technical matter is just embarrassing.

[Rt66indierock]

Are you saying that sound quality was a leading factor in the creation of the CD?

 

That was James Russell’s intent when he invented the optical technology for the compact disk. He wanted to eliminate sound degradation caused by wear on records. And improve the sound too.

 

Since he is one of two men who taught me audio still alive I’m going to try and visit him this summer.

[sdolezalek]

It is a real sign of our times that every time this temporal resolution issue comes up, both camps retreat to base principles that they believe best support a fairly absolutist view of 16/44 versus vinyl. Where is the intellectual curiosity that says: Ok, let me accept for a minute that both 16/44 and vinyl can achieve all of the temporal resolution my ears need, then what else accounts for my hearing differences or having a preference for one over the other?"

 

Jud, Mansr, elsdude, Miska, Archimago and others have already contributed a lot in other threads to laying out some of those reasons and Jud cites what I believe is the key one: "However, the Sampling Theorem contains idealizing assumptions that don't exist in the real world - perfectly band-limited signals, infinite time to do the filtering to reconvert digital to analog, etc." So much of Miska's work in HQPlayer similarly focuses on the tradeoffs between filters and how those tradeoffs ultimately require some choice in preference between time domain accuracy and frequency accuracy. Meridian, even before MQA, spent a lot of time in their best CD players looking at ways to specifically eliminate pre-ringing and reviewers who loved those players clearly heard a difference they preferred from that focus on pre-ringing.

 

If we are going to move the science of audio reproduction forward, it is these secondary principles, not the underlying Shannon Nyquist math, or the religious vinyl vs. digital debate that we need to be spending our time on.

[Jud]

PVC, I think you may want to speak to the President, or perhaps the Attorney General....

 

 

Sent from my iPhone using Computer Audiophile

[Pure Vinyl Club]

Thanks for answering that question. I too have used Channel D software for needledrops. It is excellent software.

 

Frankly Chris I was dismayed to see this article on your site. If this had been a principle at Channel D it would have put a big dent in my respect for their company. Most of the article is untrue misinformation. Old myths that are factually not so. One need not perpetuate bad info to have a passion for vinyl.

Hi elstude. I'm sorry for what I have for a long time did not respond to questions. I just have no experience of commenting on the CA and I wanted to wait and see what the discussion will go in the direction. The very title of this article lies the whole essence of what I wanted to discuss on the forum. Unlike "static" characteristics (spectral and dynamic domains), which are often discussed, I would like to emphasize the importance of what we hear in real time from our acoustic system - to "dynamic" characteristics (temporal and spatial domains ). And especially I like to emphasize the importance of temporal resolution for emotional perception when listening of music.

 

And it has nothing to do with the digital aspect. I was not going to oppose an analog (vinyl, tape) and digital (CD, Hi-Res). Just what we hear from our speakers. This temporal resolution It may be worsened by your speaker or the speaker cables or phono preamp, or cartridge, ... Any component can "slow down" transients. Just what I wanted to say.

Only once, I noticed that the CD format is not enough to reconstruct high time domain, also citing in this context (Art Dudley and Rob Robinson). But you are brought down to me hurricane criticism. All about what you say - it properly. It is generally accepted and does not require a large discus. But, once again I ask - how it relates to the topic of this article?

Now a substantive response to your first question on this topic:

 

It seems that temporal accuracy and temporal resolution are being confused here. Accuracy is a given, and for the sake of argument can be as high as one wishes - picoseconds, femtoseconds, etc.. When someone says a CD samples "accurately" to the picosecond level (that is, the sample clock is stable and has low jitter), that may be true, but that has nothing to do with the temporal resolution. The distinction between accuracy and precision / resolution is one of the prime topics emphasized early in college introductory physics and chemistry (or even grammar school advanced placement classes in the same subjects): the difference between accuracy and precision are critical in science and easily confused unless one has had experience or training in the subject.

 

Take two balance scales that are, let's say, 100% accurate. One weighs to a precision (almost the same thing as resolution) of 1 gram, the other 10 grams. Put a 10 gram mass on both scales, they will both indicate 10 grams, with perfect accuracy. Place a 12 gram mass, the more *precise* of the two scales will indicate 12 grams. Remember both scales are 100 percent accurate - but you can't expect the second scale to resolve 12 grams, because it is below the measurement *precision* of the scale. The second scale will "accurately" report 10 grams for the 12 gram mass - within a resolution of +/- 5 grams. So, at best, you know that your measurement of the mass is 10 grams plus or minus 5 grams. A 16 gram mass would be measured as 16 grams on the first scale, 20 grams on the other, etc. The second scale is accurate, but only within the specified precision. On the other hand, a scale that is not "accurate" would have some discernible error in the measurement. For example, the scales report 11 and 20 grams in the first measurement - though the resolution is the same. For the optimum result, we need both good accuracy *and* precision.

