The sampled points shown alone display exactly what is described but the examples I am familiar with include sin(x)/x reconstruction after sampling which reproduces the original waveform including the peaks correctly.
I'm not sure I understand you. It's obvious that sin(x)/x being run on the displayed sampled points will not reproduce the original waveform correctly. In fact, not only does sin(x)/x interpolation reproduce just what we saw in pa3bca's 120MHz image, but I can reproduce the exact same results by setting my DSO at any sampling rate and sending it a sine wave with the frequency of ~fs/2.08 (and other frequencies close to - but less than - the Nyquist frequency).
On DSOs that I have used under the proper conditions (I would not normally be measuring pure sine waves close to Nyquist) I can generate exactly what is shown and described with reconstruction disabled and then restore the original waveform, which is close to Nyquist but not exceeding it, with reconstruction turned on.
I don't know what you mean by 'the proper conditions', but the math above says that it would be extremely difficult to do that over much time. The Nyquist theorem simply states that if a signal contains no frequencies higher than B, it is mathematically possible to reproduce it by a series of points spaced 1/(2B). It says nothing about the length of the sampling. Leakage occurs over time; it's window dependent - e.g. if you just sample a cycle or two of a 120MHz sine wave at 250MSa/s, you can get a reproduction of the frequency of the waveform - thus satisfying the Nyquist theorem. But if you begin to sample more cycles than that, leakage WILL occur.
Yes and what we have seen has
nothing to do with the impurities of the applied signal. Yes impurities above Nyquist will fold back and show up, but even with my DSA815's 'crappy' TG this would be far down in the noise (i.e invisible).
As further proof: 24 MHz generated by my DG1032Z, DS2072A at 50 MSa/s.
Spurious of the DG1032 is at -60dB(2nd harmonic) to -70dB for others. Not stellar but quite sufficient thank you. So now we might all agree that spurious signals cannot have
any visible influence on the displayed signals.
And as expected the scope shows an 'Amplitude modulated" signal. Modulation frequency of (25-24) - (25-26) = 2 MHz, 26 MHz being the "mirror" of the 24 MHz signal wrt to Fnyquist. All as explained by Marmad.
And (but maybe I misunderstood David) reconstruction will not restore the original 24 MHz waveform.