Focus on 24/192 Misguided?.....

"nonsense! The Nyquist criteria applies to any signal that needs to be quantized. The Nyquist criteria only gives the minimum requirement; it does not say that one is forced to have only 2 samples per highest frequency."

Yes, you can have more samples (for instance 192kHz) but he claims that 44.1kHz (two samples) is all you need.

Again, Nyquist applies to continuous waves ONLY.

from Wikipedia:
"The theorem assumes an idealization of any real-world situation, as it only applies to signals that are sampled for infinite time; any time-limited x(t) cannot be perfectly bandlimited."

Perfect reconstruction of continuous signals close to Nyquist frequency (for instance 15-20kHz) is possible but when signals become very short, reconstruction is much less than perfect.

As for filters - look at typical response of 2and 8 pole 20kHz Bessel filter in dB:

2pole 8pole
20kHz -3 -3
22kHz -3.63 -3.67
40kHz -9.82 -13.68
80kHz -20.32 -51.81

As you can see there is very little attenuation difference at 44.1kHz/2=22kHz with 4x higher number of poles. You would perhaps need hundreds of poles and still not get -96dB. Dramatic difference shows at higher frequencies beyond the "knee" of the filter (160dB vs 40dB per decade). Whole purpose of converting analog to digital at higher rate is to represent bandwidth of 20kHz more accurately and not to extend bandwidth. Downsampling 24/192 master tapes to 16/44 removes some information, (audible or not) but to claim that 24/192 is inferior to 16/44 is complete nonsense.

As for dynamic range, again the point is resolution of the signals above noise floor. According to this article if I listen at 85dB peak and have 35dB ambient noise at home I should not be able to tell the difference between 16 and 8 bit recording (corresponding to about 50dB range). That's nonsense as well.

What about 192kHz being harmful? It doesn't get more silly than that.

Tubes better than SS, vinyl better than CD, Redbook better than HiRez with all the theory to prove it.

The pattern persists.

And MP3 will kill us all.

What a great thread! Civil discussion. Ruffled feathers, for sure. But, civil and respectful. Keep going guys! I am still on the fence about hi-rez and the OP really brought up a great article and it sparked a great discussion. It will ultimately come down to objectivists vs subjectivists, but who cares? Those who dismiss A/B/X testing believe that there is more to listening than can be quantified or measured, and those who believe in A/B/X think the rest of us are fools if we don't follow the science. Thanks to all for an entertaining discussion!

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

Al, What sounds inconceivable to me is that 24/192 recording supposed to gain sound quality by downsampling it to 16/44 to be upsampled again, perhaps to the same 24/192. Am I reading it right? Is downsampling + upsampling somehow improving sound by replacing real samples with artificial interpolated samples and recreating same harmful 192kHz?