Being an audio guy, I just can't resist weighing in on the audio analogy with CDs and the comment about sampling rate and analog waveforms.
Both CDs, and turntables (or analog master tapes) have errors that make neither a perfect copy. Mathematically ... and yes mathematics DOES matter, a CD, at least one created with modern recording equipment is a far closer copy of the original than a turntable is. Sure back in the old days of phase-locked loops around mechanical processes for timing, analog brick wall filters due to the lack of oversampling, etc. the CD could be rather "coarse", but again, with a modern recording and a tolerable CD for playback, the CD is a closer copy. Perhaps it does not have that poor separation of audio that a turntable has that can create a "sound" that some people like, but you could always mix that back in. Then again, with 24/96 or 24/192 available now, it is really not even close and almost the most staunch "audiophiles" would agree. They would probably agree also, especially if not told, that some of the latest in Class-D amplifiers, especially with all digital paths, are better than their favorite class-A amp.