That's interesting. I understand Nyquist, sampling, etc.,.. and although I'm not completely up on the math behind Fourier decomposition, I think I grasp it at an abstract level. But you bring up an interesting question - what about the relative phase relationships between all of these superimposed (as per Fourier) sinusoidal waveforms, that ostensibly form the original signal? Is that not actually a *third* dimension to the signal, one that isn't being recorded by the sampling process? IOW, at any particular given point in time in the signal, the phase information is lost - shouldn't the reconstructed signal use some sort of error-diffusion/dithering technique, to rebuild the signal such that the overall phase-error of all of the waveforms approaches zero.. although that still would give a waveform that only approximates the original in phase-space, and doesn't re-create it.
It makes one wonder how much of a difference phasing matters to the human ear, or whether it only primarily reacts to amplitude and frequency.
Actually, hmm, there seems to be some sort of analogous similarity between sampling a waveform's frequency and phase information, which really can only exist relative to another reference waveform, and Heisenburg's uncertainty principle with "sampling" the position/velocity of particles.. or something along those lines. If they are really only just waveforms anyways, and our conscious observation causes them to be "sampled" into particles.. does that provide just one more piece of evidence that our conscious existance is actually digital? Would that imply that God, as an infinite being, is analog?