abb

drewfx1

gswitzDrewFX, what would the time resolution of 24 bit 48kHz be? Can you figure it out? I'm curious.
 

Something on the order of 0.0000000000002 seconds.

How did you compute this value?

1/(2 * pi * quantization levels * sampling frequency)
where quantization levels = 2^(bit depth)
 
This is a theoretical limit. In reality, it's not going to be that good.

Anderton I don't know but I don't see how it relates to the question I'm asking. 

It means that for a properly band limited signal, sampling preserves timing information to a tiny fraction of the sampling period.

Bring on the quantum sampler...

Anderton

John
If I have this right the above from Craig is the argument about resolution or how many slices are being made at any given time.
 
From what I understand is it has no impact. 

That's where the controversy lies. Of course reconstruction will reconstruct a waveform; no question about that, otherwise the outputs of digital audio systems would be stair-stepped instead of continuous. This isn't about reconstructing a waveform, but about reconstructing a characteristic of the binaural listening experience which is, after all, how we hear sound.
 
The question is whether reconstruction is sufficiently precise to reconstruct the timing difference between two signals that are, say, 8 microseconds apart. I don't see how that's possible if the capture medium can't resolve differential timings under 21 microseconds.
 
Let me explain what I think is going on.
 
A 48kHz sample clock samples an incoming voltage, which is at "x" volts. So far, so good. 5 microseconds later, "y" volts is present at the input. 8 microseconds after that, "z" volts is present at the input. 5 microseconds later, "w" voltage is present at the input and that voltage lasts for 10 microseconds.
 
When the next sample occurs 21 microseconds after the first one, it will read the "w" voltage, but it will ignore the "y" and "z" values because they occurred between samples. I don't see any way the "y' and "z" values could factor into the encoding process because the system never sees them.
 

Hi Craig,  During the digitization process, signal voltage fluctuations on timescales shorter than the sample period can influence the encoded waveform by virtue of techniques like delta-sigma modulation.  This involves an initial, coarse sampling at extremely high sample rates (relative to the range of human hearing) followed by integration (which smears the sampled voltages over time).  Fig. 4 on this webpage http://www.maximintegrated.com/en/app-notes/index.mvp/id/1870 shows a block diagram of a typical sigma-delta modulator circuit.  Apparently delta-sigma modulation is quite prevalent these days, so perhaps that explains how "...the "y" and "z" values could factor into the encoding process..."   Cheers...

drewfx1

abb

drewfx1

gswitzDrewFX, what would the time resolution of 24 bit 48kHz be? Can you figure it out? I'm curious.
 

Something on the order of 0.0000000000002 seconds.

How did you compute this value?

1/(2 * pi * quantization levels * sampling frequency)
where quantization levels = 2^(bit depth)
 
This is a theoretical limit. In reality, it's not going to be that good.

Hmm, it seems that you're conflating amplitude resolution (bit depth) and temporal resolution (sampling rate).  I don't see how the two interact to increase temporal resolution.

abb

drewfx1

abb

drewfx1

gswitzDrewFX, what would the time resolution of 24 bit 48kHz be? Can you figure it out? I'm curious.
 

Something on the order of 0.0000000000002 seconds.

How did you compute this value?

1/(2 * pi * quantization levels * sampling frequency)
where quantization levels = 2^(bit depth)
 
This is a theoretical limit. In reality, it's not going to be that good.

Hmm, it seems that you're conflating amplitude resolution (bit depth) and temporal resolution (sampling rate).  I don't see how the two interact to increase temporal resolution.

No.
 
It's as I said - if you shift your waveform to be sampled in time by a fraction of a sample period before sampling, you will get different sample values than you otherwise would.
 
Is it not clear that "different sample values" implies "different signal"?
 
What's the difference between the signals? One has been shifted in time and nothing else.
 
At higher bit depths there are more possible sample values, meaning the amount you can shift your signal in time without getting different sample values (different sampled signal) is smaller. Hence greater timing resolution at greater bit depths.

.

drewfx1

abb

drewfx1

abb

drewfx1

gswitzDrewFX, what would the time resolution of 24 bit 48kHz be? Can you figure it out? I'm curious.
 

Something on the order of 0.0000000000002 seconds.

How did you compute this value?

1/(2 * pi * quantization levels * sampling frequency)
where quantization levels = 2^(bit depth)
 
This is a theoretical limit. In reality, it's not going to be that good.

Hmm, it seems that you're conflating amplitude resolution (bit depth) and temporal resolution (sampling rate).  I don't see how the two interact to increase temporal resolution.

No.
 
It's as I said - if you shift your waveform to be sampled in time by a fraction of a sample period before sampling, you will get different sample values than you otherwise would.
 
Is it not clear that "different sample values" implies "different signal"?
 
What's the difference between the signals? One has been shifted in time and nothing else.
 
At higher bit depths there are more possible sample values, meaning the amount you can shift your signal in time without getting different sample values (different sampled signal) is smaller. Hence greater timing resolution at greater bit depths.

It's easy to visualize what you're depicting.  I also fully understand what you're saying.  However what's not clear is how your argument relates to increased temporal resolution from a mechanistic perspective.  Are you saying that part of the digitization process involves shifting signals around in time?  If not I just don't understand how having more amplitude resolution will increase your temporal resolution. 
 
BTW, did you see my post above (#84)?  That's what I mean by 'mechanistic.'  Cheers...

Damn. This s*** is for real. I feel smarter having just having come across this! Thx!

abbIt's easy to visualize what you're depicting.  I also fully understand what you're saying.  However what's not clear is how your argument relates to increased temporal resolution from a mechanistic perspective.  Are you saying that part of the digitization process involves shifting signals around in time?  If not I just don't understand how having more amplitude resolution will increase your temporal resolution. 
 

 
Maybe this will help.
 
Let's express a few samples of a 10kHz sine wave sampled at 48kHz at different bit depths (they start at 35 degrees):
 
24        16       8      4 bits
4811507   18794    73     4
7882713   30791    120    7
-731116   -2856    -12    -1
-8261167  -32271   -127   -8
-3545179  -13849   -55    -4
 
Now let's sample it .001 samples later in time (which is ~.02 microseconds):
24        16       8       4 bits
4820498   18830    73      4
7878950   30777    120     7
-742054   -2899    -12     -1
-8263066  -32278   -127    -8
-3535225  -13810   -54     -4
 
In this short sequence at 4 bits the samples are all identical, at 8 bits only the last is different, whereas at 16 and 24 every sample is quite different. So the lower bit resolution limits our ability to capture a small time shift.
 
 
Note that if I bothered to do a much longer string of samples we would eventually see some changes even at 4 bit with this amount of time shift.