Question about sampling/PCM/Nyquist

[MZKM]

Got into a discussion on another forum. Trying to see if a user‘s claims have any theoretical merit.

So, Nyquist states that if you sample >2x the frequency range you want, it can reproduce that range perfectly (with quantization noise). However, what if there was a super short transient (say 1/45,000 of a second), and if that occurs between the samples (44.1kHz sampling), would it get reconstructed? This is of course not audible at all, but the discussion was if it would be present in the recording.
I‘m an idiot.

 

[LTig]

Got into a discussion on another forum. Trying to see if a user‘s claims have any theoretical merit.

So, Nyquist states that if you sample >2x the frequency range you want, it can reproduce that perfectly (with quantization noise). However, what if there was a super short transient (say 1/45,000 of a second), and if that occurs between the samples, would it get reconstructed? This is or course not audible at all, but the discussion was if it would be present in the recording.

A super short transient contains a lot of frequencies above the Nyquist frequency. The antialias filter before the DAC removes them, and what is left will be reconstructed.

 

[March Audio]

Got into a discussion on another forum. Trying to see if a user‘s claims have any theoretical merit.

So, Nyquist states that if you sample >2x the frequency range you want, it can reproduce that perfectly (with quantization noise). However, what if there was a super short transient (say 1/45,000 of a second), and if that occurs between the samples, would it get reconstructed? This is or course not audible at all, but the discussion was if it would be present in the recording.

No it wouldn't.

A Transient that occurs between samples by definition contains higher frequency signals than the bandwidth of the system.

 

[MZKM]

A super short transient contains a lot of frequencies above the Nyquist frequency. The antialias filter before the DAC removes them, and what is left will be reconstructed.

No it wouldn't.

A Transient that occurs between samples is by definition a higher frequency than the bandwidth of the system.

Ohh, duh. Of course such a transient would be insanely HF. I feel dumb, thanks.

 

[MZKM]

No it wouldn't.

A Transient that occurs between samples is by definition a higher frequency than the bandwidth of the system.

However, the other user also claimed that since research has shown that even 10 microseconds (1/100,000) is perceivable in regards to sound localization:
https://www.sciencedaily.com/releases/2017/06/170601124055.htm

That we need sampling rates of >100kHz.

 

[March Audio]

Ohh, duh. Of course such a transient would be insanely HF. I feel dumb, thanks.

It's not dumb at all. It's a good question. Many times I see people talk about transients and how they are captured in sampling systems. Many don't make the connection between bandwidth and fast transients.

 

[MZKM]

It's not dumb at all. It's a good question. Many times I see people talk about transients and how they are captured in sampling systems. Many don't make the connection between bandwidth and fast transients.

Just updated my comment, as I misunderstood the other user:

What happens if two sounds are 1/50,000 of a second apart in a recording, would the beginning of each sound be reconstructed?

 

[March Audio]

However, the other user also claimed that since research has shown that even 10 microseconds (1/100,000) is perceivable in regards to sound localization:
https://www.sciencedaily.com/releases/2017/06/170601124055.htm

That we need sampling rates of >100kHz.

Aahhh that's conflating two things.

In that case we are talking about inter aural timing, the difference between reception time of the 2 ears.

Time resolution in sampling systems is *not* related to sample rate. Its another misconception.

Let me find the video, hang on

 

[MZKM]

Aahhh that's conflating two things.

In that case we are talking about inter aural timing, the difference between reception time of the 2 ears.

Time resolution in sampling systems is not related to sample rate. Its another misconception.

Let me find the video, hang on

Yeah, it was my misconception, I thought the other user was talking about missed sounds, not small timing differences.

 

[pozz]

However, the other user also claimed that since research has shown that even 10 microseconds (1/100,000) is perceivable in regards to sound localization:
https://www.sciencedaily.com/releases/2017/06/170601124055.htm

That we need sampling rates of >100kHz.

I've seen that 10 microsecond number quoted in The Physics and Psychophysics of Music by Juan Roederer. I don't know of any work done tying it to music reproduction specifically.

 

[March Audio]

Brilliant video, watch it all, but specifically from 20:53

 

[MZKM]

Brilliant video, watch it all, but specifically from 20:53

I have, just forgot that of course a signal that is so short must be a very high frequency (I blame the cold I have right now).

