If you just change your definition of basis functions from infinite sinusoids to truncated sinusoids and your definition of bandwidth to the maxiumum frequency

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.