Time resolution of digital sampling

[pkane2001]

1 hour ago, manueljenkin said:

Do the Fourier transform of this signal (in time domain you represent it as Piecewise multiplication of a time delayed sine and a time delayed heaviside) then multiply it with Fourier transform of sinc. Now tell me what you get, whether it is band limited or not. (This sine frequency is less than fc). Passing this function through a sinc will for sure create out of band components. You cannot bandlimit this using sinc.

 

Only a delay in steady state sine (if it began from time =- infinity and runs through to time +infinity) can be bandlimited properly without having any out of band components during low passing. The above is a transient scenario and it will have out of band components. Especially high right at the point where it stops being dc 0 and starts becoming a sinusoid.

 

A DC transitioning to a sine wave and back is just another idealized signal. It's a multiplication of a square window with a sine wave. As we discussed, a perfect square edge requires infinite bandwidth to reproduce, and therefore is not possible in the real world. Therefore a transition from DC to sine cannot be reproduced perfectly. Where's the problem?

[manueljenkin]

9 minutes ago, pkane2001 said:

 

A DC transitioning to a sine wave and back is just another idealized signal. It's a multiplication of a square window with a sine wave. As we discussed, a perfect square edge requires infinite bandwidth to reproduce, and therefore is not possible in the real world. Therefore a transition from DC to sine cannot be reproduced perfectly. Where's the problem?

You keep shifting goalposts. Next thing I'll hear from you is that signals above 20khz don't exist in real world, or that real world is always steady state. This is a valid signal, take it or leave! I'm out of this discussion, not wasting my time here anymore. I got what I wanted to proceed further in my journey. Have your trophy.

[manueljenkin]

1 hour ago, pkane2001 said:

 

A DC transitioning to a sine wave and back is just another idealized signal. It's a multiplication of a square window with a sine wave. As we discussed, a perfect square edge requires infinite bandwidth to reproduce, and therefore is not possible in the real world. Therefore a transition from DC to sine cannot be reproduced perfectly. Where's the problem?

Hang on.. where did I mention I was multiplying it with a "square window". When on universe did a Heaviside function become a square window. It doesn't transistion back to dc after that, it stays a sine wave. Another classic case of you skewing the information that was conveyed to you, to suit your agenda.

 

Take derivative at any position on the sine or on the dc, they are perfectly differentiable and give finite value. The only discontinuity is the point where they meet. The slope is not infinity there, it's just undefined, just before it, slope is 0, and just after it it is cos (0) which is 1. This is a perfectly valid real world scenario where the signal moves from one state to another.

 

Again I've just given example scenario by scenario. In general, anything that deviates from an infinite time steady periodic signal, which is every single signal, would leak out of band signals when passed through the sinc filter, hence causing aliasing when sampled. Sharper transients make for a much worser scenario, these sharper need not always mean sharpest which is a direct heaviside function. Only an infinite time steady periodic signal will have its Fourier transform defined by two sharp energy concentrations at +f and -f, where f is the frequency of the periodic signal. Those optimistic numbers stated work only for steady state, not for real dynamic signals.

 

I've described the math, showed the proof and deviations and explained two scenarios. It's up to you to either understand this or blindfold yourself.

 

I also realised today why no real engineers (for the relevant domain of the topic) seem peek into this objective fi corner. You have your own opinion cocoon which you think is reality, and your intention seems to be not to understand the argument and reply, but rather just to "defend" your cocoon, and trying whatever tricks and information skewing you could do. The worst part is you don't even defend it in a legitimate way, show conclusive evidence/numbers to your system behavior claims. I lost most of my time trying to get you to read the actual question properly. Don't imagine your own question, look at what has been truly asked. You never read my comment, just looked for one extreme scenario to hang on to, when I also gave one more modest scenario in the same post, derived and visualized the whole thing, which you never looked despite me mentioning it multiple times in the comment. And time and again you skew the information/argument given. From today, I'll also be a real engineer, and stop trying to visit this corner. I'm just wasting my time being here.

 

I'm sure you'd have glossed this post only to extract one particular sentence that suits your agenda leaving all other context and questions behind.

 

Either way I'm concluding my posts here with this. Happy listening!

