If you just change your definition of basis functions from infinite sinusoids to truncated sinusoids and your definition of bandwidth to the maxiumum frequency of a nonzero truncated sinusoid coefficient you can recover an analog of Nyquist Rate just with a different idea of bandwidth. When you're talking about the typical 10^6 cycles over a song they're the same for all intents and purposes.

EDIT: Your truncated sinusoids have to be harmonics of the total signal length for this to work trivially.

I don't see how either of these papers solidly refute "because Nyquist" in the context of the article and sample rates applied to audio signals. They're both worth considering, though.

The first[1], the more theoretical of the two, is focused on digital communications where a Nyquist rate derived from the signal rate isn't enough to recover the signal function. The numerical examples given highlight recovering a sine wave from two, three, and six samples. The millions of samples in a single song might as well be infinite compared to these.

The second paper is much more practical and gives a number of real-world examples where naively applying Nyquist causes problems. The first, cutoff filters at half Nyquist to avoid aliasing, plauged many early CD players and other digital audio equipment. The second example is great as well, showing how understanding the signal being measured is important. The third example doesn't really apply to the subject at hand but is a good example of using aliasing for good. The fourth and fifth address the effect filters have on the signal. The sixth example refers to time response in control systems and minimizing phase delay to avoid oscillations.

[1]http://www.academia.edu/8412078/Is_The_Nyquist_Rate_Enough [2]http://www.wescottdesign.com/articles/Sampling/sampling.pdf

Sure, but they're including a healthy margin by not caring about frequencies above 20KHz.

The margin isn't exactly healthy at 44.1khz. The video guys went with 48khz for a reason.

Yes, timing to video frames :D

More specifically, timing to film frames, since 48kHz gives you 2000 samples per film frame (at the standard 24fps film speed).