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Um, Christine, you're dead wrong on that.

We don't have to UNDERSTAND the effects of noise and distortion, in order to be able to measure it by taking the difference between input and properly scaled (delay-compensated, etc) output.

All we have to be able to do is take the difference, and we can, to a level that makes us entirely able to calculate the MATHEMATICAL information content.

Your claim about signals near Nyquist is utterly wrong EXCEPT when you're so far up that the filter is removing the signal. You appear to be repeating a myth that many people have attempted to promulgate there, and you're just wrong. See the faq here that makes it clear that there is no problem with stuff near FS/2 as long as your filters are good enough.

And, of course, your complaint about "sinusoidal signals" ignores the simple fact that we can represent any physically realizable signal in terms of sums or integrals of sine waves. So "sine waves" show the outcome just fine.

Many people do not realize that transients may have content ABOVE half the samplign rate. If I turn on a 20kHz signal for 1 cycle, it has a spectrum many, many times over 22.05 kHz, for instance, and you have to FILTER it to bring it in band. The filtering will change the shape, but you have to remember that it's the out of band components that change the shape, not sampling, and not quantization (except at very low levels).

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