[pkane2001]

2 hours ago, manueljenkin said:

You keep shifting goalposts. Next thing I'll hear from you is that signals above 20khz don't exist in real world, or that real world is always steady state. This is a valid signal, take it or leave! I'm out of this discussion, not wasting my time here anymore. I got what I wanted to proceed further in my journey. Have your trophy.

 

I've been fairly consistent in what frequencies humans can and cannot hear:

So, yes, if you are designing equipment to reproduce music for dolphins, then you may want to worry about ultrasonic frequencies. For humans, not so much.

 

[pkane2001]

57 minutes ago, manueljenkin said:

Hang on.. where did I mention I was multiplying it with a "square window". When on universe did a Heaviside function become a square window. It doesn't transistion back to dc after that, it stays a sine wave. Another classic case of you skewing the information that was conveyed to you, to suit your agenda.

 

 

I suspect you know that most finite-length recordings (ie, all of them) have a beginning and an end. So yes, a square window is a step function at the beginning, going from 0 to 1, and then another one, at the end, going from 1 to zero. Sorry, should've said "rectangular", aka, Dirichlet window.

[jabbr]

3 hours ago, pkane2001 said:

So, yes, if you are designing equipment to reproduce music for dolphins, then you may want to worry about ultrasonic frequencies. For humans, not so much.

 

Your assumption is that humans cannot respond to frequencies beyond what sine waves humans can perceive. Stated another way: you are assuming the human auditory system is linear.

 

Not much about the human brain nor its sensory organs is linear.

Kunchur  eg http://boson.physics.sc.edu/~kunchur//papers/Temporal-resolution-by-bandwidth-restriction--Kunchur.pdf does not make that assumption.

[pkane2001]

1 hour ago, jabbr said:

 

Your assumption is that humans cannot respond to frequencies beyond what sine waves humans can perceive. Stated another way: you are assuming the human auditory system is linear.

 

Not much about the human brain nor its sensory organs is linear.

 

This discussion has been about applicability of Fourier and Nyquist to artificially constructed signals, and not about audibility. Go ahead and pick a higher sampling rate if you're worried about missing ultrasonics. And if you want a perfectly reproduced Heaviside function, then pick infinite sampling. But I warn you, you may have to pay a lot for storage for an infinite length recording.

 

I've tested myself and found no perception or detection of any ultrasonics in test signals or musical content. So, yes, I assume that I don't respond. Maybe my brain is just too linear ;)

 

[jabbr]

29 minutes ago, pkane2001 said:

 

This discussion has been about applicability of Fourier and Nyquist to artificially constructed signals, and not about audibility. Go ahead and pick a higher sampling rate if you're worried about missing ultrasonics. And if you want a perfectly reproduced Heaviside function, then pick infinite sampling. But I warn you, you may have to pay a lot for storage for an infinite length recording.

 

Thankfully I can easily afford to maintain 24/192 or even DSD512 in my library. Science and technology, and not making blind assumptions, has been very good to me.

 

Quote

 

I've tested myself and found no perception or detection of any ultrasonics in test signals or musical content. So, yes, I assume that I don't respond. Maybe my brain is just too linear ;)

 

This is where the test that you select is relevant. Have you tried to reproduce Kunchur's methodology?

 

If we are going to be objective, let's do it correctly.

[fas42]

The theory says worrying about this ultrasonic stuff is irrelevant. And everything that I've experimented with in the real world, to get best SQ, has confirmed this ... this is fidgeting about what colour the wheel nuts should be on the Lamborghini, when aiming for best acceleration figures, 😜.

[jabbr]

1 hour ago, fas42 said:

The theory says worrying about this ultrasonic stuff is irrelevant. And everything that I've experimented with in the real world, to get best SQ, has confirmed this

 

Tell me what the theory is exactly if you have any idea?

 

The reason we have 18-22 kHz upper limit is based on the anatomy of the cochlea and hair cell response to single tones. This does not extrapolate to an arbitrary pattern of frequencies at arbitrary volumes and phases (nonlinear response) nor does that extrapolate directly two two cochlea with differential signaling.

