Understanding Sample Rate

[beerandmusic]

4 minutes ago, kumakuma said:

 

Did you even bother to read what he wrote?

I read what mansr, jabbr, crenca and many others write, but I typically don't read what you write (wink)...you fall in a different category...but i see you still read and reply to me....prefer you didn't.

[jabbr]

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

[kumakuma]

4 minutes ago, beerandmusic said:

I read what mansr, jabbr, crenca and many others write, but I typically don't read what you write (wink)...you fall in a different category...but i see you still read and reply to me....prefer you didn't.

 

[mansr]

7 minutes ago, jabbr said:

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. 

Seems like we're in agreement.

[mansr]

8 minutes ago, beerandmusic said:

I read what mansr, jabbr, crenca and many others write, but I typically don't read what you write (wink)...you fall in a different category...but i see you still read and reply to me....prefer you didn't.

Not cool.

[beerandmusic]

4 minutes ago, mansr said:

Not cool.

what? that i respect you but not kumakuma?

sorry, but even I have my standards....

Do you suggest I have to respect idiot followers that do little but ridicule?  He's far from the worst, but i would put him in bottom 20%.

[jabbr]

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 ...

[Ralf11]

reminds me of the Berkeley Physics series chapter on particle in a box of rain

[fas42]

It possibly could help some people understand how 'powerful' sampling is in retaining everything, by playing around in software like Audacity - get or generate a waveform which is chockerblock of stuff above the audible range, as complex as you like; resample at 44.1kHz - voila, everything above 22k disappears - and if you isolate the 10 - 20k range now, it "looks awful". Next step, resample that to the extremely high rate that the original was in, and subtract the two: everything below 22k vanishes completely ... meaning, absolutely nothing was lost in the conversion to the Redbook standard, in the conventional audio range.

[crenca]

20 minutes ago, beerandmusic said:

 

or to be said in a different way, all sound can be accurately captured by sampling 44000 times in a second or 264000 times in a minute ....i call hogwash.

 

 

 

Putting aside your specific math, why not?  What is it about a waveform that you believe is complex, such that a finite sample rate can not describe a finite reality?  Do you assume a waveform is an infinite reality - essentially, unmeasurable? Is a waveform a transcendent reality, a kind of god?

 

Let's say you have 3 singers in the room with you, and you ask them to all sing at the same time.  How many waveforms are you hearing when they do this?  Let's say there are 300 singers in a large hall - how many waveforms are you hearing?

[beerandmusic]

2 hours ago, crenca said:

 

Folks keep telling you your "thinking is incorrect" but not why.

 

The reason is because of what mansr said, your understanding of frequency incorrect because you think it is "complex".  You are imagining that frequency somehow captures each of those "9 million" singers.  It does not, it captures a composite of those 9 million singers.  The frequency is thus simple - it is one (and not many).  

 

I am simplifying a bit for obvious purposes...

but the composite is changing every quanta time and the average is one of an infinite amount of possibilities....even between 600 and 700hz there is an infinite number of compositions, and changing an infinite amount of times in less than a pico second....the question again is what is discernible, not what is actual or accurate.

[beerandmusic]

7 minutes ago, crenca said:

 

Putting aside your specific math, why not?  What is it about a waveform that you believe is complex, such that a finite sample rate can not describe a finite reality?  Do you assume a waveform is an infinite reality - essentially, unmeasurable? Is a waveform a transcendent reality, a kind of god?

 

Let's say you have 3 singers in the room with you, and you ask them to all sing at the same time.  How many waveforms are you hearing when they do this?  Let's say there are 300 singers in a large hall - how many waveforms are you hearing?

 

for what i tried to describe previously....

 

one sample or 1/44000 of a second, call it T1, you can have an infinite number of different frequencies all within 600 to 700 hz (which the composite can be equally infinitie) and occur an infinite amount of times between T1 and T2.

 

granted, man may not be able to distinguish between 600.000001 and 600.000002 but that does not mean the frequency does not exist.  Then take a complex waveform of multiples of these same frequencies and you can sure average them out and say you cannot discern, but that is not to say they do not exist.

[fas42]

Hmmm ... a brick wall comes to mind ...

[crenca]

1 minute ago, beerandmusic said:

but the composite is changing every quanta time and the average is one of an infinite possibilities....even between 600 and 700hz there is an infinite number of compositions, and changing an infinite amount of times in less than a pico second....the question again is what is discernable, not what is actual or accurate.

