Time resolution of digital sampling

[PeterSt]

6 hours ago, manueljenkin said:

For steady state sinusoids you can reliably estimate the frequency once you have atleast the minimum required samples and either align the sampling points properly or have proper window functions.

 

Very well said !

And this is not in order here. It can't because it isn't there. There is no frequency at hand ...

 

STILL it is so that for the pulse to rise in 90 degree fahsion, an unlimited frequency is required. Nobody in this thread doubts this. And worse, because it can't exist, the steepness won't be 90 degrees but less. So no matter digital (PCM !) could imply it (and synths can really do that), in pratice that will imply distortion (formally that would be correct) because the real world is not able to do it.

Although this is not really the subject, from this follows that any means that would be able to create such samples in a file, should obey the physical (slew rate !) limits on the system it's imposed to. If not, we'll have garbage.

[PeterSt]

 

 

 

 

This would be the limit of the NOS1a (G3 is way better) on its own. Something like 50ns and 160ns respectively. Make the spacing of transients smaller, and the garbage will be your share.

And of course, filtering this out also helps sufficiently, but hey ... (see underlying subject).

 

This is a DAC. But what about the amps ? the speakers ???

So True, for various reasons the spacing of transients need to be sufficiently large in order not to mess with the system's capabilities somewhere. It will really be ugly otherwise. And that it *is* ugly to begin with (with everyone's system) is easy to prove by means of over and over again making things faster which helps hugely. That I seem to be the only one working on such project ... too bad actually, because I am slow on my own.

 

 

 

[manueljenkin]

2 hours ago, PeterSt said:

That I seem to be the only one working on such project ... too bad actually, because I am slow on my own.

I would likely get on similar tracks soon 😉.

[jabbr]

5 hours ago, PeterSt said:

Jonathan, I really wonder weather you're reading all the posts. 🤪

 

I’m not responding to all the posts! But ok ...

5 hours ago, PeterSt said:

13 hours ago, jabbr said:

 

In the case of a "missing sample", this isn't a sampled signal anymore, the digitized signal has been digitally modified.

 

This testifies of a Not, IMHO. The whole thing is about how synthesizers operate, were it about real-life examples. And this is not about real-life sampling. Haha.

It is explicitly NOT about a sampled signal hence no ADC is in order.

OK ?

 

The deeper subject at hand is not about Shannon/Nyquist being right or wong; it is about when it exactly applies and when it can't (and not even when it shouldn't - in all your given poses it should !).

 

Quote

So let's stick to signals that have been properly digitized...

 

So we already did.

However, we were talking about how such a thing as On/Off would look like. Now I could make you a file from one of my synths, but we can also manipulate an existing file in the same fashion (this is a controlled virtual test).

In the case of a synthesized series of samples, it is what it is. It’s not directly analogous to a recorded series of samples because the sequence isn’t bandwidth limited. 
 

Typically a “missing” sample is an impulse, which sounds like a click. The amplitude depends on the width. But of course in a synthesized sequence, there is nothing “in between” samples. 
 

Your upsampling software acts as a filter, of course impulses can be analyzed using Fourier analysis but if you want to know what it looks like you can look at the output of your software. 

[PeterSt]

22 minutes ago, jabbr said:

In the case of a synthesized series of samples, it is what it is. It’s not directly analogous to a recorded series of samples because the sequence isn’t bandwidth limited. 

 

Right.

As long as we remember that your preferred filter *is*.

(but mine may not be 😁)

 

23 minutes ago, jabbr said:

Typically a “missing” sample is an impulse, which sounds like a click. The amplitude depends on the width. But of course in a synthesized sequence, there is nothing “in between” samples.

 

Hmm. A missing sample is just that, and its amplitude is as deep (!) as the amplitude of the adjacent (non-missing) samples.

 

Why do I have the idea that you are working with a theoretical pile of data, while I talk about music data a.o. comprising of synthesizers ? You know, the Korgs and Yamahas and Rhodes and such.

 

28 minutes ago, jabbr said:

but if you want to know what it looks like you can look at the output of your software.

 

Do I ? ... I think I just spent a dozen of posts showing that ?

