Mshenay, you are certainly right about many of these exchanges--I almost wrote debates, but they are often, perhaps usually, not that--that occur on internet boards. It was not my intent to appear to be a braggart, or proud either of myself or my son. I apologize for giving that impression.
That said, what made me speak up was that I was offended by Monty's tone in his video. I believe that he oozes a smugness that he has not earned, and will not have earned, until he learns a lot more math. Sorry if that bothers you, but it's the math that underlies this stuff that's really important.
So, I will try to explain what I was trying to say one more time, and then I'll shut up.
Here's the thing. Everyone who says that Redbook digital is just fine and dandy because its cutoff frequency--22.05kHz--is above the upper limit of normal human hearing--20kHz--and then cites the Nyquist Theorem to back it up is citing a flawed version of the Nyquist Theorem. That theorem actually applies to continuous functions only--things that look like those sine waves that Monty put up on his scopes. Once he goes to a square wave, as he actually demonstrated, the ability to reproduce the wave through sampling no longer exists. That's what happens when you bandwidth limit that square wave--you get all those ripples, and the rise time is slower than the original square wave was, and the resulting output wave has the ripples and the slow rise time too. So Monty, instead of demonstrating the principle that digital audio is a really good reproducer of original signals, actually demonstrated the principle of garbage in, garbage out. He didn't reproduce the square wave. He reproduced his bandwidth limited version of the square wave.
As for Bigshot's issue of whether musical transients are slow enough for digital reproduction to capture them, well, some are discernible and some are not. To say that a snare drum hit takes 1/5 second isn't the relevant fact. You need to know what the snare drum hit's rise time is. I haven't been able to find that in a quick bout of googling, but I have
found that the rise time of a cymbal hit is 1ms--1/1,000 second. With the high frequencies involved in that cymbal hit, you're going to need to be very lucky to get the samples to capture them in the time of that rise. Yes, you will get the decay, but you want both, accurately. Moreover, there are lots of musical sounds that have faster rise times, indeed, infinitely fast rise times--plucked strings and hammered piano strings, for example. In both, the string starts in a deformed position and then it is released, and therefore the string's vibrations begin upon the release, so the attack portion of its wave envelope has infinite slope. That's the kind of discontinuity I'm talking about.
No sampling frequency can truly accurately convey these transients within the meaning of Nyquist-Shannon, but when you increase the sampling frequency, you increase the probability that you will do a better job of conveying the information you are digitizing. That's the point of a higher sampling frequency, and that's why, as you increase the sampling frequency you will get better and better fidelity, although admittedly you're also going to reach a point of diminishing marginal returns at some sampling frequency. The question becomes what that frequency is for the vast majority of people, and for the vast majority of critical listeners.