 

Now take the CD sampler accurate to 1 picosecond, given as an example. Yes, sample after sample are within one picosecond of the sample period (or even better is possible, with a super low jitter clock). But it simply cannot accurately resolve signal events with a temporal precision greater than the sample rate - approximately 23 microseconds (rounding to the nearest microsecond; 1/44100 is actually a transcendental number which can be represented to an arbitrary precision depending on the number of decimal places, which we don't care about here). So an event occurring at a given time can be resolved with certainty at best with a temporal resolution of roughly 23 microseconds. If you increase the sample rate to 192 kHz the temporal ACCURACY may be the same (at the same time coordinate, with the same picosecond or femtosecond accurate clock) but the temporal RESOLUTION is more than 4 times better - about 5 microseconds. (or to be precise, 5.2083333 microseconds with the 3 repeating on and on and on).

 

Temporal resolution is defined by the sample rate.

 

Taking an extreme example for illustration of a boundary condition, if the brain and auditory system only resolved sounds with TEMPORAL resolution at the second (1,000,000 microseconds) level, this would be problematic because a threat to survival such as a leopard pouncing from behind would not be detected as readily. Imagine an experiment where we played a sound of an animal springing for two human test subjects, from a loudspeaker positioned some moderate distance behind and above the subject. On the one hand the sound is sampled at 10 Hz. On the other we sample at 192 kHz. The first case has a TEMPORAL resolution of 100,000 microseconds (0.1 second), the other about 5 microseconds. Do you think that in both cases both subjects will be able to react in the same way, including detecting the position of the sound, to each stimulus? From the argument presented in one of the responses here one should be able to reconstruct the original waveform from the lower sample rate signal, ergo both subjects by the argument presented would be expected to react identically. Of course, I am saving the red herring, which is due to the fact that the 10 Hz sampled signal will be antialias filtered, removing frequencies above 5 Hz - so there would be nothing in the audio to react to! But the argument presented is that somehow one can reconstruct a signal by calculating the intersample waveform. The problem is there is no way "in the universe" to reconstruct the ORIGINAL "leopard pouncing" signal via such an operation.

 

There is absolutely no way that a signal sampled at a given sample rate to a digital waveform has the same temporal resolution as a signal sampled at higher sample rates. If it did, then all the research labs in the world (using high speed analog to digital converters for signal sampling and recording) could just go and throw away all of our expensive high speed digital sampling hardware. Same thing with our 100 GHz sampling oscilloscopes. Why waste all that money when a 100 MHz scope has putatively the same temporal resolution? Because it does not.

 

If a paper were submitted for publication to a peer reviewed technical journal and reported conclusions which depended on sampling a signal and the paper tried to infer that an event was determined to occur with a temporal precision greater than the sample rate, the paper would be rejected, with a suggestion to repeat with a more capable experimental measurement (that is, appropriate sample rate). Any argument that the original signal (that is, containing events faster than the sample rate) could be reconstructed perfectly from a lower sample rate signal would be ridiculed. There is absolutely no way this information could be extracted from a measurement made at a lower sample rate - which has lower TEMPORAL resolution. If the whole reaction we're trying to observe takes place in 100 nanoseconds and we can only sample at 1 microsecond, then we won't measure anything useful, let alone could we expect to somehow reconstruct the same data set that one would obtain at higher temporal resolution (sample rate).

 

One cannot reconstruct an ORIGINAL signal containing spectral content at frequencies above half the sample rate, from one sampled at a lower sample rate, just because "there is only one (such) signal in all the universe," because the signal bandwidth of the "one signal in the universe" that fits the points has already been band limited by the antialiasing filter, and parts of the original signal discarded. The signal you get at the lower sample rate **only corresponds to band limited version of the original signal** - which is NOT the same as the original signal. There isn't any way to determine the ORIGINAL signal without sampling at a higher rate in the first place. You can certainly calculate the sample position at arbitrary inter-sample time intervals, but that will not give you the same result as sampling the ORIGINAL signal at a higher rate. Sure, one could sample the *band limited* signal at a higher rate, and in that case the result will be exactly the same - but there would be no practical reason to oversample (as in analog to digital conversion) a (severely, in the case of analog to digital conversion) band limited signal in the first place. The scenario with analog involves ORIGINAL signals which also are band limited; in the real world, all signals are band limited to some extent - it's a matter of the criteria applied; but analog is band limited to a much lesser extent than digital, and the characteristics of the band limiting are also quite different.