OK, you want more of that. Here:

 

 

Or up to 450 KHz:

 

 

And as a bonus in-band:

 

 

Surprised ?

Anyway, is this super-sh*t (as in hash) or could this be just what we want ?

Let's keep in mind that this started out as an infinitely steep rise (infinite frequency). We made the rise slower / less steep. Still many frequencies remain. Enough to perceive that "tick" (or transient in general).

And most certainly no 10KHz whine with DC Offset on top of it.

 

... But I didn't say I was finished. 😏

 

You know what this is ?:

 

 

No, it is not the same plot as before. Look in the right-hand side. This is sinc filtered ...

Ah. Oh. Eh ?

 

This picture I showed already earlier in the thread:

 

 

It belongs to the FFT from the previous plot. A sine.

While this is what it should be:

 

 

Keep in mind that all what you see is measured at the output of the DAC. There's no theories anywhere.

It is true that this comes from manually created data, that representing the worst transients that could happen in music files (and still only coming from Klaus Schulze et al). And all we'd want is preserving these transients as much as possible, without sacrificing the frequency domain too much (low distortion).

 

Peter

 

 

 

 

[jabbr]

1 hour ago, PeterSt said:

Why do I have the idea that you are working with a theoretical pile of data, while I talk about music data a.o. comprising of synthesizers ? You know, the Korgs and Yamahas and Rhodes and such.

 

I have no idea how what you are presenting here is supposed to address the statement posted by OP.

 

What are you actually showing about whether humans can perceive actual music beyond what is sampled at 48 kHz? You know, what we are supposed to be talking about? How do any of your plots help us?

 

My statement is simply that *if* humans can perceive *anything* including timing, transients, or really anything beyond what is sampled at 48 kHz, then this means that humans are sensitive to audio frequencies >24 kHz (that is how I am defining ultrasonics here regardless of whether you like my definition).

 

What I am saying should not be controversial. I don't see how your arguments address the issue at hand here.

 

 

Quote

 

  On 2/20/2020 at 9:15 AM, manueljenkin said:

... science studies do show humans can discern a time precision way above what a 48khz sampling rate can reliably capture (5micro seconds is what I remember, check some MIT studies and stuff).

 

 

This is how the thread originated.

 

I am saying that if humans can discern a time precision way above what a 48khz sampling rate can reliably capture then this logically implies that the human auditory system (not just a single cochlea) is responsive to frequencies >24 kHz.

 

This is not saying that humans are responsive to isolated sine wave signals of 30 kHz, etc, and this response is highly likely to be due to nonlinearities, that said sampling rates of 96 or 192 or higher may be necessary to capture the full range of human hearing.

 

Alternatively the "scientific studies" may not exist or be wrong.

 

 

[PeterSt]

4 minutes ago, jabbr said:

 

  On 2/20/2020 at 3:15 PM, manueljenkin said:

Quote

 

  On 2/20/2020 at 9:15 AM, manueljenkin said:

... science studies do show humans can discern a time precision way above what a 48khz sampling rate can reliably capture (5micro seconds is what I remember, check some MIT studies and stuff).

 

 

At least something is wrong there.

I mean, you did not quote from Manuel (not your fault, I'm sure).

[manueljenkin]

You're fixated on describing everything as its frequency constituent. We are not aligning on what I'm trying to convey. Transients and pauses, are just entities of themselves, they are not periodic. What Peter demonstrated was showing how things can go falsely (mis)represented during reconstruction.

[manueljenkin]

2 minutes ago, PeterSt said:

 

At least something is wrong there.

I mean, you did not quote from Manuel (not your fault, I'm sure).

I said that sentence in another discussion. Back some 6-7 months ago when I wasn't precise with my words.

[PeterSt]

7 minutes ago, jabbr said:

This is how the thread originated.

 

However, it is Manuel where I started responding to. And he (virtually) responded late to something Jud said, who responded to Archimago, who quoted form Mansr's work.

 

As many threads this one went in a different direction than the OP intended (although it remains related).

 

I don't see the problem ... (apart from you consistently working with your own subject (which indeed could be the OP's subject).

