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In so many words, Shannon gave a proof showing that in general the sample rate of a digital sensor puts an upper bound on the frequency of any signal that sensor is able to detect.

Unlike the Nyquist-Shannon theory, compressed sensing is not generally applicable: it requires a sparse signal.

As with many other optimization techniques, it’s a trade off between soundness and completeness.

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that is not correct. digital sensors detect frequencies above the nyquist limit all the time, which is why they need an analog antialiasing filter in front of them. what they can't do is distinguish them from baseband aliases

you could just as correctly say 'nyquist-shannon theory is not generally applicable; it requires a bandlimited signal' (which is why compressed sensing doesn't violate it)

Thank you for the clarification, great point about the importance of distinguishing the acts of "detecting" and "making sense of" some signal/data/information

Great way to explain it!

Loved this:

> As with many other optimization techniques, it’s a trade off between soundness and completeness

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