Time Domain Example of Nyquist/Shannon?
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.