Correlation between sample rate and audible frequency?

[IowAudio]

I read an article probably years ago now that mention higher sample rates can benefit some people with very good hearing and trained ears because it has a lower auditoy time delay. Something to do with how fast your ears or brain can distinguish differences in sound like dynamic range, tone, tamber, pitch etc. Usually lands somewhere in the 6 to 10 milli second range. Basically said higher sampling rate = more samples per second = more changes in sound per milli second = smoother more realistic sound. Idk I vaguely remember the article. I've never been wowed by high sample rates really. I find a better recording and mastering makes a bigger difference.

 

[NTK]

I read an article probably years ago now that mention higher sample rates can benefit some people with very good hearing and trained ears because it has a lower auditoy time delay. Something to do with how fast your ears or brain can distinguish differences in sound like dynamic range, tone, tamber, pitch etc. Usually lands somewhere in the 6 to 10 milli second range. Basically said higher sampling rate = more samples per second = more changes in sound per milli second = smoother more realistic sound. Idk I vaguely remember the article. I've never been wowed by high sample rates really. I find a better recording and mastering makes a bigger difference.

From Wikipedia, (Nyquist–Shannon sampling theorem) and here is an excerpt from the introduction.

Sampling is a process of converting a signal (for example, a function of continuous time and/or space) into a sequence of values (a function of discrete time and/or space). Shannon's version of the theorem states:[2]

If a function x(t) contains no frequencies higher than B hertz, it is completely determined by giving its ordinates at a series of points spaced 1/2B seconds apart.​

A sufficient sample-rate is therefore anything larger than 2B samples per second. Equivalently, for a given sample rate fs perfect reconstruction is guaranteed possible for a bandlimit B < 2 fs.

In other words, you can reproduce exactly a signal with contents up to frequency fs/2 Hz when it is sampled at frequency fs Hz. In practice, it is slightly lower than fs/2 because the anti-aliasing (low pass) filter cannot be a perfect brick-wall and has a finite slope.

Since it is generally accepted that the vast majority of human adults cannot hear above 20 kHz, the sampling rate of CD (44.1 kHz) is sufficient. Anything above is more than sufficient and is mostly to give a peace of mind.

 

[IowAudio]

Ok I found something similar to what I read years ago. Its not Auditory time delay. Its Auditory Temporal Processing and Temporal Resolution. Supposedly high sample rate audio has more samples per second allowing for more subltes and sudden changes in sound per second producing a higher resolution representation of music. Here's a link that kinda touches on this but I can't find the article I read years ago. I'm still not sold on hi-res audio or DSD.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5063729/#__sec1title

 

[hellboundlex]

The only convincing argument I have heard for high sample rates in the real world is that some DAW plugins sound "better" when used at 96 kHz and that some sample rate converters are terrible.

Practically, I have found that some of the "Hi-Res" music sounds better, but really because it was just mastered with newer and better equipment. Also, for reasons mentioned above, errors with sample rate converters, I like buying brand new music in the format the DAW spits out as the master. Usually that is 48/24, but sometimes 96/24.

I doubt I could tell the difference between these and 44.1/16, unless the resampling algorithm used was terrible.

[EDIT: One real world case is HDCDs. "Right in Time" by Lucinda Williams was my wedding song, and unlocking those HDCD bits years later made a difference in my appreciation of that album.]

Supposedly high sample rate audio has more samples per second allowing for more subltes and sudden changes in sound per second producing a higher resolution representation of music.

I don't think that link is relevant to sampling theory, although it explains my bad ear. For sampling theory explained in detail, see the first video on the first page of this discussion. It's brilliant.

 

[Julf]

Ok I found something similar to what I read years ago. Its not Auditory time delay. Its Auditory Temporal Processing and Temporal Resolution. Supposedly high sample rate audio has more samples per second allowing for more subltes and sudden changes in sound per second producing a higher resolution representation of music.

To repeat what NTK wrote: "In other words, you can reproduce exactly a signal with contents up to frequency fs/2 Hz when it is sampled at frequency fs Hz".

Notice "reproduce exactly". Including timing.

 

[andreasmaaan]

Ok I found something similar to what I read years ago. Its not Auditory time delay. Its Auditory Temporal Processing and Temporal Resolution. Supposedly high sample rate audio has more samples per second allowing for more subltes and sudden changes in sound per second producing a higher resolution representation of music. Here's a link that kinda touches on this but I can't find the article I read years ago. I'm still not sold on hi-res audio or DSD.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5063729/#__sec1title

In any case, even the most discriminating of musicians in that study was capable of gap detection of no better than 1.6ms, which corresponds to about 70 samples at 44.1kHz.

