Time Domain Example of Nyquist/Shannon? I looked at an old thread, Nyquist Frequency Phase Shift, but was left wondering still about oversampling.

I learned Shannon 40 years ago, then worked 30 years in (s/w) engineering, but now retired I have only begun using/configuring complete digital audio setups. I find myself baffled by exactly the sort of hands-on question that was posed in the referenced thread. Yet most of the relatively simple (IMO) questions I've thrown at the search engines have landed on generic "Nyquist says" posts, and almost all graphs have been frequency domain.

Like the author of the referenced post, if I draw a simple sine wave and "sample" it with something just over twice its frequency, then vary the phasing of the sample points (or the wave) a few times, I end up with very different squarewave patterns. Especially for an illustratively short burst, it's impossible for me to deduce how even the most perfect linear-phase brickwall filter could regenerate the exact analog input (amplitude plus phase), which would be critical in preserving harmonic structure for any instrument. Certainly Nyquist had little to draw upon except filters as a physical 'decoder'.

It is very easy to picture that, for a tiny increment over 2*Fm, something very similar to the zero-output example given in the referenced post would be generated for a fairly long burst. It's equally hard to see how any procedure would regenerate a perfect image of the input burst, intermediate oversampling etc. notwithstanding, whereas for a much lower frequency (same Fs) it looks feasible.

Since available hw/sw has improved so radically since CDs and DAT first showed up, has anyone seen a genuine graphed experiment? Something like a 20khz pure tone riding on a (reasonably short) 2khz tone burst (or any such two-tone combination to give a gauge for zero phase shift), sampled at a rate just higher (say 5% e.g.) than twice the higher frequency. I would love to see the results, in time domain, input vs. output. I'd also love for them to be exact over multiple sample/decode tests. Then I could get over the feeling that not just oversampling but huge oversampling might be a good idea after all.

Or does insistence on a readable burst of short length throw such a monkey wrench into the spectrum being sampled that Fmax would in reality be way, way higher?
A short burst of frequency f contains a ton of higher frequency spectra energy which is needed to make the burst short, or rectangular windowed, rather than infinitely long.  Thus, a finite burst no longer meets the Nyquust criteria for sampling at just a bit over 2 times f.

The transform of a rectangular window is a Sinc, which has infinite support in the frequency domain.  But a really really long window has a Sinc that decays faster, and thus may go below your noise floor soon enough.

If you want to sample at just a bit over 2 times f and not end up with aliasing, the signal may need to be stationary for a very very long time to allow reconstruction.

Or you can sample at a higher sample rate to acquire a sufficient amount of the spectra of the window that limits the length of a much shorter time domain burst.

So there's a trade-off between how close you can get to Nyquist frequencies versus the length of the signal.