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Understanding Sample Rate


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50 minutes ago, beerandmusic said:

i "think" this coincides with my statement that with greater sample rate comes greater accuracy to the point where engineering cannot process without error?


Sample rate guarantee nothing. But if limit frequency band of "accuracy" (0 ... 20 kHz, as example), higher sample rate give easier abilities to proper analog filter building.

Real digital-analog conversion always have errors.

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15 minutes ago, audiventory said:

 higher sample rate give easier abilities to proper analog filter building.

what is your opinion regarding example  unlimited frequency band between 300 and 301 hz.....

 

example:

300.0000001

300.000000000000000000000001

300.00000000000000000000000000000000000000001

to infinite number of 0's?

 

these frequencies can exist in real world and are audible.

if you have many of these infinite frequencies starting and stopping in time, in your honest opinion can all be captured with perfect accuracy at 700hz sample rate.

 

 

 

 

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26 minutes ago, beerandmusic said:

what is your opinion regarding example  unlimited frequency band between 300 and 301 hz.....

 

example:

300.0000001

300.000000000000000000000001

300.00000000000000000000000000000000000000001

to infinite number of 0's?

 

these frequencies can exist in real world and are audible.

if you have many of these infinite frequencies starting and stopping in time, in your honest opinion can all be captured with perfect accuracy at 700hz sample rate.

 

 

 

 

Now the Russians KNOW you're clueless.

 

And an infinite  series of zeros can't have a one at the 'end' :D

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1 hour ago, Spacehound said:

Now the Russians KNOW you're clueless.

 

And an infinite  series of zeros can't have a one at the 'end' :D

 

It is not permitted to call other members clueless !

 

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10 hours ago, beerandmusic said:

 

and i agree to disagree...in the poll that is running more than 2 to 1 believe that 44.1K is not the end all game.

 

According to the Oxford Dic "belief is an acceptance that something exists or is true, especially one without proof."

 

You have been presented with proof and yet you choose to believe because you don't like or agree with the facts. What else is there to discuss?

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1 hour ago, beerandmusic said:

what is your opinion regarding example  unlimited frequency band between 300 and 301 hz.....

 

example:

300.0000001

300.000000000000000000000001

300.00000000000000000000000000000000000000001

to infinite number of 0's?

 

these frequencies can exist in real world and are audible.

if you have many of these infinite frequencies starting and stopping in time, in your honest opinion can all be captured with perfect accuracy at 700hz sample rate.

 

The frequencies can be captured with perfect accuracy in your example, with two caveats.

First, the extra frequencies generated by their starting and stopping must not exceed 350 Hz. (The more abruptly they start and stop, the higher the frequencies that will be generated. Remember, a sudden start or stop is a transient.)

 

Second, the closer the frequencies are together, the more accurately you must record them. The Shannon-Nyquist theorem assumes that the accuracy is infinite. In real world digital, the accuracy is limited by the bit depth. Alternatively, the closer the frequencies are together, the longer you must record them.

 

You can see this by trying to tell the frequencies apart.

Take the frequencies

300.1 Hz

300.01 Hz

To tell them apart, you can measure the duration of one cycle. To do this, you need to know very accurately where the cycle begins and ends. With perfect resolution, this is easy. But with real digital, the cycle begin and end  will vary slightly due to quantisation error (the bit depth or resolution). The closer the frequencies are together, the higher the bit depth you will need per sample.

 

The alternative measurement method is where you count cycles for a known time.  The problem with this is that you have to count whole cycles.

So for 300.1 Hz, you need to count for 10 seconds to arrive at 3001 cycles.

But for 300.01 Hz, counting for 10 seconds would only give a count of 3000.

For 300.01, you would have to count for 100 seconds, to give 30001 cycles.

 

In summary, to record (or measure) very close frequencies you need high bit depth or long duration. So the final answer to your question is, "it depends..."

 

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The forum would be a much better place if everyone were less convinced of how right they were.

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3 hours ago, beerandmusic said:

what is your opinion regarding example  unlimited frequency band between 300 and 301 hz.....

This is limited band, because "between..." term there. May be you meant unlimited precision? The precision do not depend on sample rate and bit depth.

Analog filter have abour 20 .. 48 dB per octrave (range = 2 times between low and high borders).

When we use digital filters we works with -200 dB at stop band of filter.

So 200 dB / 48 dB ~ 4 octaves = 20000 Hz * 2^4 = 320 000 Hz.

I.e. there is need 300 kHz transient band to proper suppressing of aliases.

 

Thus sample rate should be 320 kHz * 2 = 640 kHz.

 

We can apply digital filter with transient band 20 ... 22 kHz from 0 to -200 dB. And it will almost ideal system.
Of course, we can "play" with the transient band to reducing of digital filter ringing.

However, may be issues with implementation 0 ... -200 dB and, may be, 0 ... -125 dB (for 24 bit) filter "on chip". Because there may be resource limitation of the chip.
-125 dB is taken because electrical noise of analog circuits about -120 dB is expected.

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2 hours ago, beerandmusic said:

can these errors that always exist be improved (not perfected but made more accurate) with higher sample rate?

 

Higher sample rate give abilities to work in higher frequency range of analog filter, where it have higher alias suppression.
See picture "Sigma-delta modulation and analog filter" here https://samplerateconverter.com/educational/r2r-ladder-dac-vs-sigma-delta

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2 hours ago, beerandmusic said:

 

example:

300.0000001

300.000000000000000000000001

300.00000000000000000000000000000000000000001

to infinite number of 0's?

 

Why don't you calculate the beat frequency between these (a simple task), and then consider if you are asking meaningful questions.

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So in practical terms, your three frequencies are same as a single tone, like the two forks in tune in this video.