 

Any signal which is lowpass filtered to prevent aliasing at lower sample rates is going to have a greater variation in group delay / phase shift near a fixed signal frequency (say, always at 10 kHz) than a signal sampled at a higher sample rate, presuming the antialias filtering is chosen appropriately for the sample rate (and it would always be, otherwise one wouldn't go to the trouble of using higher sample rates). A signal reproduced on a vinyl LP sourced from analog sources doesn't encounter the brickwall filter used in analog to digital converters / CDs. There is a high frequency roll off, but it is a gentle 6 dB per octave above the cutter head resonance of typically 50 kHz. By comparison the brickwall filter used to record CD format audio has a much steeper slope, about 100 dB of attenuation in a small fraction of an octave (antialiasing filters aren't even expressed in terms of dB per octave; just passband, stopband, ripple and attenuation). Furthermore, compared to our analog 6 dB per octave rolloff, there is a much greater phase shift variation among frequencies in the sampled signal. And just above about 20 kHz, there is NO signal left; on the other hand with analog, and vinyl, there is considerable signal energy, continuing for octaves above. And that is a key difference between analog and digital. So, in digital recording, we try to get closer to the TEMPORAL characteristics of analog by increasing the sample rate and pushing our brickwall filter higher and higher in frequency, so that the disruption of time relationships / coherence between the frequencies comprising our audible frequency range (up to 20 kHz, more or less) audio is minimized. Then, our music signal (or sound of the panther pouncing) is reproduced with the temporal relationships between different frequencies closer to (if not entirely preserved) compared to the actual sound found "in nature" and accordingly our auditory system / brain / emotional state responds more favorably by comparison. "Engaging, toe tapping, PRAT." As a bonus we can enjoy knowing about the technical elegance of capturing more of the frequency range of analog (and vinyl LPs) which extends strongly at least two octaves above the bandwidth limit of a CD (as proven by many measurements using spectrum analysis of signals from LPs, including those referenced in the post).

 

Sorry for the long post.

Good weekend!

 

Regards

 

Pure Vinyl Club

[Pure Vinyl Club]

Excuse me!

 

It was another hacker attack from Russia to the United States!;-))))

 

I'm still poorly understood with the forum and checked the English version of his post through Google translate and mistakenly sent the Russian transcription.

[sdolezalek]

[/font]One cannot reconstruct an ORIGINAL signal containing spectral content at frequencies above half the sample rate, from one sampled at a lower sample rate

 

A signal reproduced on a vinyl LP sourced from analog sources doesn't encounter the brickwall filter used in analog to digital converters / CDs. There is a high frequency roll off, but it is a gentle 6 dB per octave above the cutter head resonance of typically 50 kHz. By comparison the brickwall filter used to record CD format audio has a much steeper slope, about 100 dB of attenuation in a small fraction of an octave (antialiasing filters aren't even expressed in terms of dB per octave; just passband, stopband, ripple and attenuation). Furthermore, compared to our analog 6 dB per octave rolloff, there is a much greater phase shift variation among frequencies in the sampled signal. And just above about 20 kHz, there is NO signal left; on the other hand with analog, and vinyl, there is considerable signal energy, continuing for octaves above. And that is a key difference between analog and digital.Pure Vinyl Club

 

Maybe this needs a CA poll to go with it:

a) do you believe the sonic differences between CD/Vinyl are attributable to spectral content over 20kHz?

b) do you believe the important sonic differences are actually below 20kHz and are the result of filters and other D/A conversion artifacts that cause changes between 20Hz and 20kHz?

 

For those, like me, who can't hear above 16kHz, I very much fall into the latter camp, but I also worry that in many cases even when we do the best in converting a 16/44 signal to analog, too much unrecoverable damage was already done at frequencies below 20kHz upstream in the recording and mastering process that cannot be fixed in the final D/A process.