 

Ah, but what is the rate of that change?  Your not saying that the change is radom - at one point in time going this way, and at another point in time going another way.  No, the waveform - that which is changing - is changing in an orderly way correct?  Your not asserting sound is simply chaos, or is random movement like heat?  Why would a creature benefit from the sensory perception of pure randomness?  No, a waveform is an orderly change, and that order can be measured (and in the case of our hearing, sensed and perceived).

 

Your emphasizing the wrong thing in your imagination.  Try to imagine order in the chaos, a form in the midst of infinity...

 

 

[beerandmusic]

Or to put it even differently...and put simply...

 

man can hear both 600.00001 and 600.00002 frequencies very easily.  They cannot discern between them, but if

2 minutes ago, crenca said:

 

Ah, but what is the rate of that change?  Your not saying that the change is radom - at one point in time going this way, and at another point in time going another way.  No, the waveform - that which is changing - is changing in an orderly way correct?  Your not asserting sound is simply chaos, or is random movement like heat?  Why would a creature benefit from the sensory perception of pure randomness?  No, a waveform is an orderly change, and that order can be measured (and in the case of our hearing, sensed and perceived).

 

Your emphasizing the wrong thing in your imagination.  Try to imagine order in the chaos, a form in the midst of infinity...

 

 

Agree....this is where i completely blew all of this stuff off, when the suggestion comes into play about transition...the point being, in a complex waveform you can have an infinite number of transitions starting, occuring, and stopping in any fraction of any timeslice.

[crenca]

4 minutes ago, beerandmusic said:

 

 

one sample or 1/44000 of a second, call it T1, you can have an infinite number of different frequencies all within 600 to 700 hz (which the composite can be equally infinitie) and occur an infinite amount of times between T1 and T2.

 

 

 

No you can not  - or there would be no such thing as "frequency" .  A frequency is an orderly waveform defined and bound by both time and the rate of the movement of the medium.  You are claiming that the medium (in this case air) can move in more than one direction at the same time - "infinitely".   Essentially, you are claiming that waveforms don't exist...

 

[crenca]

Just now, beerandmusic said:

Or to put it even differently...and put simply...

 

man can hear both 600.00001 and 600.00002 frequencies very easily.  They cannot discern between them, but if

Agree....this is where i completely blew all of this stuff off, when the suggestion comes into play about transition...the point being, in a complex waveform you can have an infinite number of transitions starting, occuring, and stopping in any fraction of any timeslice.

 

What is, exactly, a "complex waveform"?  Further, are you claiming sound is this complex waveform?

[beerandmusic]

5 minutes ago, crenca said:

 

Ah, but what is the rate of that change?  Your not saying that the change is radom - at one point in time going this way, and at another point in time going another way.  No, the waveform - that which is changing - is changing in an orderly way correct?  Your not asserting sound is simply chaos, or is random movement like heat?  Why would a creature benefit from the sensory perception of pure randomness?  No, a waveform is an orderly change, and that order can be measured (and in the case of our hearing, sensed and perceived).

 

Your emphasizing the wrong thing in your imagination.  Try to imagine order in the chaos, a form in the midst of infinity...

 

 

If you try to apply order, that may be easier to apply to math, but in reality, there is no order.

[beerandmusic]

Just now, crenca said:

 

What is, exactly, a "complex waveform"?  Further, are you claiming sound is this complex waveform?

I am a layman, but i do have a high iq, and i am certain i don't have the correct terminology....when i say a complex waveform, I am just talking about a waveform with a lot of frequencies....or a composition if you will.

[crenca]

1 minute ago, beerandmusic said:

If you try to apply order, that may be easier to apply to math, but in reality, there is no order.

 

If that were the case, then sound itself, to say nothing of sound reproduction would not exist - it would be an impossibility.

 

What is real, is the somewhat counter-intuitive fact that sound is a relatively simple (and simply described) waveform phenomena that even the crudest of 19th century electronics could reproduce.

[beerandmusic]

8 minutes ago, crenca said:

 

No you can not  - or there would be no such thing as "frequency" .  A frequency is an orderly waveform defined and bound by both time and the rate of the movement of the medium.  You are claiming that the medium (in this case air) can move in more than one direction at the same time - "infinitely".   Essentially, you are claiming that waveforms don't exist...

 

you can have a million different frequencies occuring at any time....take example of a million different frequencies all between 600 and 700 hz such the composition averages to 650hz in one pico second 651 in another pico second etc....but then granulate it even smaller.....e..g... 650.00001, 650.0005, etc...

are they discernable, no....is one more accurate than the other depending on sample rate...yes.

[crenca]

3 minutes ago, beerandmusic said:

I am a layman, but i do have a high iq, and i am certain i don't have the correct terminology....when i say a complex waveform, I am just talking about a waveform with a lot of frequencies....or a composition if you will.

