[StanD]

  Found this on Wikipedia:

24-bit digital audio has a theoretical maximum SNR of 144 dB, compared to 96 dB for 16-bit; however, as of 2007 digital audio converter technology is limited to a SNR of about 123 dB^[12][13][14] (21-bit ENOB) because of real-world limitations in integrated circuit design. Still, this approximately matches the performance of the human auditory system.^[15][16] (While 32-bit converters exist, they are purely for marketing purposes and provide no practical benefit over 24-bit converters; the extra bits are either zero or encode only noise.)^[17][18]

The great P.T. Barnum was overheard saying, "There's a sucker audiophile  born every minute." He went on to become the most successful marketing expert on DACs.

 

[Arpiben]

   
Yeah I've gone through audiocheck's stuff before. This paragraph from there seems to be related to my issues:
 
 
So we see both the -48 value and the higher -36 that you mentioned. But I can hear stuff happening way before the -36dB mark, so I'm still at a loss for how you make a # for "where does the bit depth start to suck because of truncation". But I guess what I'm hearing proves your point: the errors happen way above -48dB.
 
 
The car analogy doesn't really do it for me, sadly.

 
Allow me to try another way since previous analogies didn't work for you.
Basically I truncated two 44.1 kHz/16 bit files (no dither) into 44.1 kHz/16bit keeping only the 8 MSB:

1. 1 Hz sine 44100 samples/1s in order to maximize sample distribution
2. 10 kHz sine 44100 samples/1s

 
Truncation was performed with excel  with help of audacity sample export/import function.
For sure real audio signals are much more complex than simple sine. For sure there were some roundings in the process.
But the purpose was trying to show the truncation issue.
 

• 1Hz

1. Time domain:

1. Frequency Domain:

 
2. 10 kHz:
 

1. Frequency Domain:

 
With the truncated signals (8 bit MSB) you will notice the noise level increase at frequency domain as well as some added clipping for the first signal.
Hope it helps.
Rgds.

 

[pinnahertz]

   
Allow me to try another way since previous analogies didn't work for you.
Basically I truncated two 44.1 kHz/16 bit files (no dither) into 44.1 kHz/16bit keeping only the 8 MSB:

1. 1 Hz sine 44100 samples/1s in order to maximize sample distribution
2. 10 kHz sine 44100 samples/1s

 
Truncation was performed with excel  with help of audacity sample export/import function.
For sure real audio signals are much more complex than simple sine. For sure there were some roundings in the process.
But the purpose was trying to show the truncation issue.
 

Wouldn't you need a reconstruction filter in your excel truncation? 

 

[RRod]

I think we are losing sight of what was the original issue: "how loud are the errors you get from truncating 16 bits to 8?"
 
G's answer, as I'm interpreting it, is "it depends", which I agree with now that I'm thinking about reconstruction rather than just the samples themselves. My end-goal in all this is to be able to say "if you're hearing something when you truncate to 8-bits, then it can only be *this* loud, since it has to be lower than the peaks." We don't hear peaks, of course, but being able to bound something by the peak would have been nice. Since we can't, it would be nice to know if the RMS for X samples has some bounding properties that might be useful.

 

[Yuri Korzunov]

   
Allow me to try another way since previous analogies didn't work for you.
Basically I truncated two 44.1 kHz/16 bit files (no dither) into 44.1 kHz/16bit keeping only the 8 MSB:
 
...
 
With the truncated signals (8 bit MSB) you will notice the noise level increase at frequency domain as well as some added clipping for the first signal.

 
If you remove (put in zero) 8 lesser significant bits, signal lose a bit energy, comparing 16 bit original. Hence there overload is impossible.
 
After removing the 8 bits energy of signal distributed in rest band as quantization noise. But total energy of 8 bit (signal + noise) is decreased comparing 16 bit on energy of lesser 8 bits.
 
So check, please, rounding or calculations or plot drawing function.

 

[Arpiben]

  Wouldn't you need a reconstruction filter in your excel truncation? 

Yes if I didn't lost sight of the original issue as @RRod replied:
I think we are losing sight of what was the original issue: "how loud are the errors you get from truncating 16 bits to 8?"
I stopped at FFT(Blackman-Harris) added noise when dealing with sample truncation only.
How this affects the interpolation/reconstruction I have not the skills to do it.

