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
# 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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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.
'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.
With no reconstruction filter the downstream electronics will have a very hard time contributing zero IMD.
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?
O.k., let's just change the example to 20-bit then.
Let's pretend the electronics have zero IMD.
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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....
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.
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.
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).
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.
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.
Hi,
I'm not discussing that, the thread title says "without quantization noise", I don't care about the noise parameter, I'm looking for answers within the resolution parameter.
Thanks though.
I think you're still talking about noise, the 16-bit resolution of a sine-wave looks like this.
An externally hosted image should be here but it was not working when we last tested it.
Are you saying no one can hear that?
Now we are getting somewhere!
So do we need to use oversampling with a 24-bit R2R DAC? Or is the blockiness already far beyond perceivable limits?
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This is a red herring since you cannot really predict auditory performance by the visual display of the waveform. More importantly, the "blockiness" is gone when the reconstruction filter is applied. This filter is essential in DSP applications.
Let's just entertain that you're correct.
A 16-bit waveform once it has the reconstruction filter applied to it, suddenly becomes 100-bit or higher in blockiness terms.
Thus, it's a satisfactory or perfect recreation of the waveforms of reality.
O.k., this still doesn't answer the question where human hearing lies, somewhere between 24-bit and 1000-bit?
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"practical human hearing" has to include the conditions for hearing at the ultimate threshold's low levels
many minutes of accommodation are required in a anechoic chamber for get to the point you hear you own pulse, blood flow noise - not happening day-to-day music listening in a even very good sound treated listening room
many minutes of accommodation are required in a anechoic chamber for get to the point you hear you own pulse, blood flow noise - not happening day-to-day music listening in a even very good sound treated listening room
Very true and this is much like hearing the noise of an air-conditioner in a studio recording or a little power supply noise in a DAC. Which, as you say, in practicality is very irrelevant if that noise is the only difference.
However, the aural difference of the bit-depth I'm referring to here of 16-bit versus 32-bit resolution in a filterless R2R DAC is very clearly perceived.
There is no 32-bit R2R but via upsampling the sixteen bit we hear a clear difference.
I've read that upsampling a 24-bit R2R provides a clear difference, considering my experiments with the 16-bit this seems very likely to be the case.
This tells me that the human hearing of bit depth resolution is very likely above 24-bit.
Intuitively, I think it's at least 64-bit, personally.
It'll be interesting if there are no hard numbers for this.
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I'm not clear what difference you're hearing - if you upsample you'll be running the DAC faster but you can't get rid of the noise on the input no matter how many bits come out of the upsampling filter. So even with 10^8 bits on the output, for a 16bit input the noise can't be better than -93dB.
Humans don't hear 'bit depth'. They hear distortion. The thread title talks about 'quantisation noise' so are we talking of noise or distortion? With or without a reconstruction filter? Note that without a reconstruction filter you will be listening to ultrasonic images, which may or may not be audible and may or may not add to a perception of distortion. The 'blockiness' (in the time domain) and images (in the frequency domain) are one and the same - you did know that, didn't you?
I suspect that this is going to be one of those threads in which the OP does not understand his own questions.
I suspect that this is going to be one of those threads in which the OP does not understand his own questions.
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If you or anyone else tend to personally dislike upsampling, the reason which comes to mind is that there are various different ways to upsample, there are different interpolation techniques.
A few DAC's have different filters to select, thus we can experiment with the differences.
The static image equivalent is this
Image scaling - Wikipedia, the free encyclopedia
The video image equivalent is this
Toolfarm.com :: In Depth: Upscaling or Upsizing Video
As you can see, there are a high number of different techniques available!!
In the second link it states
"After going through all of these options available for upscaling, I can ultimately surmise that there is really no method that will magically turn your SD footage to amazing looking HD."
The audio equivalent, in theory, would be
"after trying all the different interpolation / upsampling techniques available, I can ultimately surmise that there is really no method that will magically turn your 16-bit audio into amazing looking 64-bit"
You either
- use your favourite
- you take the viewpoint that the audio reconstruction filter / interpolation / upsampling is a perfect or acceptable reconstruction of reality
- you avoid the upsampling altogether
- you advocate the theory 64-bit ADC and 64-bit DAC
Nonetheless, that isn't the discussion here and I am not personally taking a specific position in any of the above.
I'm taking the position in that filter-less 16-bit R2R upsampled 4x via software sounds like it has more detail.
The sinusoidal and non-sinusoidal waveforms are filled in with more detail.
Similarly, if I were to upsample a VGA image to XVGA, the pixels are moved farther apart and the new pixels present more detail to the image.
The same is true of video
The same is true of colour
The same is true of audio
See the example picture, 4xBRZ here or any of the techniques in the Wikipedia image scaling link can in theory be applied to an audio technique as well.
An externally hosted image should be here but it was not working when we last tested it.
Let's just pretend the ultrasonic images and the IMD are accounted for so they are totally removed from the listening.
In that case, then you're saying I can't hear the blockiness at all, of 16-bit versus 24-bit blockiness?!
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Apparently. In the best case, he'll spend a bit of time doing some study to get the basics, followed by a few experiments to sharpen his understanding.
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