 

What is sound at any point in time (remember your basic math and physics- a point has no dimensionality) - is the waveform complex or singular?

[tmtomh]

7 minutes ago, beerandmusic said:

 

or to be said in a different way, all sound can be accurately captured by sampling 44000 times in a second or 264000 times in a minute ....i call hogwash.

 

Calling hogwash on digital sampling theory is like calling hogwash on the theory that a feather and a bowling ball dropped from the same height will (in the absence of air resistance) hit the ground at the same time. It's not a matter of opinion; it's a proven scientific theory. If digital sampling theory were untrue in the way you are suggesting, then digital music systems simply wouldn't work.

 

Frequencies are not additive: If  you and I both strike the same 440Hz A note/key on two different pianos at the same time, the result will not be an 880Hz fundamental. It will be a 440Hz fundamental, but at twice the amplitude as if you'd just played the key on your piano (assuming ideal miking/listening conditions and no phase cancellation). A 44.1k sample rate and a 192k sample rate system will both capture that 440Hz sound, with equal accuracy.

 

In fact, for a 440Hz note, a digital sampling system operating at only a 0.88kHz sample rate would still capture that 440Hz note, just as accurately (putting aside for simplicity's sake the practical need for some "cushion" for filtering out other frequencies above Nyquist for that system - so to be generous we'd use perhaps a 2kHz sample rate just to be safe; still a tiny fraction of 44.1kHz).

 

Yes of course the sample rate describes how many times per second the signal gets sampled. But the function of sample rate is not to sample the music really fast so we don't notice the "gaps" between the samples. We never listen to the digital samples - we listen to a continuous, smooth, analogue waveform that is reconstructed by a DAC from those digital samples.

 

The function of sample rate is to describe/encode a range of frequencies. A 44.1k sampling rate actually is capable of sampling frequencies above 22.05k: if you feed higher frequencies into an unflitered 44.1k sample-rate system, it will encode them - and that's a problem. When you have 44,100 samples per second, frequencies above and below 22.05kHz can be represented by the same binary sample code. So frequencies must be limited to half the sample rate in order to ensure that each binary sample (aka digital word) corresponds to one and only one unique frequency.

 

So an 88.2k, 96k, or 192k sample rate permits the capturing of higher frequencies. It does not capture frequencies below 22.05k more smoothly or precisely than a 44.1k sample rate. The "speed" or frequency of the sample rate correlates with with the "speed" or frequency of each sound - the oscillation of the sound wave. The speed or frequency of the sample rate does not have anything to do with making the reconstructed waveform sound more "precise" or "smooth" by capturing the original sound more times per second. Again, a 0.88kHz sample rate system will reconstruct the frequencies it's capable of encoding with exactly the same precision, "smoothness," and "refinement" as a 192k system - the 0.88k system just will be able to encode a far narrower range of frequencies.

 

Similarly, increased bit depth allows for more dynamic range because it creates a lower noise floor. But increased bit depth does not allow for more or smoother gradations of volume within the same range of volumes. To oversimplify, 16-bit gives about 96dB of dynamic range while 24-bit gives about 144dB. You can't squeeze 24 bits' worth of volume gradations or "resolution" into 96db worth of volume range. It doesn't work like that.

[beerandmusic]

3 minutes ago, crenca said:

 

If that were the case, then sound itself, to say nothing of sound reproduction would not exist - it would be an impossibility.

 

What is real, is the somewhat counter-intuitive fact that sound is a relatively simple (and simply described) waveform phenomena that even the crudest of 19th century electronics could reproduce.

 

Let's talk about real...

 

what does 600hz sound like

what does 600.000001 sound like

 

no one can discern the difference, but both are very real and both are very easily heard.

one can be a composite of 2 frequencies at T1 and the other at T2, but if T1.5 was averaged in (that doesn't exist) , it would be 600.000005, which would be more accurate...

[crenca]

2 minutes ago, beerandmusic said:

you can have a million different frequencies occuring at any time....take example of a million different frequencies all between 600 and 700 hz such the composition averages to 650hz in one pico second 651 in another pico second etc....but then granulate it even smaller.....e..g... 650.00001, 650.0005, etc...

are they discernable no....is one more accurate than the other depending on sample rate...yes.

 

Sample rate does not describe the points (i.e the discernable differences), but rather the rate of change in the waveform - and it calculates this fully (i.e. there is no error) and thus it fully describes the waveform.

 

Think of it this way - you are counting the atoms - no, the subatomic particles in the paint of the Mona Lisa - you have forgotten what a painting is - she is a waveform, not the particles themselves...