[klaff]

I'm kinda shocked that there's no discussion of sinc interpolation and adapting it's theoretical need for infinite signals to some finite kernel length.

For a sampled signal, if you know the sampling satisfied Nyquist (i.e., there was no frequency content above fs/2) then the original signal can be reproduced exactly at any point in time using sinc interpolation. Unfortunately that theoretically requires an infinite length sample, but the kernel can be bounded based on accuracy requirements or other limiting factors (such as the noise which was mentioned). Other interpolation techniques should be viewed as approximations to sinc.

Sinc interpolation is available on most oscilloscopes and is useful when the sample rate is sufficient but not greatly higher than the signal of interest.

[oakwhiz]

Sinc interpolation is somewhat resource-intensive / latency inducing which is why it's not used as frequently in realtime audio.

[klaff]

Agree, but it's like knowing a limit imposed by the 2nd law of thermodynamics. You can't do better and if you get close enough you are done.