 

[pkane2001]

2 hours ago, jabbr said:

This is where the test that you select is relevant. Have you tried to reproduce Kunchur's methodology?

 

If we are going to be objective, let's do it correctly.

 

If I were to try Kunchur's methodology, I'd change at least one thing that he got wrong. He didn't level match the filtered and unfiltered signals. Level differences at or just below 0.2dB can still be detected in the audible band, so the results of Kunchur's test are suspect. 

 

He had assumed that level differences below 0.7dB are inaudible. The detection results he reported were more likely caused by the level differences at 7kHz than any ultrasonic content. His test subjects detected differences just at the 0.23dB level. Where the detection was even more consistent and reliable is also where the level differences were greater, so that does cast some doubt on the study conclusion.

[manueljenkin]

8 hours ago, manueljenkin said:

 

Nevermind!

[fas42]

Quote

 

Tell me what the theory is exactly if you have any idea?

 

The reason we have 18-22 kHz upper limit is based on the anatomy of the cochlea and hair cell response to single tones. This does not extrapolate to an arbitrary pattern of frequencies at arbitrary volumes and phases (nonlinear response) nor does that extrapolate directly two two cochlea with differential signaling.

 

 

All the things that Paul is pointing to ... while the ear "in perfect shape" may be capable of registering those very top frequencies, in the sense that one is conscious of a difference when those frequencies are present, as against not being present - in the real world of live music, and how sensitive the older person, the one who is usually most interested in the subtleties of the texture of the sound, is to those aspects, it is such low importance that it doesn't bear worrying about ...

[manueljenkin]

13 minutes ago, pkane2001 said:

 

If I were to try Kunchur's methodology, I'd change at least one thing that he got wrong. He didn't level match the filtered and unfiltered signals. Level differences at or just below 0.2dB can still be detected in the audible band, so the results of Kunchur's test are suspect. 

 

He had assumed that level differences below 0.7dB are inaudible. The detection results he reported were more likely caused by the level differences at 7kHz than any ultrasonic content. His test subjects detected differences just at the 0.23dB level. Where the detection was even more consistent and reliable is also where the level differences were greater, so that does cast some doubt on the study conclusion.

I'd recommend you to publish this as a paper/journal. As of now this is just your speculation.

[pkane2001]

1 minute ago, manueljenkin said:

I'd recommend you to publish this as a paper/journal. As of now this is just your speculation.

No need, I’m not the one claiming anything about audibility of ultrasonics. Just reporting what’s been published in many studies and the results of my own tests.
 

Kunchur’s results stand out as very different compared to most everyone else, so some skepticism is not out of place here. 

[jabbr]

33 minutes ago, pkane2001 said:

 

If I were to try Kunchur's methodology, I'd change at least one thing that he got wrong. He didn't level match the filtered and unfiltered signals. Level differences at or just below 0.2dB can still be detected in the audible band, so the results of Kunchur's test are suspect. 

 

He had assumed that level differences below 0.7dB are inaudible. The detection results he reported were more likely caused by the level differences at 7kHz than any ultrasonic content. Where the detection was more consistent and reliable in his result is also where the level differences were greater, so that does cast some doubt on the study conclusion.

If you have a counter hypothesis, yes you could repeat the experiment with tighter leveling.

 

Just because other tests haven’t demonstrated anything is irrelevant because this is a specific hypothesis. Has anyone refuted this by repeating the experiment?

[pkane2001]

58 minutes ago, jabbr said:

If you have a counter hypothesis, yes you could repeat the experiment with tighter leveling.

 

Just because other tests haven’t demonstrated anything is irrelevant because this is a specific hypothesis. Has anyone refuted this by repeating the experiment?

Why ask me? You brought up his paper. I’m not interested in defending or refuting it, but there are obvious problems with methodology that need to be addressed.

[danadam]

1 hour ago, pkane2001 said:

 

If I were to try Kunchur's methodology, I'd change at least one thing that he got wrong. He didn't level match the filtered and unfiltered signals. Level differences at or just below 0.2dB can still be detected in the audible band, so the results of Kunchur's test are suspect. 