 

The argument Pure Vinyl seems to be trying to make here is that there can be two different 10kHz waveforms, where additional "precision" is required to reconstruct the two different, but same kHz tone waves. This has always struck me as the "my bass drum has an attack shape in its waveform that exists at 50Hz that makes it sound different than other 50kHz notes. Isn't the real science that my 50Hz bass drum wave is accompanied by higher spectral content, i.e. at 10kHz and 30kHz that further informs the sound and you need to preserve all of the content in order to capture the original sound?

[esldude]

Hi elstude. I'm sorry for what I have for a long time did not respond to questions. I just have no experience of commenting on the CA and I wanted to wait and see what the discussion will go in the direction. The very title of this article lies the whole essence of what I wanted to discuss on the forum. Unlike "static" characteristics (spectral and dynamic domains), which are often discussed, I would like to emphasize the importance of what we hear in real time from our acoustic system - to "dynamic" characteristics (temporal and spatial domains ). And especially I like to emphasize the importance of temporal resolution for emotional perception when listening of music.

 

And it has nothing to do with the digital aspect. I was not going to oppose an analog (vinyl, tape) and digital (CD, Hi-Res). Just what we hear from our speakers. This temporal resolution It may be worsened by your speaker or the speaker cables or phono preamp, or cartridge, ... Any component can "slow down" transients. Just what I wanted to say.

Only once, I noticed that the CD format is not enough to reconstruct high time domain, also citing in this context (Art Dudley and Rob Robinson). But you are brought down to me hurricane criticism. All about what you say - it properly. It is generally accepted and does not require a large discus. But, once again I ask - how it relates to the topic of this article?

Now a substantive response to your first question on this topic:

 

It seems that temporal accuracy and temporal resolution are being confused here. Accuracy is a given, and for the sake of argument can be as high as one wishes - picoseconds, femtoseconds, etc.. When someone says a CD samples "accurately" to the picosecond level (that is, the sample clock is stable and has low jitter), that may be true, but that has nothing to do with the temporal resolution. The distinction between accuracy and precision / resolution is one of the prime topics emphasized early in college introductory physics and chemistry (or even grammar school advanced placement classes in the same subjects): the difference between accuracy and precision are critical in science and easily confused unless one has had experience or training in the subject.

 

Take two balance scales that are, let's say, 100% accurate. One weighs to a precision (almost the same thing as resolution) of 1 gram, the other 10 grams. Put a 10 gram mass on both scales, they will both indicate 10 grams, with perfect accuracy. Place a 12 gram mass, the more *precise* of the two scales will indicate 12 grams. Remember both scales are 100 percent accurate - but you can't expect the second scale to resolve 12 grams, because it is below the measurement *precision* of the scale. The second scale will "accurately" report 10 grams for the 12 gram mass - within a resolution of +/- 5 grams. So, at best, you know that your measurement of the mass is 10 grams plus or minus 5 grams. A 16 gram mass would be measured as 16 grams on the first scale, 20 grams on the other, etc. The second scale is accurate, but only within the specified precision. On the other hand, a scale that is not "accurate" would have some discernible error in the measurement. For example, the scales report 11 and 20 grams in the first measurement - though the resolution is the same. For the optimum result, we need both good accuracy *and* precision.

 

Now take the CD sampler accurate to 1 picosecond, given as an example. Yes, sample after sample are within one picosecond of the sample period (or even better is possible, with a super low jitter clock). But it simply cannot accurately resolve signal events with a temporal precision greater than the sample rate - approximately 23 microseconds (rounding to the nearest microsecond; 1/44100 is actually a transcendental number which can be represented to an arbitrary precision depending on the number of decimal places, which we don't care about here). So an event occurring at a given time can be resolved with certainty at best with a temporal resolution of roughly 23 microseconds. If you increase the sample rate to 192 kHz the temporal ACCURACY may be the same (at the same time coordinate, with the same picosecond or femtosecond accurate clock) but the temporal RESOLUTION is more than 4 times better - about 5 microseconds. (or to be precise, 5.2083333 microseconds with the 3 repeating on and on and on).

 

 

 

By the way I understand the difficulty of posting via translation.

 

The timing precision of CD is less than the sample rate in terms of time periods. Yes it is +/- 56 picoseconds. Yes it can precisely inform between samples when a waveform began as long as the waveform is below 20 khz.

 

Now are you thinking of events that begin, and conclude in less than 23 microseconds? That would be missed, but would also by definition be above 22,050 khz. So I cannot agree with the idea the timing precision (temporal resolution) is the 23 microsecond time of sampling rate. I have shown graphs where the precision was better than that.

 

Can you give an example of a signal condition which has no content above 20 khz, and yet is not resolved between samples at the sample rate of 44.1 khz?