It could be better to stick with the current subject instead of nobody understanding why you are so persistent in talking "frequency" while no frequency is in order since Sept. 20.

haha

[manueljenkin]

8 minutes ago, PeterSt said:

 

However, it is Manuel where I started responding to. And he (virtually) responded late to something Jud said, who responded to Archimago, who quoted form Mansr's work.

 

As many threads this one went in a different direction than the OP intended (although it remains related).

 

I don't see the problem ... (apart from you consistently working with your own subject (which indeed could be the OP's subject).

It could be better to stick with the current subject instead of nobody understanding why you are so persistent in talking "frequency" while no frequency is in order since Sept. 20.

haha

Everything we've discussed so far are related. They are necessary for a holistic picture/understanding of the problem in hand, for analysis of different scenarios.

 

I'm sorry about the sequence/braches it happened through. I guess this thread has become a case of speculative/out of order execution haha

[PeterSt]

12 minutes ago, jabbr said:

Alternatively the "scientific studies" may not exist or be wrong.

 

About that and mere to the OP's subject - maybe. Or let me put it differently (could be interesting):

 

Where you persistently talk about

a. a steep rise implying a high frequency in the file (my translation of your words)

b. while we are able to perceive a transient and THUS will be able to perceive a high frequency (like 30KHz) (your own words)

...

this is all putting on the wrong foot because nobody says or claims that.

Do you never perceive the vinyl-like ticks ? ah, probably not, because you listen through a sinc filter.

Would you look in the file for this, you will not find a frequency. Why ? because it just is not. A transient is sufficient to do it. A tick. Probably with some DC offset beyond it (to make it better audible).

 

The studies won't be wrong. But they skip this phenomenon (maybe not strange if it is so difficult to bring it across; sadly my English does not help with this - sorry about that).

 

[manueljenkin]

Studies exist: http://boson.physics.sc.edu/~kunchur//Acoustics-papers.htm . What I've claimed in my comment is true. If the studies are wrong, you're welcome to prove it, peer review, publish and then showcase it.

[PeterSt]

Apologies - I only now see (and remember again) that this all sprung from Manuel indeed. But Don Hills made it a topic. OK.

 

Something else, for fun and maybe offtopic but not sure:

 

How can it be that I showed the Gibbs phenomenon at (IIRC) 14MHz, measured from the output from my DAC ?

Mind you please, this was from a MHz sampler (ADC) thus not fully legal (which the plot shows and which I mentioned). Now ...

 

1/14,000,000 = 0,000-000-071-42x

71ns.

 

Can we hear that (it *is* a frequency this time) ? No.

Not sure where the math in the OP (from Don) originates, but 71ns is what I would say. Just because my DAC shows that, and which is the result of a transient which originally requires infinite frequency to do its job (but which transient I flattened 16x).

It is electrical behavior which I think can be calculated with math (Voltage jump is +2V, but the one sample turned into 33 samples).

FWIW, have fun. But let's notice that when we'd upsample 8x instead of 16x, this ("Gibbs") frequency will change. The amplitude of it also will change. So apparently the sampling rate can imply a resolution (better : an implied frequency) and to me it seems that the lower the sampling rate, the higher this frequency (I did not check this), if only the transient remains the same. Something like : the less the sampling is suitable to catch the transient (in digital) the more the amplitude and frequency of Gibbs will be.

What to do with this ? nothing. 

[PeterSt]

15 minutes ago, manueljenkin said:

Studies exist: http://boson.physics.sc.edu/~kunchur//Acoustics-papers.htm .

 

Oh, but Mr Kunchur is also into cables. Now nobody will believe him.

Anyway, wow.

[manueljenkin]

Kunchur isn't the only one to have done these studies. Few other studies do exist and results are similar to the above results. I just happened to state one example I'm familiar with.

[yamamoto2002]

On 9/27/2020 at 5:08 PM, PeterSt said:

 

Although my filtering is named Arc Prediction, it doesn't need to predict the placement of the (new) samples because remember, it genuinely interpolates. All what happens is that around the original sample (in our case the Dirac Pulse) a predicted path towards the sample emerges as well as a  predicted path after the sample. The original sample can be seen as sitting in the middle.

 

 

Is it cubic Hermite spline interpolation ?