 

He had assumed that level differences below 0.7dB are inaudible. The detection results he reported were more likely caused by the level differences at 7kHz than any ultrasonic content. His test subjects detected differences just at the 0.23dB level. Where the detection was even more consistent and reliable is also where the level differences were greater, so that does cast some doubt on the study conclusion.

Agreed.

Some further reading :-)

https://hydrogenaud.io/index.php?topic=73598.0

and about the level differences specifically at the end of this post and in the next one: https://hydrogenaud.io/index.php?topic=73598.msg701379#msg701379

[jabbr]

51 minutes ago, pkane2001 said:

Why ask me? You brought up his paper. I’m not interested in defending or refuting it, but there are obvious problems with methodology that need to be addressed.

I’m just saying that it takes exactly one valid observation to refute a theory/dogma. It is easy (and reasonable) to criticize, but if you really want to refute the observation then repeat it with tighter specs.

 

I don’t really care one way of the other. I have no dog in this pony show. I am keeping an open mind.

[pkane2001]

36 minutes ago, danadam said:

Agreed.

Some further reading :-)

https://hydrogenaud.io/index.php?topic=73598.0

and about the level differences specifically at the end of this post and in the next one: https://hydrogenaud.io/index.php?topic=73598.msg701379#msg701379

That FAQ is particularly telling. Kunchur states that the incorrect JND estimate he had used is not something he can go back and redo, as that’s too much work.

 

He then, incorrectly, states that despite the audible level differences, this somehow does not invalidate the conclusions. This is curious, as it clearly can provide a completely different explanation for the results that is wholly unrelated to timing differences or frequency contents of the signal. Hmm..

 

PS: by the way, @sandyk is a beautiful human being. I know he’ll disagree, but he’s just too modest ;)

[PeterSt]

4 hours ago, pkane2001 said:

Kunchur’s results stand out as very different compared to most everyone else, so some skepticism is not out of place here.

 

Oh wow ...

[fas42]

Interesting how people react to the concept that capturing higher than 20kHz stuff doesn't matter - I have seen absolutely nothing over the years that has made me edge even slightly in the direction of believing this to be wrong; IOW, I have zero interest in wanting >20kHz stuff to be in the signal.

 

Yes, it will always be easy to have a track with, and without, content at ultrasonic frequencies sound different. But this almost certainly will always be down to the behaviour of the playback hardware reacting to the presence, or absence of these frequencies - that is, artifacts from misbehaviour of some part of the chain is actually what is being sensed.

[manueljenkin]

31 minutes ago, PeterSt said:

 

Oh wow ...

Buddy. You and I know the truth, and can visualize it. Thank you very much for the interaction, I guess we exchanged a lot of information among ourself. I would be obliged if you can share me more references/articles/links on how to proceed with my reconstruction algorithm.

 

Let them run with this thread with their "opinions". Skepticism is still an opinion, only when you truly analyse verify and set bounds, it becomes something worthy of consideration. Not worth looking into unless they provide it as a verified paper. As of now, there is no official verified publication that these guys have provided to refute kunchur's study.

[sandyk]

4 hours ago, pkane2001 said:

PS: by the way, @sandyk is a beautiful human being. I know he’ll disagree, but he’s just too modest ;)

I disagree because I am able to hear clear differences between 16/44.1  and 24/96, and  demonstrated that in Frederick V's X and Y thread, even though people like yourself, fas42 etc. claim that it isn't possible.  BTW, am I often way off base with my reports in J.D's little PM group that you are also a member of ? 😉 John always follows up my reports after the sometimes initial scepticism. Do we even agree that Feral-A is not a real factor in many cases there ? 

 

 All we appear to have here is a rerun of the High Res is BS dogma from the measurements are the be all, end all crowd.

Well, I have news for you guys,  you lost the battle years ago, and millions of people worldwide are able to hear improvements over RBCD with SACD. high res LPCM (24/96 and 24/192), and now DSD of different  varieties

 Hell , they can also hear improvements with modern Vinyl recordings of wider bandwidth than previously.(>30kHz in many cases) over typical RBCD.

AND, there is NO putting the Genie back in the Bottle, as much as Hydrogen Audio and others would like to be able to do.  😋

[PeterSt]

Frank and Alex, a small reminder that this board is for objective stuff.