Time resolution of digital sampling

[pkane2001]

10 minutes ago, manueljenkin said:

Whoa!! Finally!!

 

 

I finally witnessed it.

 

 

You have replied straight to what was being asked, without modulating the question/post to your own imaginations. First time, I've seen a situation where I didn't have to ask you to actually read the post fully.

 

That comment could get a direct, to the point response from you. In that context, it sure is a contribution to this thread, compared to what has been happening in the last 2 pages.

Last two pages were about the limits of human hearing. I’ve no interest in arguing about this limit being 20kHz or 200kHz. I know the answer for myself, and that’s all that I’m interested in. 
 

If you have any real, objective input on this other than attacking everything I post, then share it.

 

Until then, maybe take a hearing test using the software I created and tell me what frequencies you can reliably detect. 

[pkane2001]

1 minute ago, manueljenkin said:

If that's all the information you've retained (out of all the mathematical derivations I've posted, steady state vs transients, so forth) I guess your sampling rate of viewing these posts is not enough.

I’ve already responded to everything you posted that I had a comment on. Anything   I didn’t respond to you can safely assume I ignored, had no interest in responding to, or had no comment.

[pkane2001]

2 minutes ago, manueljenkin said:

Or was a valid scenario/argument that you had no counter for. 😀. So you try your best to forcibly ignore divert attention from it. You're still open to show any real transients, that can be perfectly bandlimited using a sinc low pass. Scenario 6 is one example, scenario 5 is one, you're free to choose another.

Im guessing you haven’t understood a thing that I posted if you think that I ever said a perfect transient can be reproduced by a band limited signal. 

[pkane2001]

 

4 minutes ago, PeterSt said:

Maybe we should account this all under "our" English not being decent enough to bring something across.

It's sad, because "your" English isn't utilized at all.

 

 

So what was that then* ?!?

 

*): in response to something at least I could understand for merit, from either Manuel (or myself - haha).

 

Maybe we* should try a bit harder.

 

*): We ?

OK, We.

Maybe. More than that, I think that terminology is extremely important. When one uses terms such as “delay” it is important to understand what the term really means, and how it’s different from the term “transient”, for example.

[pkane2001]

10 minutes ago, manueljenkin said:

No. It will still have aliasing components. Please read scenario 6 and derive for yourself.

 

Let me show you what scenario 6 is.

 

Input Signal

Piecewise multiplication of "x" units time delayed heaviside function, with "x" units time delayed sine function.. basically it's a sine that begins at time x, and before time x the signal is a dc 0. There is no jump discontinuities, it is continuous and defined with a specific amplitude at all times, and the slew rate also doesn't blow up to infinity.

 

Take Fourier transform of this and Fourier transform of a perfect sinc at whatever frequency you want, and show me how you'll end up with a truly band limited spectrum at the output.

 

Let me ask you: what's the slope of the signal (first derivative) at the exact point where it transitions from DC to sine wave?

[pkane2001]

4 minutes ago, jabbr said:

Honestly the analysis of transients using Fourier transforms is what ?freshman level sort of stuff Here is your homework. https://link.springer.com/chapter/10.1007%2F0-387-28799-X_4. 

 

Whether you pass or not is irrelevant to me. I and many others have been analyzing and publishing the analysis of transients using Fourier transforms for 30 years. Anyone is free to investigate this type of analysis using google, or better if one has access to a library... Marvin Minsky obtained a patent in 1957 https://en.wikipedia.org/wiki/Confocal_microscopy 

 

This is really getting silly. Here's the simple analysis of the DC to Sinewave example. It was easy enough to add it to my distortion toolkit. Blue is the original sinewave at 1kHz, white is the "processed" one. Sampled at 176kHz. I offset the derived/processed curve a little in Y so it's easier to tell them apart:

 

No filtering:

 

 

Low-pass filtered at 20kHz. Notice the Gibbs phenomena just before the sharp transition. As expected with a strongly band-pass limited system:

 

 

Now, let's raise the filter to 48kHz. Notice less Gibbs fluctuations near the transition from DC:

 

Move the low pass filter to 88.2k, and this is almost entirely like the original, sharp transition from DC:

 

 

Let's zoom in on that last one to see what we can see:

 

I'd say that's a pretty good reproduction of a perfect transition from DC to sinewave. As you can see, increasing the allowed frequencies improves the accuracy of reproduction. There's no magic here, that's what @jabbr was referring to, and what I've been stating from the beginning:

 

Quote

Given sufficient sampling, any transient can be sampled sufficiently. 

