Understanding Sample Rate

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1 hour ago, beerandmusic said:

So the sampling itself is just an approximation or probable of what that timeslice sounds like...it is not accurate, and a higher sampling rate would be more accurate.

 

No. If the signal is bandwidth limited, and the sample rate is sufficient (e.g. 2x) then the sampling is accurate. That's the point.

 

 

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Just now, beerandmusic said:

 

this doesn't take into consideration the infinite frequencies...

It doesn't take into account other things that don't exist.

 

At some point you will run into physics no matter how hard you resist.

Shit like Nitrogen and Oxygen atoms, Brownian motion -- you know, the stuff Einstein got a Nobel prize for ... and shit like quantum equations ... but no matter

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6 minutes ago, beerandmusic said:

e.g. what does 9million singers sound like compared to 10 million singers sound like?

 

Ok, so lets suppose each singer produces a bandwidth limited signal 20-20kHz (for the sake of discussion), and lets assume the sounds are linearly additive (for the sake of discussion). 9million vs 10million singers will still be 20-20kHz bandwidth limited *but* the signal itself may have a higher dynamic range e.g. the bit depth would be greater.

 

At this point the discussion would be whether 20 vs 24 bits is enough of a bit depth, rather than the sampling frequency.... this is all math.

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1 minute ago, beerandmusic said:

 

 

are you suggesting that an infinite amount of frequencies don't exist?

or just that they may not be discernible to hearing?

 

I know they aren't relevant to hearing.

 

They don't exist for sound transmission in air.

 

According to my understanding of physics, they don't exist in the universe.

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23 minutes ago, mansr said:

I don't see the photoelectric effect being of particular relevance here.

 

Its rather interesting history of our quantum understanding of physics. Series of papers not just the "photoelectric effect" but essential for the concept of a light "wave" being understood as a quantized photon. Thus we understand the universe, and via other papers including Einstein's general relativity but many many papers all together, where space-time itself via not a smooth continuum equation rather a quantized  equation. The point being that our fundamental understanding of the universe is quantized, and hence an infinite number of frequencies do not physically exist. I was asked this very question.

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11 minutes ago, beerandmusic said:

 

Let me ask this....

is it possible to have an infinite amount of frequencies between 600hz and 700hz?

e.g. is it not possible to have 600hz 600.001, 600.002, 600.003, etc...

whether it is discernible to hear the difference from one person's voice to another, not being the question.

 

 

Ah ... this is a good question, actually!

 

The uncertainty principle limits the number of closely spaced frequencies to be resolved in the same way as the Heisenberg uncertainty principle does for position and time i.e. the fourier transform

 

The number of resolvable frequencies is determined by the SNR of the signal and is not infinite.

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7 minutes ago, mansr said:

The quantisation is small enough that for practical purposes it doesn't exist. More importantly, the sampling theorem is fine with a true continuum of frequencies whether or not they can all physically exist.

That's a common misconception:

 

https://arxiv.org/pdf/1108.3135.pdf

https://arxiv.org/pdf/0802.1348.pdf

 

(you may need to read the references in these papers to understand)

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1 hour ago, mansr said:

I don't recall the sampling theorem relying on a quantised frequency.

 

Of course the sampling theorem works. Quantised frequency is where the fourier transform becomes the discrete fourier transform, and yes it also works. The uncertainty theorem determines the frequency resolution limits. The first article (Millette) discusses the relationship between Heisenberg Uncertainty Principle and Shannon-Nyquist! Remarkable actually. (1)

 

(1) https://www.researchgate.net/publication/280444525_The_Heisenberg_Uncertainty_Principle_and_the_Nyquist-Shannon_Sampling_Theorem

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1 minute ago, mansr said:

Seems like we're in agreement.

Yes, I hope so  

 

I wanted to clarify/support my assertion that frequencies are not infinite/continuous in the physical world. Don't typically like to invoke quantum mechanics here on CA but in this case ...

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15 minutes ago, beerandmusic said:

 

From what i read yesterday, it does both....most of these people are tied to just part of what increasing the sample rate does, while totally disregarding the other thing it does....

