Forget the “3 bits” that people are mentioning. It’s a red herring (or maybe the sound of axes grinding). I already described in message
https://www.audiosciencereview.com/...-music-on-tidal-to-test-mqa.22549/post-759747 how, with a digital audio recording of actual music, it is possible to create a hidden data channel in the least significant bits without losing resolution or “bits.” So forget about MQA for now and consider the following thought experiment (which has nothing to do with “deblurring,” “leaky” reconstruction filters, B-splines, etc):
Imagine that I have a 24-bit audio file of the music from which I extracted that room tone recording mentioned earlier, sampled at 2Fs (88.2kHz). I would like to create a version of that file that will play with a baseband sample rate (44.1kHz) in systems with antique D/A converters but also play at the original 88.2kHz sample rate in my big rig.
I take that 24-bit file and using a complementary pair of low- and high-pass digital filters, I split it into two 24-bit files: one containing content below 22.05kHz so that it can now be considered as having an effective sample rate of 44.1kHz; the other containing content from 22.05kHz to 44.1kHz. As long as the filters used are of a specific type, the band splitting will be transparent.
I examine the spectrum of the background analog noise in the baseband file and calculate that I can create a hidden data channel in the 5 LSBs (bits 19-24), which are 2 bits (12dB) below the lowest amplitude of the audio data. I then examine the spectrum of the 2Fs file. I find that, as expected, the ultrasonic content both has a self-similar spectrum that declines in amplitude with increasing frequency and is at a low level. The level is so low, in fact, that the actual quantization is close to 5 bits.
So, if I encrypt the 5-bit/2Fs data as pseudorandom noise with a spectrum identical to the background noise in the baseband file, I can bury those data in the hidden 5-bit data channel. I now have a single 24-bit file sampled at 44.1kHz that will playback with the same audio quality as the original file (other than the low-pass filtering at 22.05kHz).
For playback in the big rig, a flag that I have embedded in the file’s metadata tells the D/A processor that it has to extract and de-encrypt the 5-bit audio data in the hidden channel. It then upsamples those data to 2Fs, attenuates the data to the level in the original file – this pushes the 5-bit quantization noise below the original background noise floor – and adds the result to the baseband file that has also been upsampled to 2Fs.
In theory, I am playing back the 24-bit baseband file as if it were a 2Fs file with no loss of bandwidth or information or resolution or “bits.” (That would be the “thought experiment” equivalent of the “MQA Stereo original resolution” files in the 2L screenshot you included in your post.)
The devil, of course, lies in the details. How do I encrypt the low-bit-rate content between 22.05kHz and 44.1kHz so it resembles pseudorandom noise? I have no idea, even though I had discussions with the late Michael Gerzon about this back in the day. What if the starting point is a 16-bit file, where there is much less information space in which to embed a hidden data channel beneath the analog noise floor? (That is the “thought experiment” equivalent of the “MQA-CD” files in your 2L screenshot.) Again, I don’t know. What if the statistics of the original audio don’t conform with the self-similar spectrum that I am expecting? That, of course, is how GoldenOne “broke” the encoder.
But again, to talk about “losing 3 bits” or “truncating” the audio data is incorrect.
John Atkinson
Technical Editor, Stereophile