Simply: raise the corner frequency of the filter such that it preserves any characteristic of the transient you are interested in. Second, set the sampling rate appropriately.

 

[pkane2001]

54 minutes ago, pkane2001 said:

 

This is really getting silly. Here's the simple analysis of the DC to Sinewave example. It was easy enough to add it to my distortion toolkit. Blue is the original sinewave at 1kHz, white is the "processed" one. Sampled at 176kHz. I offset the derived/processed curve a little in Y so it's easier to tell them apart:

 

No filtering:

 

 

Low-pass filtered at 20kHz. Notice the Gibbs phenomena just before the sharp transition. As expected with a strongly band-pass limited system:

 

 

Now, let's raise the filter to 48kHz. Notice less Gibbs fluctuations near the transition from DC:

 

Move the low pass filter to 88.2k, and this is almost entirely like the original, sharp transition from DC:

 

 

Let's zoom in on that last one to see what we can see:

 

I'd say that's a pretty good reproduction of a perfect transition from DC to sinewave. As you can see, increasing the allowed frequencies improves the accuracy of reproduction. There's no magic here, that's what @jabbr was referring to, and what I've been stating from the beginning:

 

And since the claim was that there will be aliases in the bandpass region due to the transient (DC->sine transition) being filtered, let's take a look at the spectrum of that last result (with the 88k LP filter):

 

 

I don't see any aliases all the way to Nyquist frequency.

 

In case you're wondering about the shape of the filter that was used here, here it is (auto-generated, linear-phase, FIR), shown at a large zoom-in:

 

 

Maybe aliases will show up with a lower corner frequency? Here's the LP filter @20kHz. You can see the LP filter cut in right at 20k, but still no aliases:

 

[pkane2001]

1 minute ago, sandyk said:

 Can you repeat that at 10kHz ? After all ,you keep stating that 16/44.1 is more than good enough for clean and accurate sounding  audio, not just Telecoms grade audio.

Where did I state any of this?

And what does the frequency of the sine wave have to do with Manuel’s claims of aliasing?

[pkane2001]

13 minutes ago, sandyk said:

A recent example.

In your replies , you aren't just sticking to Manuel's claims of aliasing.

I note also that you picked a nice and easy 1kHZ sinewave to illustrate your  point, then showed that you really needed way more than 16/44.1 to properly clean up the waveform, which is a good argument for 24/96 or 24/192 , and is inconsistent with your view that we need no more than 16/44.1 for clean and accurate HIGH FIDELITY Audio with a bandwidth approaching 22kHz.

 

And I didn't start this topic, nor did I say I wanted to have this argument, though others have been trying. I've repeatedly said I'm not interested in the discussion about limits of audibility. I know what mine is, and I'm not going to tell you what's yours -- that's your business. If you believe it's 200kHz, I'm happy for you! ;)

 

 

 

[pkane2001]

1 minute ago, manueljenkin said:

What are these (image)? You've done a theoretical simulation, I'm expecting just one spike at 1khz and nothing else.

 

 

Also what was the window you used for this visualization? Show me the fft plot, let's see how great it resolves it at 1 second. Or window it in periods of about 0.12 seconds and show me how the frequency looks from 0.96 second to 1.08 second.

 

Wasn't your claim theoretical? This was a simple computer simulation of the exact case you were describing: delayed sine wave transitioning from DC, sampled and low-pass filtered.

[pkane2001]

Just now, manueljenkin said:

Now tell me what exact formula/algorithm your tool was using. If the tool stops it's decomposition at 88khz it won't show anything above that, even if content was there.

 

As I said, it was sampled at 176kHz, therefore the largest frequency that can be analyzed (that pesky Nyquist, again) is 88kHz. This is standard stuff, simple sampling algorithm, and then analysis using an FFT. For the FFT, I used a peak-hold method which shows the maximum value for each bin with overlapping windows, not an average. Window type was Kaiser.

 

[pkane2001]

13 minutes ago, jabbr said:

 

I notice your plot goes down to -200 dB ... what about harmonics at -300 dB?

 

Rob Watts said -200dB is about the limit of audibility, and I follow what he says religiously :)

 

 

[pkane2001]

35 minutes ago, manueljenkin said:

Ok so you've done this visualization after chopping and reconstruction, not before!! Do it prior to sampling, but after low passing (you can only do this mathematically, since computer would always operate it's algorithms on the data it gets after sampling) and show me how the frequency bins look like (till infinity would be great).

