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Old 23rd July 2014, 11:41 PM   #1
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Default Highest resolution without quantization noise

Hi,


# bits SNR Possible integer values (per sample) Base ten signed range (per sample)

4 24.08 dB 16 −8 to +7
16 96.33 dB 65,536 −32,768 to +32,767
24 144.49 dB 16,777,216 −8,388,608 to +8,388,607
32 192.66 dB 4,294,967,296 −2,147,483,648 to +2,147,483,647
64 385.32 dB 18,446,744,073,709,551,616 −9,223,372,036,854,775,808 to +9,223,372,036,854,775,807


http://en.wikipedia.org/wiki/Audio_bit_depth

http://en.wikipedia.org/wiki/Signal-to-quantization-noise_ratio


A 24-bit resolution has -144.49 dB noise, due to quantization error in the ADC.

This is considered lower than the human hearing limit, thus it's estimated we can hear around 22-bit in ideal conditions.

However, that is noise.

If we remove noise from the equation, what is the highest resolution we can hear of a sine-wave, or any kind of wave?


12-bit? 32-bit? 50-bit? 100-bit? Where is the limit?

Thank you

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Last edited by Kastor L; 26th July 2014 at 04:44 AM. Reason: Clarification
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Old 23rd July 2014, 11:46 PM   #2
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Quote:
Originally Posted by Kastor L View Post
If we remove noise from the equation, what is the highest resolution we can hear of a sine-wave, or any kind of wave?
To hear something at all we'd need a DAC and amp - both will add noise. So it doesn't look practical to 'remove noise' and therefore it appears your question can't be answered through experiment.
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Old 23rd July 2014, 11:56 PM   #3
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Hi Abraxalito,

Here is my thought experiment.

If I record reality with a 24-bit ADC, transfer that to 24-bit media like Blu-ray, then play that with a 24-bit R2R DAC, without dither and without a reconstruction filter......

Then, is that 24-bit resolution of the waveforms satisfactory?
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Old 24th July 2014, 12:07 AM   #4
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'Satisfactory' means satisfactory to the eye when looking at the waveform on a screen? If you had a true 24bit ADC I don't believe you'd need dither as the source would have more noise than -140dB, it would be self-dithering.

With no reconstruction filter the downstream electronics will have a very hard time contributing zero IMD.
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Old 24th July 2014, 12:24 AM   #5
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Quote:
Originally Posted by abraxalito View Post
'Satisfactory' means satisfactory to the eye when looking at the waveform on a screen?
Correct, raw 16-bit and 24-bit waveforms do not look satisfactory to the eye, because they don't look like the waveform which they're supposed to be reproducing, i.e. the sound of reality.

Thus I'm inclined to think that raw 24-bit waveforms are not satisfactory, i.e. in relation to the limits of our perception?

Thus, the 22-bit limit is a misperception, since that only relates to the intertwined noise, not the waveform itself, is this not correct?


Quote:
Originally Posted by abraxalito View Post
If you had a true 24bit ADC I don't believe you'd need dither as the source would have more noise than -140dB, it would be self-dithering.
O.k., let's just change the example to 20-bit then.


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Originally Posted by abraxalito View Post
With no reconstruction filter the downstream electronics will have a very hard time contributing zero IMD.
Let's pretend the electronics have zero IMD.
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Old 24th July 2014, 12:35 AM   #6
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You can get the waveform looking as close to satisfactory as you wish on an LCD screen - just ensure the step sizes at any frequency are less than the screen's resolution. Thus use a high degree of oversampling - say 1024X. I don't see why how a waveform appears though has any bearing on how its going to sound....
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Old 24th July 2014, 12:45 AM   #7
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Quote:
Originally Posted by abraxalito View Post
You can get the waveform looking as close to satisfactory as you wish on an LCD screen - just ensure the step sizes at any frequency are less than the screen's resolution. Thus use a high degree of oversampling - say 1024X. I don't see why how a waveform appears though has any bearing on how its going to sound....
A 20 megapixel camera and a 7 megapixel camera produce photos which look the same. We have a pretty good idea of the resolution which is necessary, not considering zooming in that is.

If audio does not have any idea where the resolution limit of fine detail is, then we may as well just make 64-bit ADC, 64-bit DAC and get rid of the dither and reconstruction filter altogether.
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Old 24th July 2014, 12:48 AM   #8
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Quote:
Originally Posted by Kastor L View Post
get rid of the dither and reconstruction filter altogether.
In order: Why? And you apparently don't know what a reconstruction filter does.

Instead of vague thought experiments, it might help to do some actual ones. Much more educational.
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Old 24th July 2014, 12:50 AM   #9
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Depends how big a print you want to make - there will come a print size where the 20MP will show its improved resolution over the 7MP. But if you just care about getting rid of the 'blockiness' then by all means use resolution enhancement techniques - like interpolation (in audio this is called oversampling).
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Old 24th July 2014, 01:11 AM   #10
sreten is offline sreten  United Kingdom
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Hi,

Or you can take a simple dose of reality regarding the noise
level of real electronics which don't get past 100dB, even
on a good day. Discussing -140dB and hearing 22 bits
is utter nonsense in any sensible analysis of the issue.

You can hear hear sod all resolution of a sine wave,
above about 8 bits (it varies with people), 12 bits
is plenty to encompass absolutely everyone.

rgds, sreten.
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