As others have said, multiple frequencies combine into a waveform so if they are within the audible band then 16/44 will capture multiple frequencies just as well as a single tone.

 

 

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5 hours ago, Don Hills said:

Well, let's take the worst case and add an order of magnitude to be sure. Say 500 nano seconds.

 

1/(2pi * quantization levels * sample rate).

1/(2 pi * 8 * 44100) = 450 nano seconds if I've done the sum correctly.

That's 3 bits.

So even 3 bit encoding is more than enough as far as timing is concerned. You'd have trouble hearing a 3 bit (of 16) encoded signal at all, let alone discern a timing difference. And if you boosted it to normal listening levels it'd be too noisy to be called "hi fi". 

 

Can we agree that time resolution, even at 16/44.1, is a non issue?

I must correct you guys on one important thing regarding this calculation. The time accuracy depends on the frequency of the signal, not the sample rate. Instead of 44100 Hz in your formula, you must use the frequency of the signal. At 22050 Hz, 16-bit sampling gives an accuracy of 110 ps. At 1 kHz, it is about 2.5 ns. Another way of looking at it is that the sample precision determines the minimum detectable phase shift regardless of frequency. At higher frequencies, the same phase shift corresponds to a shorter time.

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12 minutes ago, mansr said:

I must correct you guys on one important thing regarding this calculation. The time accuracy depends on the frequency of the signal, not the sample rate. Instead of 44100 Hz in your formula, you must use the frequency of the signal. At 22050 Hz, 16-bit sampling gives an accuracy of 110 ps. At 1 kHz, it is about 2.5 ns. Another way of looking at it is that the sample precision determines the minimum detectable phase shift regardless of frequency. At higher frequencies, the same phase shift corresponds to a shorter time.

And for better time accuracy, 24 bit can give this without changing the sample rate.

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Just now, psjug said:

And for better time accuracy, 24 bit can give this without changing the sample rate.

Of course. Sample rate isn't even part of the calculation for time accuracy. Only signal parameters and sample precision matter. That said, the sample rate obviously needs to be high enough to capture the signal in the first place.

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As @mansr, says, the frequency quantization or time accuracy depends on the sample precision. The sample precision is limited by the baseline noise and can not be arbitrarily reduced by “better electronics” because the uncertainty principle determines the limit of our ability to reduce “noise”.

 

This is no real concern waveforms add in known ways. It all works!

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27 minutes ago, mansr said:

Of course. Sample rate isn't even part of the calculation for time accuracy. Only signal parameters and sample precision matter. That said, the sample rate obviously needs to be high enough to capture the signal in the first place.

 

I remember this from last year over in the "MQA is Vaporware" thread.

The formula with the sampling rate in it came from 'JJ' Johnston. I'll ask him.

"People hear what they see." - Doris Day

The forum would be a much better place if everyone were less convinced of how right they were.

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1 hour ago, mansr said:

I must correct you guys on one important thing regarding this calculation. The time accuracy depends on the frequency of the signal, not the sample rate. Instead of 44100 Hz in your formula, you must use the frequency of the signal. At 22050 Hz, 16-bit sampling gives an accuracy of 110 ps. At 1 kHz, it is about 2.5 ns. Another way of looking at it is that the sample precision determines the minimum detectable phase shift regardless of frequency. At higher frequencies, the same phase shift corresponds to a shorter time.

I remember working thru this coming to the same conclusions.  People who should know better than me insisted the other formula was correct based upon sample rate.  In any case time resolution was below 10 microseconds people worry about. So I dropped it.

And always keep in mind: Cognitive biases, like seeing optical illusions are a sign of a normally functioning brain. We all have them, it’s nothing to be ashamed about, but it is something that affects our objective evaluation of reality. 

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6 minutes ago, Don Hills said:

 

I remember this from last year over in the "MQA is Vaporware" thread.

The formula with the sampling rate in it came from 'JJ' Johnston. I'll ask him.

Robert Stuart uses the same formula.  Working the geometry of sine waves I had the same idea as mansr. And that amplitude would matter.

 

Seems obvious that a 10 khz sine that barely changes the next sample by 1 LSB would have too small a difference in the same time period at 5khz.

And always keep in mind: Cognitive biases, like seeing optical illusions are a sign of a normally functioning brain. We all have them, it’s nothing to be ashamed about, but it is something that affects our objective evaluation of reality. 

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1 minute ago, esldude said:

I remember working thru this coming to the same conclusions.  People who should know better than me insisted the other formula was correct based upon sample rate.

They were wrong or answering a different question (what is the minimum time shift detectable an any frequency).

 

1 minute ago, esldude said:

In any case time resolution was below 10 microseconds people worry about. So I dropped it.

At 20 Hz we get a precision of 120 ns. Really nothing to worry about. Those minimum phase filters people seem to like do a lot more damage.

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1 hour ago, psjug said:

And for better time accuracy, 24 bit can give this without changing the sample rate.

 

Could you elaborate a bit on this?

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13 minutes ago, esldude said:

Robert Stuart uses the same formula.  Working the geometry of sine waves I had the same idea as mansr. And that amplitude would matter.

 

Seems obvious that a 10 khz sine that barely changes the next sample by 1 LSB would have too small a difference in the same time period at 5khz.

Correct, and amplitude matters too. In the formula, the figure for the number of levels should be in relation to the signal peak, which might be smaller than the maximum possible.

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Just now, psjug said:

I think someone else probably has the formula on hand and can post it.  @mansr already said that sample rate is not part of the calculation.

 

Ok, thanks. It would be nice to understand this.

"Science draws the wave, poetry fills it with water" Teixeira de Pascoaes

 

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