How High of a Sample Rate is Enough?

[Krunok]

Ok sure, we agree I think. This is why in post #3, I suggested 88.2 or 96KHz is safer: these allow for a wider margin of error in applying the low-pass filter during recording and mastering.

Even so, if the mastering engineer has used an incorrect (or no) filter at whatever sample rate they've mastered it at, this will be a problem, i.e. no sample rate is high enough if the engineer uses a sufficiently poor (or no) filter.

And we don't have a problem in the first place if we're using properly mastered RBCD. Filtering at higher sample rates just tends to be harder to stuff up.

Yes, this process is a kind of self fulfilling prophecy: in first step during mastering we cut every frequency above some limit and then during reproduction we say "ok, no need to go higher as there's nothing above it".

But my question is this: if you have the non-sine signal at base frequency of say 18 kHz for which you would need say 5 harmonics to represent accurately would you be able to hear the difference between that signal and 18kHz sine signal?
We can agree that all 5 harmonics of that signal are above hearing range but my question is can you hear them if they are "bundled" in the base 18kHz signal?

I mean, if you can't hear the difference between non-sine and sine 18kHz wave, why measure the THD at 18kHz as you want be able to tell the difference anyhow. But on the other hand, if you can tell the difference, in that case you need to raise the upper floor from 22kHz (hence 44kHz in RBCD) to something higher.

 

[Blumlein 88]

Yes, this process is a kind of self fulfilling prophecy: in first step during mastering we cut every frequency above some limit and then during reproduction we say "ok, no need to go higher as there's nothing above it".

But my question is this: if you have the non-sine signal at base frequency of say 18 kHz for which you would need say 5 harmonics to represent accurately would you be able to hear the difference between that signal and 18kHz sine signal?
We can agree that all 5 harmonics of that signal are above hearing range but my question is can you hear them if they are "bundled" in the base 18kHz signal?

I mean, if you can't hear the difference between non-sine and sine 18kHz wave, why measure the THD at 18kHz as you want be able to tell the difference anyhow. But on the other hand, if you can tell the difference, in that case you need to raise the upper floor from 22kHz (hence 44kHz in RBCD) to something higher.

No you will not hear the harmonics.

Why measure THD there? More importantly is why you need to measure IMD there. If a device had high IMD it can cause artifacts at lower frequencies. Not from those removed harmonics of 18 khz, but from 18 khz interacting with other frequencies in the signal if there are any. The analog section can have poor IMD performance beyond the sample rate, and distortions of other signals could intermodulate with your 18 khz and put something into the audible band which could be heard.

Also remember any waveform can be decomposed into a series of sine waves that create the same waveform via Fourier. So your non-sine wave 18 khz and harmonics can still be a collection of various sine waves.

 

[Wombat]

Maybe, maybe not.

FWIW: Research in another field: http://www.icben.org/2017/ICBEN 2017 Papers/Keynote02_Koch_4163.pdf

I think that intermodulation by ultrasound into the sub-20kHz region would be captured in the recording process and would be present in replay even though a low-pass 20kHz filter is subsequently applied.

 

[Krunok]

No you will not hear the harmonics.

Also remember any waveform can be decomposed into a series of sine waves that create the same waveform via Fourier. So your non-sine wave 18 khz and harmonics can still be a collection of various sine waves.

So, you're saying we can't tell the difference between a sine 18kHz signal and non sine 18kHz signal as we can't hear the harmonics above 20kHz?

Does it also mean we can't hear the difference between 11kHz sine signal and a 11kHz non-sine signal which contains 11kHz sine wave and a 22kHz sine wave of say 50% lower amplitude?

Btw, can you quote some paper where this has been tested and proved to be non-hearable?

 

[Krunok]

I think that intermodulation by ultrasound into the sub-20kHz region would be captured in the recording process and would be present in replay even though a low-pass 20kHz filter is subsequently applied.

Probably so, but I'm not talking about intermodulation. I'm talking about a signal that consists of 11kHz base wave and 22kHz harmonic and asking if we can hear the difference between that signal and a 11kHz sine signal.

 

[Wombat]

Probably so, but I'm not talking about intermodulation. I'm talking about a signal that consists of 11kHz base wave and 22kHz harmonic and asking if we can hear the difference between that signal and a 11kHz sine signal.

Well in terms of ears hearing, the 22kHz signal would need to inter-modulate the 11Khz signal giving an audible 'beat' frequency of 16.5 kHz. The 22kHz frequency would not be heard. This is a normal occurrence regardless of subsequent 20kHz cut-off filtering in the replay chain.

 

[SIY]

Faster than doing a search for the numerous papers on audibility of bandlimiting, which statistically aren't likely to have that specific pairing (I'm anticipating the "but it's not an 11kHz and 22kHz in 1:2 amplitude ratio, that's just a general look at bandlimiting" objection), you can generate the signals and listen yourself. Take you about 2 minutes.

Some general looks at bandlimiting audibility include Nishiguchi, Toshiyuki; Hamasaki, Kimio; Ono, Kazuho; Iwaki, Masakazu; Ando, Akio (2009-07-01). "Perceptual discrimination of very high frequency components in wide frequency range musical sound". Applied Acoustics. 70 (7): 921–934, this paper from NHK, this paper, and quite a few others.