[Don Hills]

...

It seems that temporal accuracy and temporal resolution are being confused here. Accuracy is a given, and for the sake of argument can be as high as one wishes - picoseconds, femtoseconds, etc.. When someone says a CD samples "accurately" to the picosecond level (that is, the sample clock is stable and has low jitter), that may be true, but that has nothing to do with the temporal resolution. The distinction between accuracy and precision / resolution is one of the prime topics emphasized early in college introductory physics and chemistry (or even grammar school advanced placement classes in the same subjects): the difference between accuracy and precision are critical in science and easily confused unless one has had experience or training in the subject.

Easily confused, yes. That's why it is a common misconception. You are still making the same mistake in thinking that digital sampling resolution is limited to the time between samples.

Take two balance scales that are, let's say, 100% accurate. One weighs to a precision (almost the same thing as resolution) of 1 gram, the other 10 grams. Put a 10 gram mass on both scales, they will both indicate 10 grams, with perfect accuracy. Place a 12 gram mass, the more *precise* of the two scales will indicate 12 grams. Remember both scales are 100 percent accurate - but you can't expect the second scale to resolve 12 grams, because it is below the measurement *precision* of the scale. The second scale will "accurately" report 10 grams for the 12 gram mass - within a resolution of +/- 5 grams. So, at best, you know that your measurement of the mass is 10 grams plus or minus 5 grams. A 16 gram mass would be measured as 16 grams on the first scale, 20 grams on the other, etc. The second scale is accurate, but only within the specified precision. On the other hand, a scale that is not "accurate" would have some discernible error in the measurement. For example, the scales report 11 and 20 grams in the first measurement - though the resolution is the same. For the optimum result, we need both good accuracy *and* precision.

 

This is an unfortunate choice of analogy. It argues for accuracy / resolution in amplitude, not time, which is also an area where digital has a large superiority in resolution over vinyl.

Now take the CD sampler accurate to 1 picosecond, given as an example. Yes, sample after sample are within one picosecond of the sample period (or even better is possible, with a super low jitter clock). But it simply cannot accurately resolve signal events with a temporal precision greater than the sample rate - approximately 23 microseconds (rounding to the nearest microsecond; 1/44100 is actually a transcendental number which can be represented to an arbitrary precision depending on the number of decimal places, which we don't care about here). So an event occurring at a given time can be resolved with certainty at best with a temporal resolution of roughly 23 microseconds. If you increase the sample rate to 192 kHz the temporal ACCURACY may be the same (at the same time coordinate, with the same picosecond or femtosecond accurate clock) but the temporal RESOLUTION is more than 4 times better - about 5 microseconds. (or to be precise, 5.2083333 microseconds with the 3 repeating on and on and on).

 

Here you repeat your misunderstanding. You say that an event that occurs between sample times can only be captured to a time matching the closest sample time. This is incorrect. It is captured accurately, to the resolution defined by the equation in my earlier post. Your continued failure to understand how this can be so shows you lack the "training and experience on the subject" you talked of above. Have you watched the video I posted the link to? Starting from about 17:20 it shows, in real life, with a cheap DAC at 16/44.1, a transient being accurately sampled in time between sample times.

... There is absolutely no way that a signal sampled at a given sample rate to a digital waveform has the same temporal resolution as a signal sampled at higher sample rates. If it did, then all the research labs in the world (using high speed analog to digital converters for signal sampling and recording) could just go and throw away all of our expensive high speed digital sampling hardware. Same thing with our 100 GHz sampling oscilloscopes. Why waste all that money when a 100 MHz scope has putatively the same temporal resolution? Because it does not.

 

Here you display a lack of understanding of digital oscillosopes and how they are used. The biggest difference is that they do not depend on being able to sample at twice the rate of the highest frequency being measured. It's quite common to use such a scope in an undersampled mode. But for our purposes (audio), we stick to the classic Shannon-Nyquist model.

... You can certainly calculate the sample position at arbitrary inter-sample time intervals,...

 

Make up your mind. Either digital can resolve transients in between samples, or it can't.

 

In the rest of your post, all you have done is make the case that 16/44.1 is marginal (but close enough for rock'n'roll), and that 24/96 is enough to capture everything that might possibly be significant. You have also completely avoided mentioning the other part of the equation, namely the amplitude accuracy - often referred to as the "dynamic range" or "signal to noise ratio", an area where vinyl fares much worse than digital.