 

[Arpiben]

   
If you remove (put in zero) 8 lesser significant bits, signal lose a bit energy, comparing 16 bit original. Hence there overload is impossible.
 
After removing the 8 bits energy of signal distributed in rest band as quantization noise. But total energy of 8 bit (signal + noise) is decreased comparing 16 bit on energy of lesser 8 bits.
 
So check, please, rounding or calculations or plot drawing function.

I will check, thanks.

 

[Yuri Korzunov]

 
I will check, thanks.

Me seems, that points of overload was restored for drawing by truncated data via interpolation. I can't see it exactly in screenshot resolution.
 
If it so, interpolation as oversampling can create virtual points with level higher, that original samples.

 

[gregorio]

  I think we are losing sight of what was the original issue: "how loud are the errors you get from truncating 16 bits to 8?"
 
[1] G's answer, as I'm interpreting it, is "it depends", which I agree with now that I'm thinking about reconstruction rather than just the samples themselves.
[2] My end-goal in all this is to be able to say "if you're hearing something when you truncate to 8-bits, then it can only be *this* loud, since it has to be lower than the peaks." We don't hear peaks, of course, but being able to bound something by the peak would have been nice. [3] Since we can't, it would be nice to know if the RMS for X samples has some bounding properties that might be useful.

 
1. Just to be clear, my answer of "it depends" was based on two points: ...
2. We always have to be careful with the term "loud" because loudness is a perception rather than a property. We have to be particularly careful about this term when talking about bit reduction because in effect, any correlation between level and loudness is often inverted. IE. The method of bit reduction which produces the highest RMS level of artefacts is the method with the least "loud" artefacts.
3. The RMS value of truncation error is known, (if memory serves) it is: 1 divided by the square root of 3, LSB. This result is a constant regardless of the input signal. How this RMS level is distributed cannot be known though, because it's signal dependent. I don't know for sure that there is no way to calculate the freq distribution and peak value of truncation error but if there is, you would obviously have to know the input signal, IE. The result is not constant, unlike the RMS amount and unlike quantisation error (which is nearly constant).
 
G

 

[Arpiben]

   
1. Just to be clear, my answer of "it depends" was based on two points: ...
2. We always have to be careful with the term "loud" because loudness is a perception rather than a property. We have to be particularly careful about this term when talking about bit reduction because in effect, any correlation between level and loudness is often inverted. IE. The method of bit reduction which produces the highest RMS level of artefacts is the method with the least "loud" artefacts.
3. The RMS value of truncation error is known, (if memory serves) it is: 1 divided by the square root of 3, LSB. This result is a constant regardless of the input signal. How this RMS level is distributed cannot be known though, because it's signal dependent. I don't know for sure that there is no way to calculate the freq distribution and peak value of truncation error but if there is, you would obviously have to know the input signal, IE. The result is not constant, unlike the RMS amount and unlike quantisation error (which is nearly constant).
 
G

 
Completing your post regarding RMS value with the help of some previous readings since my memory is not serving me as much as yours,
 
 

 
Error function:
  
 
With proper choice of dither function, dither noise and quantization error will be uncorrelated from each other and therefore the total error noise power will be additive:
 

 

 
Q: Quantization width   R:Range   B: bits
 

 
 
As you rightly mentionned the total error function is signal dependent. Using triangular nonsubstractive dither makes the power spectrum of  the error independent of the input by whitenning the error function. For deeper readings in quantization & dithering one may check Lip****z & R.Wannamaker related documents
 
Thanks @gregorio for having enlightened me with your posts.
 
N.B. Edited but still not able/allowed to write Lip ****z corectly, sorry.

 

[Traveller]

So how many bits am I looking at with my "GOTG2" setup... ?

 

[Mr Rick]

To roughly quote Rhett Butler:  " Frankly, my dear, I don't give a bit !" 

 

 

[Yuri Korzunov]

  So how many bits am I looking at with my "GOTG2" setup... ?

 
10 bit?

 

[LajostheHun]

That's probably generous.

 

[protoss]

how about 24bit vs 32bit? (32 bit 384khz)