Look you are trying to be understand this by “thinking about it” without understanding the underlying math. To me this all sounds like you are trying and trying to argue that 1+1=3 ??‍♂️

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4 minutes ago, beerandmusic said:

 

 

 

provide the link again....does it also talk about the improved accuracy by the higher sample rate?  That is where my focus will be.

 

Increased accuracy by higher sampling rate is not present in PCM encoding the way you are imagining. Until you have a solid understanding of the basics, topics like multibit SDM are going to be hopeless.

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1 minute ago, beerandmusic said:

 

I do NOT want to talk about the highest possible frequency range, i want to talk about the accuracy of transitions occuring across the x asis.

Again, typically increasing the bit depth will increase the dynamic range.

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2 hours ago, beerandmusic said:

 

ok, well i am willing to put a couple hours into it...and see if my understanding is any better....and if not, people that suggeset SACD is not superior to CD, can just consider me ignorant even though my ears and my logic tell me differently.

 

You aren’t even addressing the comparisons between SACD and CD. 

 

Its not all like “if SACD is better than CD them I’m right” ... whether you prefer one format over the other has nothing to do with the mathematical concepts.

 

what is true about SACD namely single bit SDM, is that increasing bit rate does increase SNR and hence frequency resolution to a certain degree but unless you understand the math you won’t understand why. 

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With Sigma Delta Modulation, increasing the sampling rate does improve the “accuracy” but the presumption on this thread is that we are dealing with PCM. That’s why if you are trying to use this concept to compare SACD to CD it’s frought. In all cases whether increasing the bit depth in PCM or sampling rate SDM the limit is the SNR of the signal itself so blindingly increasing ceases to be a benefit. 

 

@beerandmusic you stated “CD” in the OP, hence the pushback but perhaps DSD/SDM is a more natural way for you to think? Hmmm ... it’s often though that SDM is less intuitive than PCM but it’s also described as “analog” and however, perhaps that’s how you are thinking about this?

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2 hours ago, beerandmusic said:

 

even man can create sound at an "infinite rate"...the plucking of a guitar for instance.

 

???

 

2 hours ago, beerandmusic said:

the complex waveform has an infinite number of frequencies, at an infinite number of time slices,  within it's own frequency range (between 50 and 300hz) that man just is not able to record accurately.

 

Aside from whether a truly infinite number of frequencies can exist — as I’ve said above they physically can’t — you should perform an exercise to demonstrate to yourself how close frequencies affect a common waveform:

 

Take an 8hz and a 10hz sine wave over a few seconds and additively combine the waves and plot. What do you see?

 

Take two 8hz waves having different phases and additively combine. What do you see?

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4 hours ago, mansr said:

Whether an infinite number of frequencies can exist isn't important in practice. What matters is that they can't be infinitely high.

 

Whether a frequency can be infinitely high is neither important in practice because you can't detect it. 

 

The uncertainty principle places a limit on the ability to resolve closely space frequencies and SNR.

 

In any case the range of frequencies is similar to the range of velocities. Both have instantaneous values when used to describe objects. Both are real numbers whose measured values are described/bounded by physics.

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15 minutes ago, beerandmusic said:

The more i read, the more i believe that i would want to sample more than just twice the highest frequency.....unless you just want "good enough".

 

That’s fine. A certain degree of over engineering is reasonable. So let’s say record at 24/96 or 24/192 ... but recording beyond that is really really hard pressed to justify any benefit (unless you were doing a ton of post-processing — even then)

 

On the other hand, upsampling for the purpose of improving the DAC is totally reasonable and an excellent technique — in fact the argument that you don’t need it would be the harder one to justify.

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3 hours ago, beerandmusic said:

I know many people here upsample everything to quad dsd and suggest it is notably better.

 

I upsample to DSD512 to feed to the iFI Micro DAC. This works great unless ... you start with DSD256 recordings in which case it chokes my system.

 

Having higher and higher res recordings just for the sake of it isn't necessarily better, it becomes worse.