Duration discrimination was even worse, at no better than 17ms (approx. 750 samples at 44.1kHz).

 

[mansr]

https://troll-audio.com/articles/time-resolution-of-digital-audio/

 

[BDWoody]

Supposedly high sample rate audio has more samples per second allowing for more subltes and sudden changes in sound per second

That's not really how it works...

That article had nothing to do with sampling theory.

It's not like connect the dots where more dots is a smoother line.

 

[Wes]

 

[JustAnandaDourEyedDude]

To repeat what NTK wrote: "In other words, you can reproduce exactly a signal with contents up to frequency fs/2 Hz when it is sampled at frequency fs Hz".

Notice "reproduce exactly". Including timing.

What about a single tone of any non-zero amplitude and of frequency fs/2 Hz, and sampled at fs Hz, but the timing happens to be such that the samples are taken at the zero crossings of the signal? Curious whether this gets aliased to a zero frequency signal of zero amplitude in the DFT representation. Too lazy to go through the math

 

[hellboundlex]

What about a single tone of any non-zero amplitude and of frequency fs/2 Hz, and sampled at fs Hz, but the timing happens to be such that the samples are taken at the zero crossings of the signal? Curious whether this gets aliased to a zero frequency signal of zero amplitude in the DFT representation. Too lazy to go through the math

Answered on video by Monty Montgomery on first page. It works, and he proves it with an experiment.

Edit: fs/2 is too close, but in theory any number less than is fine, in practice you better have a perfect low pass filter.

Edit 2: I believe, actually, your question contains a proof that it wouldn't work for fs/2 and perfectly demonstrates why.

 

[JustAnandaDourEyedDude]

Answered on video by Monty Montgomery on first page. It works, and he proves it with an experiment.

Edit: fs/2 is too close, but in theory any number less than is fine, in practice you better have a perfect low pass filter.

Okay, thanks for clarifying that.

 

[JustAnandaDourEyedDude]

Answered on video by Monty Montgomery on first page. It works, and he proves it with an experiment.

Edit: fs/2 is too close, but in theory any number less than is fine, in practice you better have a perfect low pass filter.

Edit 2: I believe, actually, your question contains a proof that it wouldn't work for fs/2 and perfectly demonstrates why.

Yes, something special about the corner frequency.

 

[scott wurcer]

What about a single tone of any non-zero amplitude and of frequency fs/2 Hz, and sampled at fs Hz, but the timing happens to be such that the samples are taken at the zero crossings of the signal? Curious whether this gets aliased to a zero frequency signal of zero amplitude in the DFT representation. Too lazy to go through the math

Folks constantly dwell on the limiting cases of a theory to try and imply that it is never valid.

 

[JustAnandaDourEyedDude]

Folks constantly dwell on the limiting cases of a theory to try and imply that it is never valid.

I am not one of those illogical folks. Theorems are theorems, and math is a subject I greatly admire, along with physics. I coded the DFT a long time ago, to process computational acoustic data of self-noise (due to turbulence) of a fluid jet. But soon after that I found FFTW on the web, and deleted my little DFT routine.

 

[JustAnandaDourEyedDude]

Taking a second look at the Wikipedia page in question, it does state precisely that B < fs/2, a strict inequality. And there is a section titled "Critical Frequency" which explains why the inequality is strict, along with the last figure on the right which I am guessing illustrates the most general form of the ill-determination that I referred to.

 

[thewas]

Exactly, it is an inequality.
Also what people easily forget that Shannon's theorem is only about the time discretization but not the value discretization which also happens at an analogue to digital conversion, so due to the second the input and output won't be usually exactly the same, but with the wisely chosen 16 bits value discretization depth of the 1982 CD players standard the discretization errors are small enough to be inaudible.

 

[ReaderZ]

I always thought you can use 24/192 and still use all the bits to record useful information that's mostly in audio-able range and not up to 96khz which no one can hear anyway.

 

[Julf]

I always thought you can use 24/192 and still use all the bits to record useful information that's mostly in audio-able range and not up to 96khz which no one can hear anyway.

Not quite sure what that means. If you use a 192 kHz sampe rate, 75% of the bits are wasted. 24 bits is also overkill - have you come across a commercial recording (or domestic listening room) with a noise floor low enough to allow eve a 96 dB dynamic range?

 

[Frank Dernie]

Folks constantly dwell on the limiting cases of a theory to try and imply that it is never valid.

Exactly.
Like the response to a single full scale sample at ½ sampling rate.
How often does a half cycle at 22.05kHz happen in music and how many of us can hear it?
Count them on the thumbs of one foot.