 

[LTig]

Just updated my comment, as I misunderstood the other user:

What happens if two sounds are 1/50,000 of a second apart in a recording, would the beginning of each sound be reconstructed?

Yes.

 

[LTig]

However, the other user also claimed that since research has shown that even 10 microseconds (1/100,000) is perceivable in regards to sound localization:
https://www.sciencedaily.com/releases/2017/06/170601124055.htm

That we need sampling rates of >100kHz.

No, we don't. People who claim this have not understood what Nyquist and Shannon have mathematically proved.

 

[LTig]

No it wouldn't.

A Transient that occurs between samples is by definition a higher frequency than the bandwidth of the system.

No, a single transient contains energy in a very wide range of frequencies starting at 0 Hz (DC). The part of energy which is below the Nyquist frequency is captured and reproduced.

 

[March Audio]

No, a single transient contains energy in a very wide range of frequencies starting at 0 Hz (DC). The part of energy which is below the Nyquist frequency is captured and reproduced.

I wasn't talking about a Dirac pulse, but yes you are correct.

An audio transient is not, and would never be a single uni directional excursion.

The question, by definition, referring to signal content above system bandwidth.

 

[LTig]

I wasn't talking about a Dirac pulse, but yes you are correct.

An audio transient is not, and would never be a single uni directional excursion.

But even then it would contain low frequencies.

 

[March Audio]

But even then it would contain low frequencies.

Yes, already said you are correct

My wording was poor. I have rephrased my initial response to say

A Transient that occurs between samples by definition contains higher frequency signals than the bandwidth of the system.

So no the original transient will not be reproduced, only content that falls within the bandwidth of the system.

However the important bit to note is that the timing resolution is still much higher than the sample rate implies.

 

[tmtomh]

Got into a discussion on another forum. Trying to see if a user‘s claims have any theoretical merit.

So, Nyquist states that if you sample >2x the frequency range you want, it can reproduce that range perfectly (with quantization noise). However, what if there was a super short transient (say 1/45,000 of a second), and if that occurs between the samples (44.1kHz sampling), would it get reconstructed? This is or course not audible at all, but the discussion was if it would be present in the recording.
I‘m an idiot.

You are not an idiot. This is a very common point of confusion about digital sampling. Partly it's because there are elements of digital sampling theory that do not seem intuitive, at least initially. And part of it is because we've all had the nonsense "digital is blocky stair step" claims and diagrams shoved down our throats ever since CDs became commercially available 35+ years ago.

At some point in the past, many of us probably have had the same epiphany you have about this exact issue.

 

[PaulD]

Interesting question! I just read the linked paper - at least the online links to it - and it never seems to mention 1/45,000 of a second, and it's testing mice and gerbil brains... It DOES mention that mammalian brains have developed a specialised structure with minimal synaptic delays (SD) because accurate LF sound localisation requires better timing precision than the general nervous system! That's pretty damn interesting (I teach some of this stuff at uni), it describes the physical changes in the cellular structures required to achieve this. Looks like it was a survival advantage to be able to do this, and we developed a specialised mechanism for it - super! The paper also goes on to say hundreds of microsecond timing precision is required to do this.

"Overall, we found a similar overall trend of increasing SD when comparing onset (385.6 ± 46.2 µs, mean ± standard deviation) to ongoing responses (439.6 ±73.0 μs, mean ± standard deviation, Fig. 2A)." It is examining gerbil and mouse brains.

Later the paper says "Functionally, stable synaptic delays seem to represent a specific adaptation for faithful ITD processing, because it would prevent fluctuations in the relative timing of direct excitation and indirect inhibition for responses to onsets vs. ongoing sounds in the range of tens to hundreds of microseconds. Such fluctuations may be negligible for most neuronal computations, but not for microsecond ITD processing of low-frequency sounds."

Since timing accuracy is not related to sampling frequency, this is all rather moot and you can go back to your other forum with confidence that this is not related to their audio systems and listening in any way. Trying to make such a claim is a VERY long stretch, and really just grasping on something to reinforce a prior prejudice.

Hope that helps! (BTW, the full article is here https://www.pnas.org/content/114/24/E4851)