 

But year upconverting to DSD works absolutely great for DACs that prefer DSD (lots and lots). In the same way upsampling PCM works great for DACs that prefer PCM (less but for example Phasure NOS1a)

 

So yeah I use @Miskas HQPlayer and @PeterSt XXHE to upsample/upconvert on the fly and they are absolutely great and I use @audiventory AuI for offline conversion (DSD ISOs -> DSF in particular!) --- but not for the reasons you are concerned with -- they are great because they make the DAC work better. This has to do with the DAC output filter. Upsampling does not add information to the system but it makes the sound coming out of the DAC better.

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2 hours ago, adamdea said:

Hmm alot of people go along with recording up to 96khz (but probably still distribution at 44.1) but quite a few people argue that 192 is actually too much. The problem is that you are actually letting in a whole lot of spuriae which might be better filtered out and in any event not all the editing and production tools work at that rate anyway. 

 

Yeah if the master is at 24/192 then that's what i'd like and if at 24/96 then that, or if the master is at DSD64,128 or even 256 then that's what I'd like. I have no control of how the master is created but I'd like the recording as close to the master as possible/if possible and I can handle any conversion I want to do from there.

 

You know @beerandmusic, just consider obtaining source material (music) as above, and use software as above to convert to whatever format your DAC prefers ... and don't worry -- its all good  

 

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3 hours ago, beerandmusic said:

My main objective for this thread really is a totally different issue anyway, and really had to do with why an SACD sounds better than a CD, and i thought everyone believed that, but apparently not....

 

Do an experiment for yourself:

 

1) start with a CD source.

2) compare sending the CD source files directly to your DAC vs. convert to DSD and send to your DAC

 

Which do you like better?

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9 hours ago, audiventory said:

Sometimes for improving of played back sound need to cut information. I mean ultrasound, that can cause audible distortions due intermodulations. The intermodulation products may be listened as noise. In this case cutting of ultrasound above 20 kHz can remove noise.

Oohh ... a system that produces IM distortion with information only above 20 kHz is not so well designed. 

 

Typical DSD DACs might use 80-100 kHz as a corner for the filter.

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5 hours ago, beerandmusic said:

the theorem does not speak to infinite frequencies that really exist.

 

it has criteria of a "band limited signal", which i do not understand, and it is my current belief, that it is in that criteria that makes it not applicable.

 

You remain stuck on this idea of infinite frequencies. ??‍♂️ Do you accept that a physical velocity cannot exceed the speed of light? Why would you think a physical frequency could be infinite? Consider calculating the kinetic energy of a particle having such a frequency ...

 

In any case as @mansr noted above, when doing wideband recordings we don’t see frequencies above 100 kHz (at best) so in that case you should be quite happy with 192kHz sampling and call it a day. 

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2 minutes ago, beerandmusic said:

 

infinite number of frequencies and infinite number of time slices.

Nope

[jabbr]

2 minutes ago, beerandmusic said:

nope what?

No infinite frequencies period — read the papers I posted

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6 hours ago, beerandmusic said:

 

infinite number of frequencies and infinite number of time slices.

 

Here is what should be an understandable explanation about why there aren’t an infinite number of distinct frequencies between say 1kHz and 2kHz:

 

When 2 equal amplitude waves are supposed (added together) the resultant wave frequency is the mean of the 2 and the amplitude varies with a frequency which is the difference between the two.

 

There are many examples on the web which explain and graph this — take a look. 

 

As two waves of slightly different frequencies are added and as the frequencies move closer together, the amplitude variation lessens to the point where it cannot be resolved within the signal SNR. It is not possible of improve the SNR without limit, At this point the two frequencies are indistinguishable. This is the uncertainty principle applied to frequency. The limit of SNR is the uncertainty principle applied to amplitude — essentially the Heisenberg Uncertainty Principle. 

 

In s digital system, the bit depth forms and be bound on the SNR aside from the physical bound in the SNR. This is why a discrete Fourier transform works with a finite number of bins.