[Jud]

11 minutes ago, manueljenkin said:

Kunchur isn't the only one to have done these studies. Few other studies do exist and results are similar to the above results. I just happened to state one example I'm familiar with.

 

Kunchur I believe comes out at about half the time of previous studies. But the previous studies IIRC identified a limit of about 10ns, Kunchur about 5.

 

However, these aren't transients but arrival time differences (how small must the arrival time difference be between two sound waves before we perceive them as simultaneous rather than distinct).

 

This is different from Shannon-Nyquist, which I agree works, as I said much earlier in the thread; and it is possibly different from the briefest transient sound perceptible to humans, as seems to be indicated by additional reading I've done.

[manueljenkin]

46 minutes ago, Jud said:

 

Kunchur I believe comes out at about half the time of previous studies. But the previous studies IIRC identified a limit of about 10ns, Kunchur about 5.

 

However, these aren't transients but arrival time differences (how small must the arrival time difference be between two sound waves before we perceive them as simultaneous rather than distinct).

 

This is different from Shannon-Nyquist, which I agree works, as I said much earlier in the thread; and it is possibly different from the briefest transient sound perceptible to humans, as seems to be indicated by additional reading I've done.

Even with regards to arrival time differences, the first pulse is a transient scenario. And sometimes that first pulse is all that we have (say a clap), it's just an impulse + it's echo, another time delayed impulse (or slight deviated sound from impulse due to selective absorption by ambeance etc). When you low pass it for sampling, you'll be modulating the content. Quite badly so if you're low passing at 20khz since it'll be crushing the ringing of previous impulse of still high amplitude together with the echo impulse. Remember ideal sinc would cause ringing both in forward and reverse directions, so both the content of echo and content of original signal would mix in the paused area. And when you sample this, at 44khz rate for this 10us delayed clap and echo low passed at 22khz, you'll be introducing far more deviations than just ringing because the signal is not really an ideal band limited sample for our Nyquist Shannon sampling. It consists of a signal in its transient state. If you low pass it at a higher band, say 80khz, then the leakage will be low since it'll decay in amplitude quick (but still ring to infinity, that can never be stopped unless you have infinite bandwidth). The time precision quoted in the first post here is an extremely optimistic scenario, taken at steady state, which is not a real world occurence. Unless you're trying to validate oscillators in their steady state, it doesn't work out that well. And things don't stop here. During Reconstruction, you're doing another sinc convolution over the samples = an additional transient smearing. In steady state, you can put a sinc filter with 20khz over a 5khz sine of amplitude X how many times you want and you'll still get an output of X, because there's an infinite train of 5khz behind and ahead to support the math. But in reality we don't have such signals sampled for infinite time. In the transient states you will actually get a ringing (and gets worser each iteration).

 

I'll try to check the other studies. I remember one of them having super sophisticated signal generators for this purpose.

[jabbr]

3 hours ago, manueljenkin said:

Studies exist: http://boson.physics.sc.edu/~kunchur//Acoustics-papers.htm . What I've claimed in my comment is true. If the studies are wrong, you're welcome to prove it, peer review, publish and then showcase it.

Im not claiming the studies are wrong, rather that when a decision is made regarding sampling frequency, the sampling frequency should cover everything that we could possibly hear.

 

In fact, reference [2] http://boson.physics.sc.edu/~kunchur//papers/Temporal-resolution-by-bandwidth-restriction--Kunchur.pdf

supports exactly what I have been posting here (as nauseum)

 

 

The reason a frequency analysis is necessary is because of the way digital sampling has to select a frequency. It is well known that 44khz was selected for CD/redbook to encompass 22kHz or what is considered the upper linear limit of cochleae frequency response. 
 

Can you talk about filters without talking about frequencies? What is the characteristics of an XXX input filter for a sampler such that an audible transient will not be blurred so much that the blur is audible? What blur width will you accept. 
 

Also the inability to think about the frequency domain leads to this mistake in thinking that the slope between two synthesized samples 0 to 1 is infinite. Of course it’s not ever infinite. 
 

 

[Jud]

Kunchur used an analog signal generator (not sure how "super sophisticated" it was) because of some of the problems with sampling people have been discussing.

