It says nothing about noise, distortion, dynamic range. In these areas it is impossible to create a "perfect" DAC, although granted the best DACs are indistinguishable from perfect as far as human perception is concerned.
> If a function x(t) contains no frequencies higher than B hertz, it is completely determined by giving its ordinates at a series of points spaced 1/(2B) seconds apart
I took this to mean that it's any continuous function x(t), including amplitude information. I took a quick read through the proof and that's correct as far as I can tell.
Does that not mean that "noise, distortion, and dynamic range", as they are all encoded in the continuous function that is air pressure over time, can be perfectly captured and reproduced? All you need to do is throw out all information outside of human hearing range to have no frequencies higher than B hertz, and that's all you need for perfect reproduction.
If there exists a transformation f(x(t)), then said transformation can also be captured by the same sample, can it not?
Wires without resistance, capacitance and inductance. Resistors without capacitance and inductance. Capacitors without resistance and inductance. Inductors without capacitance or resistance.
While we're at it, semiconductors with perfect linearity and so on and so on..
I'm not going to argue that audiophiles generally achieve much of these, or even that it's especially important for the perceived audio quality.. But, perfectly recording and reproducing anything is still not possible, not in audio, not in video.
Which is an argument in favor of getting the signal into the digital domain as early as possible and maintaining it there for as long as possible.
The audiophile's stereotypical myth of analog supremacy is the assumption that the opposite is somehow true. Weird, but everybody needs a hobby.
There are costs associated with digital that, like with analog, must be managed.