Say I have a 1kHz sine, so no higher harmonics, then I need to sample it at least at 2kHz to be able to reconstruct it.
But if I sample at 2kHz, but all my samples are on the zero-crossing, then my sampled signal doesn't show a sine at all, rather the ECG of a deceased patient. How can that be explained?
This can be expanded to higher sampling frequencies too. If I sample a more complex waveform at 10kHz, I should at least get the first 5 harmonics, but if the waveform is such that the samples are each time zero, then again we get nothing. This isn't far-fetched, it's perfectly possible for a rectangle wave with a duty cycle < 10%.
So why is it that the Nyquist-Shannon criterion seems to be invalid here?