 

So you want me to demonstrate that a transient with an undefined/infinite slope cannot be represented perfectly in a band-limited system? That's hilarious, since that's what I've been saying from the beginning. I'll repeat again what @jabbr said earlier, and what I've been saying all along and even demonstrated visually with your own example:

 

 

[pkane2001]

3 minutes ago, manueljenkin said:

There is no infinite slope in this scenario.

 

I asked you before, but didn't get an answer: What's the derivative at the inflection point?

 

[pkane2001]

6 hours ago, Jud said:

@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.

Delay isn’t the same thing as a transient. A point I tried to make earlier, and yet even Kunchur seems to use these terms interchangeably. You don’t need higher sampling rates to represent timing differences (delays) below 1 sample. Timing resolution of redbook is well below 5 microseconds.

I’d like to hear from @PeterStas to his definition of inharmnonic content produced by transients and why it’s so hard to record it.
 

 

[pkane2001]

2 hours ago, Audiophile Neuroscience said:

 

and...

... and Redbook format can record delays of much less than 5 microseconds.

[pkane2001]

1 hour ago, asdf1000 said:

 

This topic of timing resolution, transients etc is right up the alley of what @Rob Watts of Chord Electronics discusses a lot.

 

I wonder if he can chime in.

Funny, I mentioned Rob before in this thread for a different reason ;)

[pkane2001]

 

9 minutes ago, asdf1000 said:

 

Hehe. Can you show the source for this?

 

And the specific context of the -200dB he talks about?

 

I've seen him mention numbers like this but I don't think he is directly talking about hearing sounds at -200dB...

 

 

At the risk of being reprimanded by Alex and Peter for being off topic, here it is :)

 

https://www.head-fi.org/threads/chord-electronics-dave.766517/page-270#post-12770432

 

[pkane2001]

2 minutes ago, asdf1000 said:

 

I think it may have something to do with being able to use simpler analogue stage/filtering designs? Which sounds reasonable to me?

 

See here, especially last part highlighted:

 

As an engineering pursuit, reducing noise floor is always a good thing.
 

As a claim of -200dB noise floor modulation being audible — I don’t accept this for a minute or even for 5 microseconds ;)

 

Thermal noise in electronics is way, way above this level.

[pkane2001]

7 minutes ago, asdf1000 said:

 

Here are his words, exactly, and I'm not sure these can be interpreted any other way:

My own tentative conclusions (or rule of thumb) are that one can hear levels of noise floor modulation down to -200dB

 

Audibility of a modulating signal at -200dB in, say, a -120dB noise floor is just completely unbelievable. And, again, this will be swamped by thermal noise long before there's any detection possible.

 

[pkane2001]

20 minutes ago, manueljenkin said:

"Hearing down to -200db" is not the same as "you cannot hear better than that". Rob never said that. He just said that he can reliably demonstrate precision down to -200db. 

 

What does "reliably demonstrate precision down to -200db" mean? 

 

Hearing down to -200dB means (to me, at least) being able to detect, with ears, a signal (or its effects/modulation of another signal) at -200dB. No? Maybe it's that language barrier thing that Peter was talking about.

 

My own tentative conclusions (or rule of thumb) are that one can hear levels of noise floor modulation down to -200dB

[pkane2001]

1 hour ago, sandyk said:

 Ask Miska or Paul R, as their Naval service let them clearly hear differences below the noise level (Submarines) 

Miska provided training in that area , IIRC.

 

This is like saying you can train people to bend the bullet trajectory by flipping your wrist quickly while firing a gun. Sounds plausible and looks great when Angelina is doing it, but it's simply impossible in real life.

 

PS: To make it explicit, I’m referring to being able to train someone to hear a -200dB signal below a -120dB noise floor.

 

[pkane2001]

1 hour ago, Jud said:

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.

 

Yes, the lower threshold of ITD (interaural time difference) has been measured to be about 10 microseconds. This has to do with spatial perception and the evolutionary need of our ancestors to be able to tell where the sound is coming from. Probably to detect a possible dinner, or to not become one.

 

Quote

i.e., our ear-brain system isn't doing Fourier analysis in processing at least some aspects of acoustic signals.

There's no reason to think that the ear or the brain are using Fourier analysis here -- that'd be silly. But, it's just as silly to assume that because the ear is using another type of phase difference detection, that Fourier analysis somehow doesn't apply to the original signal. 

 

1 hour ago, Jud said:

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).

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.

 

1 hour 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

 

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.