On the question of continuous vs. non-continuous waveforms, I think that part of the reason for the disagreement is that the word "continuous" is misleading in this context. No waveform is truly "continuous." Regardless of the nature of the waveform, the Sampling Theorem will only be perfectly accurate (i.e., to 100.00000000...%) when an infinitely long sample record is available, covering the period from the beginning of the universe to the end of time. :-)
Any real-world waveform, whether sinusoidal or not, and "continuous" or not, will not meet that criterion. As a result there will always be some non-zero loss of information, at and near the times when the waveform begins, when it ends, and when it changes character. In theory the spectral content of those transitions extends out to infinity Hertz, although as a practical matter much of the high frequency spectral content of those transitions will be at amplitudes that are utterly negligible.
The information that is lost in those transitions will correspond to the spectral components that lie above the cutoff point of the anti-aliasing filter. The lower the cutoff point of the anti-aliasing filter, and the more abrupt the transitions are in the waveform that is being sampled, the greater the amount of information that will be lost.
Will any of that particular form of information loss be audibly significant when a music waveform is sampled at 44.1 kHz? It's hard to say, and I doubt that empirical assessment (by listening) can yield a meaningful answer considering how many other variables and unknowns are involved in the recording and playback processes. My guess is that it probably has some significance, especially on high frequency transients such as cymbal crashes, but only to a relatively small degree.
Is oversampling plus noise shaping an essentially perfect means of overcoming the problems inherent in sampling just slightly above the Nyquist rate, as the article seems to suggest? It's probably fair to say that it can work pretty well, but IMO it would be hard to argue that it is "essentially perfect." Can the ultrasonic frequency content that is retained by hi rez formats have adverse consequences, as claimed in the article, as a result of intermodulation effects within the system's electronics, or things like crosstalk effects for that matter? It certainly seems conceivable, to a greater or lesser extent depending on the particular components that are in the system. Will sampling at a higher rate result in sampling that is less accurate, assuming equal cost and comparable design quality? That would seem to be a reasonable expectation. But complex and sophisticated digital signal processing does not come for free either.
What does it all add up to? I would have to say that the paper referenced by the OP, and also the Lavry paper, make better cases against hi rez than I would have anticipated, but they are certainly not conclusive as I see it. And given the many tradeoffs and dependencies that are involved, my suspicion is that there will ultimately be no one answer that is inarguably correct.
Best regards,
-- Al