 

[SIY]

Well in terms of ears hearing, the 22kHz signal would need to inter-modulate the 11Khz signal giving an audible 'beat' frequency of 16.5 kHz. The 22kHz frequency would not be heard. This is a normal occurrence regardless of subsequent 20kHz cut-off filtering in the replay chain.

True if you have a nonlinear transducer (I assume you would want non-harmonically related signals to demonstrate this). When that distortion is removed, so is the in-band distortion product.

 

[Krunok]

Faster than doing a search for the numerous papers on audibility of bandlimiting, which statistically aren't likely to have that specific pairing (I'm anticipating the "but it's not an 11kHz and 22kHz in 1:2 amplitude ratio, that's just a general look at bandlimiting" objection), you can generate the signals and listen yourself. Take you about 2 minutes.

Some general looks at bandlimiting audibility include Nishiguchi, Toshiyuki; Hamasaki, Kimio; Ono, Kazuho; Iwaki, Masakazu; Ando, Akio (2009-07-01). "Perceptual discrimination of very high frequency components in wide frequency range musical sound". Applied Acoustics. 70 (7): 921–934, this paper from NHK, this paper, and quite a few others.

11kHz and 22kHz in 1:2 amplitude ratio was just an example. I have no software to generate this on my notebook and I also don't trust my ears any more to claim to be any kind of hearing reference. So, are we able to hear the difference between a "11kHz and 22kHz in 1:2 amplitude ratio" signal and a pure 11kHz sine wave?

 

[SIY]

How many specific pair examples do you want?

Here's a way you can convince yourself quickly.

 

[Krunok]

How many specific pair examples do you want?

Here's a way you can convince yourself quickly.

Nice!

Ok, I'm for sure able to tell the difference between those 4 waveforms at 10kHz and I'm not really sure for 11kHz.

How exactly are those tones played on my notebook? Does my soundcard generate those waveforms or ..?

 

[Blumlein 88]

11kHz and 22kHz in 1:2 amplitude ratio was just an example. I have no software to generate this on my notebook and I also don't trust my ears any more to claim to be any kind of hearing reference. So, are we able to hear the difference between a "11kHz and 22kHz in 1:2 amplitude ratio" signal and a pure 11kHz sine wave?

You can download Audacity and make any pairs of tones you wish to listen to.

 

[Krunok]

You can download Audacity and make any pairs of tones you wish to listen to.

Ok, I used the link and was for sure able to tell the difference at 10kHz, I'm pretty sure I can tell the difference at 11kHz as well. It obviously means that waveforms containing harmonics can be differentiated from sine waveforms at 11kHz. Younger person can probably hear the difference with higher base tones as well.

How exactly are those waveforms being played at my notebook? (Current settings of my soundcard are 48kHz/24 bit)

 

[Krunok]

So, as the difference between waveforms can be heard at 11kHz, what is the conclusion? All of those 3 non sine waveforms for sure have harmonics above 44.1 kHz which would not be captured by RBCD.

 

[Wombat]

So, as the difference between waveforms can be heard at 11kHz, what is the conclusion? All of those 3 non sine waveforms for sure have harmonics above 44.1 kHz which would not be captured by RBCD.

Which is better than our ears in capability.

 

[Blumlein 88]

So, as the difference between waveforms can be heard at 11kHz, what is the conclusion? All of those 3 non sine waveforms for sure have harmonics above 44.1 kHz which would not be captured by RBCD.

Probably aliasing. Depends upon how they generate the non sine waves.

Here is the FFT from a square wave at 12,100 hz in 48 khz sample rates without aliasing.

Here is the same exact thing generated in Audacity with just plain square wave. You obviously would hear a difference. So making two or three sine tones and adding them together would be the way to go.

 

[Krunok]

Which is better than our ears in capability.

If we can hear the difference betwenn different 11kHz waveforms than obviously our ears can take into accounts harmonics of those waveforms and those harminics are clearly higher than the high limit of of hearing range.

What also makes me wonder is how can I tell the difference between those 11kHz waveforms when I practically can't hear anything above 13kHz.

 

[Krunok]

Here is the same exact thing generated in Audacity with just plain square wave. You obviously would hear a difference. So making two or three sine tones and adding them together would be the way to go.

That's exactly what I meant when I said take 11kHz sine wave and add 22kHz sinewave with 50% lower amplitude to it. That was of course just an example.

 

[Wombat]

Probably so, but I'm not talking about intermodulation. I'm talking about a signal that consists of 11kHz base wave and 22kHz harmonic and asking if we can hear the difference between that signal and a 11kHz sine signal.

If the intermodulation frequency in the audio band is audible. At 50% I it is highly likely if loud enough. Am I missing something?

 

[Krunok]

If the intermodulation frequency in the audio band is audible. Am I missing something?

I believe @SIY already answered that: https://audiosciencereview.com/foru...gh-of-a-sample-rate-is-enough.4037/post-95673