[jabbr]

I haven't read the entire paper in detail, but the upshot is what I have been saying for a long time about why higher resolution recordings might be better -- that the 20kHz dogma about cochlear response is just that, not some law of nature, and that the human auditory system might have response >20kHz. I personally try to get recordings in as close to the native recording resolution as is possible.

[Don Hills]

8 hours ago, PeterSt said:

... Not sure where the math in the OP (from Don) originates, but 71ns is what I would say. Just because my DAC shows that, and which is the result of a transient which originally requires infinite frequency to do its job (but which transient I flattened 16x).

It is electrical behavior which I think can be calculated with math (Voltage jump is +2V, but the one sample turned into 33 samples). ...

 

It came from JJ. It is the math describing the effect.

A transient might occur between sample times. When you (correctly) low pass filter the transient before sampling, the filtering spreads the transient energy over a period of time. The sample times before and after the time of the transient then capture the energy. If you move the transient occurrence to a different time between samples, the values sampled will change. To detect that the transient has "moved", at least one digital sample value has to change. The formula describes how far the transient has to "move" to change at least one bit.

[Don Hills]

7 hours ago, manueljenkin said:

... The time precision quoted in the first post here is an extremely optimistic scenario, taken at steady state, which is not a real world occurence. Unless you're trying to validate oscillators in their steady state, it doesn't work out that well. And things don't stop here. During Reconstruction, you're doing another sinc convolution over the samples = an additional transient smearing. In steady state, you can put a sinc filter with 20khz over a 5khz sine of amplitude X how many times you want and you'll still get an output of X, because there's an infinite train of 5khz behind and ahead to support the math. But in reality we don't have such signals sampled for infinite time. In the transient states you will actually get a ringing (and gets worser each iteration).

...

The time precision quoted does not depend on a "steady state". As I pointed out in my previous post, it is just as valid for a transient.

 

You'll need to provide some proof of the "ringing" getting worse for each iteration. In Monty's video, as well as showing the effect of moving a transient event between sample times, he showed that once the signal has been filtered during the ADC - DAC process, it can be run through the chain again and the "ringing" does not change. For there to be "ringing" at the output of the filter there has to be signal presented to the filter that is outside its passband. Once that signal has been removed by the filter, there is nothing to increase the "ringing" on subsequent passes.

 

* I dislike the term "ringing" to describe Gibbs effect, but its (mis)use is sadly far too common.

 

[manueljenkin]

47 minutes ago, Don Hills said:

 

The time precision quoted does not depend on a "steady state". As I pointed out in my previous post, it is just as valid for a transient.

 

You'll need to provide some proof of the "ringing" getting worse for each iteration. In Monty's video, as well as showing the effect of moving a transient event between sample times, he showed that once the signal has been filtered during the ADC - DAC process, it can be run through the chain again and the "ringing" does not change. For there to be "ringing" at the output of the filter there has to be signal presented to the filter that is outside its passband. Once that signal has been removed by the filter, there is nothing to increase the "ringing" on subsequent passes.

 

* I dislike the term "ringing" to describe Gibbs effect, but its (mis)use is sadly far too common.

 

1. Monty's video is not a "proof", it's just a demonstration using one overtly optimistic scenario.

 

2. It was done in steady state for a continuous train of square wave pulses.

1 hour ago, Don Hills said:

 

It came from JJ. It is the math describing the effect.

A transient might occur between sample times. When you (correctly) low pass filter the transient before sampling, the filtering spreads the transient energy over a period of time. The sample times before and after the time of the transient then capture the energy. If you move the transient occurrence to a different time between samples, the values sampled will change. To detect that the transient has "moved", at least one digital sample value has to change. The formula describes how far the transient has to "move" to change at least one bit.

I am expecting math proof. Also the very act of low passing this transient, and spreading the energy across is destroying the pause information. Whether that is audible or not is another thing, but sampling this 10us transient instance, even after low passing at 44.1khz will surely result in serious artefacts, unless you have a consistent repeating pattern of this 10us delay and repeating pattern of that signal (doesn't occur in real life, objects move, echo/delay patterns change)