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I don't understand:

(a) how Stereophile derives bit depth from Spectral Analysis?

If you can know the peak signal and total noise energy over the audio band, and the noise energy is more or less constant with different input signals, then you can easily calculate the effective bit depth. You divide the SNR, measured in dB, by 6.02, and you get EFFECTIVE bit depth.

Using Matlab (tm) or Octave (not tm) you can do this pretty trivially.

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I don't understand:
(a) how Stereophile derives bit depth from Spectral Analysis?

As a rule of thumb and all things being equal, each increase in digital word length lowers the noise floor by around 6dB. So if increasing the data word length fed to a DAC from 16 to 24 bits drops the noisefloor by 18dB rather than the expected 8x6=48dB, the DAC's own noisefloor is limiting resolution to 16 + 18/6 = 19 bits. (Which is still excellent, given that the current state of the DAC art is around 20 bits.)

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(b) why bit depth/resolution is randomly reported in Measurements (i.e., reported in review of a particular CD Player or D/A processor and not a particular CD Player or D/A processor in another review)?

I test all products with 16-bit data (the CD standard) and with 24-bit data (the maximum some products will handle). However, the limited space in any particular review means I can't publish all the graphs, just the ones that best illustrate the points I am making in the accompanying text.

John Atkinson
Editor, Stereophile

I still say the 2772 in Taiwan is a smokin' deal. It has all the right extras. I'm still drooling.

So I always thought that more bits provided finer resolution in the amplitude axis and a higher sample rate provided a finer resolution in the time axis.
But I don't understand how more bits increases S/N ratio.
I would think that the noise floor and the max signal level would be fixed and increasing the number of bits would just smooth out the amplitude steps. Obviously I am wrong, but I don't understand why.

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So I always thought that more bits provided finer resolution in the amplitude axis and a higher sample rate provided a finer resolution in the time axis.
But I don't understand how more bits increases S/N ratio.
I would think that the noise floor and the max signal level would be fixed and increasing the number of bits would just smooth out the amplitude steps. Obviously I am wrong, but I don't understand why.

The noise floor in a PCM capture (if it works ideally, which of course is another matter) is sqrt(1/12) of an amplitude step.

So, the more bits, the lower the noise floor. In, again in an idea PCM capture, the noise level is the same for any input value. This requires triangular PDF dither as well as a perfect quantizer, so it never works out quite like that, of course.

In short, more resolution in the amplitude axis is exactly the same as lowering the noise floor.

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[ I assume -- & correct me accordingly -- the ~20 max bits you note is the sum result of the topological D/A processor architecture, which may include, in addit. to the DAC IC, the digital filter, analog output stages, etc. -- not just the DAC IC?

That's correct. By "DAC," I meant the entire black box - digital data input processed to produce analog audio output.

John Atkinson
Editor, Stereophile