Time resolution of digital sampling

[Jud]

Hi Don - Can you put "intersample overs" in this context?

[Jud]

4 hours ago, Don Hills said:

there's only one correct curve that joins the slopes before and after the peak.

 

That's really the conceptual key to me. If you think of it in terms of the Shannon-Nyquist proof, when you've got two points (sampling at just twice or less the highest frequency of interest), there are an infinite number of curves that could include them. As soon as you add a third point (more than twice the highest frequency), there's only one curve. And that's a continuous curve, no "steps."

[Jud]

I propose a simple experiment. All we need is Audacity or similar software and a method to compare two files that is blinded.

 

Compare two files, one with a steady tone, the other the same but with a single missing sample at 44.1kHz sample rate. As I understand it volume may need to be reasonably high.

 

Can you tell which file contains the missing sample?

[Jud]

6 hours ago, PeterSt said:

Silencing one sample would imply a silence of 22us if you'd ask me (44.1KHz). This will never ever remain silent after even one step of upsampling (the silent sample will have broadened to 3 samples).

 

Thought about that, but recall we are told any Gibbs effect ringing will be silent also, so all should be quiet as a mouse, eh?

[Jud]

24 minutes ago, jabbr said:

 

Peter it is a mathematical fact that *any* time dependent signal of arbitrary complexity can be represented in frequency space. The transform between time and frequency domain is of course known as the Fourier transform. 

 

Dirac knew this 

 

So obviously any impulse response may also be represented in the frequency domain. 

 

This is math.

 

But it isn't necessarily how the ear-brain does signal processing, is that correct?

[Jud]

3 minutes ago, jabbr said:

Of course not. 

 

My point, simply is that if gaps of 10 usec are audible, then it implies that frequencies > 22 Khz are audible.

 

You simply cannot reasonably state that human hearing is bandlimited to 22 kHz (or whatever) and also maintain that samples "between" 44 kHz have any effect on audibility.

 

Nyquist is so misunderstood. It is simply math.

 

I've done some reading that seems to indicate reasonably reliable sources (a Handbook of Acoustics was mentioned - doesn't sound radical, though of course it doesn't have to be correct) state a missing sample would be audible as a "tic."

 

Recall also that a single sample impulse is said to contain all frequencies.

 

So we have to be a little careful about translating between the two.

[Jud]

44 minutes ago, jabbr said:

 

Right! The signal isn't bandwidth limited!!!

 

What do you think happens to the impulse when the low-pass filter is applied?

 

https://src.infinitewave.ca

 

What happens when a low-pass filter is applied to a file with a sample missing?

[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.

[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.

[Jud]

If someone cares to show me where in the Shannon or Nyquist proof of the theorem a "steady state" is required....

 

Again I'll say the question of the briefest audible transient may be different, and Kunchur et al. are different yet again, being occupied with minimum time difference before we no longer perceive simultaneity.

[Jud]

@jabbr, if I recall correctly, other experimenters found a time for minimum noticeable difference between two non-simultaneous signals about double that of Kunchur, about 10ns vs. Kunchur's 5. So even granting Kunchur is an outlier, @pkane2001, the other experimental work in this area appears to show we can notice timing differences smaller than 1/20,000th of a second.

 

Of course this isn't the same issue as whether we can hear signals above 20kHz or whether we can arrive at a very reasonable if imperfect facsimile of a reasonably if imperfectly bandlimited signal given an appropriate sampling rate (which was the original thread topic).

 

My own interest lies more in the area of what sort of sampling rate is appropriate to capture audible inharmonic attack transients present in music. (As I think @PeterSt said, pretty much everything in music has an (inharmonic) attack phase.) "Inharmonic" doesn't mean non-periodic, it just means one needs higher harmonics to reconstruct them. And that's the reason for my interest in whether very brief sounds are audible.

[Jud]

On 10/4/2020 at 6:31 AM, pkane2001 said:

Delay isn’t the same thing as a transient.

 

Yes, I agreed with this earlier in the thread.

