Time resolution of digital sampling

[jabbr]

6 minutes ago, PeterSt said:

 

Maybe the honored opponents should respond to this. I mean, I notice that they never do.

I too said it several times.

It this a theoretical math discussion, then I will use a non-discrete Fourier transform. Oh c'mon. You wan't to go infinite slope? Infinite bandwidth... this argument degenerates. Let's ask Dirac 

 

Let's see ... every particle has a wave equation ... duh!

 

Really this discussion is getting dumb. Sorry.

[PeterSt]

7 minutes ago, jabbr said:

Oh c'mon. You wan't to go infinite slope?

 

I am sorry to observe that you, the Honored Opponent keep on making things up which are not presented in my Thesis. Chapter 6 and such.

If you don't let me pass, I'll go elsewhere with it.

 

[jabbr]

Just now, PeterSt said:

 

I am sorry to observe that you, the Honored Opponent keep on making things up which are not presented in my Thesis. Chapter 6 and such.

If you don't let me pass, I'll go elsewhere with it.

 

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 

[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:

 

[sandyk]

3 hours ago, pkane2001 said:

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:

 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.

[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?

[sandyk]

Just now, pkane2001 said:

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?

A recent example.

Quote

But there are also plenty of studies that show humans can't hear much above 20kHz, and this also gets significantly worse with age. So, even if we are missing some components of the Heaviside function in the recording above 22kHz, is this really significant for audio reproduction (for humans)?

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.

[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! ;)

 

 

 

[fas42]

What people are really worrying about, is whether some 'magic' can be generated in the replay, if frequencies above 20kHz are 100% accurately reproduced ... well, the answer is, No!!! ... and, yes, this is very much so a subjective position, in an 'objective' thread, 😜.

 

The listening brain adjusts for bits "that are missing" - automatically ... I just saw yesterday, in one of the papers, that the experimental results were thrown, when people listened to replay with ultrasonics missing, directly after hearing the same track, with. The listeners had 'learnt' what the ultrasonic content was doing, and unconsciously added it back in, when it was no longer there - and couldn't distinguish the two versions any more ... unfortunately, the ear/brain is too clever for us poor inquiring sods - it will always outsmart us ... 😁

[jabbr]

2 hours 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.

 

Alex, the take home message is that if you are getting aliasing, etc with your sampling rate, then increase it.

 

Forget audibility, let's take a real world transient sound, like a rifle shot, or a clap, or whatever. If you aren't reproducing it exactly (exactly means close enough to measurement limits) then increase the sampling rate.

 

The problem isn't that digital sampling and reproduction doesn't work, it works fine. You just need to pick a sampling rate >2x the highest frequency in your signal.

 

If your microphone has a frequency response out to 40 kHz then sample at >80 kHz.

[manueljenkin]

5 hours ago, pkane2001 said:

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.

What are these (image)? Why does your graph stop at 88khz. Also let me know the exact formula you have used to visualize this, if the tool stops it's decomposition at 88khz it won't show anything above it even if it were there. 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.

[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.

[manueljenkin]

6 minutes ago, pkane2001 said:

 

Ignore.

[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.

 

[manueljenkin]

1 minute ago, pkane2001 said:

 

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.

 

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).

[jabbr]

4 minutes ago, pkane2001 said:

 

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.

 

 

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

[sandyk]

Just now, jabbr said:

Forget audibility, let's take a real world transient sound, like a rifle shot, or a clap, or whatever.

 Even a sneeze has components WAY above 22kHz.

[kumakuma]

14 minutes ago, sandyk said:

 Even a sneeze has components WAY above 22kHz.

 

Do you have a reference for this?

[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 :)

 

 

[jabbr]

3 minutes ago, kumakuma said:

 

Do you have a reference for this?

Haven't you seen those little Covid particles bouncing around?

[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:

 

 

[manueljenkin]

4 minutes ago, pkane2001 said:

 

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 demonstrated visually with your own example:

 

 

There is no infinite slope in this scenario.

[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?

 

[Audiophile Neuroscience]

10 hours ago, pkane2001 said:

 

You are always a breath of fresh air, David, with your sarcasm and personal attacks you add value to every conversation.

 

 

Funny, I was agreeing with other posters' comments. It's ironic that you make a sarcastic personal attack about what you perceive to be a sarcastic personal attack. Perhaps you have a "App" that detects sarcasm and personal attacks in *every* conversation". I would like to know if this is "self validating"?   😁 <- emoji of absolution -> 😜