 

I of course agree with all the proven mathematical theorems that have been brought up in the thread. I have no interest in rehashing the math.

 

My interest lies much more along the lines of whether there are differences in the ways the ear-brain perceives these various acoustic phenomena. For example, 1/20,000th of a second is 50 microseconds, yet even if one is duly skeptical of Kunchur's 5 microsecond figure (thanks to whoever pointed out I was incorrectly stating nanoseconds), the consensus of prior experiments was that humans were capable of sensing delays on the order of 10 microseconds. I am virtually certain this doesn't imply we can hear 100kHz sounds, so the ear-brain must be doing something different with delays than with frequency perception. Fourier analysis is undoubtedly mathematically correct, yet at least some aspects of our acoustic perception don't depend on it (https://phys.org/news/2013-02-human-fourier-uncertainty-principle.html), i.e., our ear-brain system isn't doing Fourier analysis in processing at least some aspects of acoustic signals.

 

And so I wonder whether the ear-brain's perception of transients similarly is based on something distinct from frequency perception occurring in the brain (while noting that this, like the perception of delays, does not imply and cannot require that we hear sounds above 20kHz).

 

If it is the case, I don't know that this ought to surprise anyone. Certainly our visual frequency range (the range of the visible spectrum) has nothing to do with how quickly our visual system can react to light, or what the briefest flash of light we can perceive might be. So long as it doesn't require us to perceive signals above 20kHz (or in my case 16kHz as of a few years ago, very likely lower now), there's no necessity for evolution to have made our brains use Fourier analysis to perceive the sharpness of a transient.

 

I'm interested in transients (as part of the inharmonic attack phase of a musical sound) because it's been known for decades that they are critical to aspects of music listening as fundamental as knowing what instrument is playing.

[Jud]

11 hours ago, pkane2001 said:

13 hours ago, Jud said:

 

Sure. A leading edge detection or a first zero crossing detection can be used without involving frequency analysis. There are other ways. It is very impressive, though, that the human brain can detect such tiny differences, considering the relatively much slower speeds of electrochemical processing in neurons.

 

13 hours ago, Jud said:

I'm interested in transients (as part of the inharmonic attack phase of a musical sound) because it's been known for decades that they are critical to aspects of music listening as fundamental as knowing what instrument is playing

Expand  

 

The main point of the discussion up until now was that transients can be analyzed with Fourier, sampled up to any desired frequency, and are just as subject to Nyquist-Shannon as any other signal. Microsecond, nanosecond, or even picoseconds delay does not require higher sampling rates to be captured in a PCM recording. Redbook is sufficient for that. 

 

All agreed. Combining these first and second points, though, leads me to wonder if the system (not forgetting mics and speakers as well) should be set up to reproduce frequencies in excess of 20kHz in order to give us the proper perception of some of the sharper/faster initial attack transients. I have no idea of the answer (haven't found any relevant academic work), just wondering.

[Jud]

11 hours ago, JoshM said:

 

How much do you think we should worry about intersample overs? Are they audible?

 

Not Don, and this is completely anecdotal, but:

 

Depends what you mean by "audible." As an audibly evident defect, I haven't experienced it. I assume a difference of 1 or more dB in response would be audible if, for example, carefully comparing two files, which I have not done.

 

This was with HQPlayer, fooling around with volume levels. I don't know whether HQPlayer has any sort of "graceful failure" mode for intersample overs that may have affected my experience.

[Jud]

33 minutes ago, Don Hills said:

I feel that music with aspirations to high fidelity won't have been pushed to the limit in mastering, and conversely music that has been pushed hard will likely already have more audible damage.

 

From your lips to producers' ears. 😉 I found they happened occasionally in my listening without attenuation (admittedly not all of which has aspirations to high fidelity).

 

33 minutes ago, Don Hills said:

 

The simplest prevention method is to attenuate the digital signal before the DAC by exactly 1 bit (6.02dB).

 

With HQPlayer, -3dB seemed to be enough for virtually everything I tried.