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Re: OK, this is my final post

I won't reply to real_jj's posts, since he/she's clearly foaming at the mouth and has no real understanding of sampling theory.

*** Of course you can't sample and recover a continuous signal perfectly when the samples are quantized. ***

Which is what I have been saying all along.

*** Shannon even gives you a bound for the required data rate needed to transmit the signal given a maximum tolerable amount of quantization error. ***

Shannon's analysis is a bit simplistic, and pertains to communications theory rather than music reproduction. If you take into account other factors in digital audio, such as filter imperfections, jitter and truncation error from finite precision computation in the digital filter, then the error can be quite large (based on my modelling).

All I was suggesting in the first place is that it is possible to construct a test signal that illustrates how large these errors can be.

*** Thus it does not "break" the sampling thereom. ***

I never said the sampling theorem "breaks", but it is undefined, since a necessary prerequisite has not been met.

This is simply logic: If a theorem states that A is true if B and C are true, but C is not true, then strictly speaking we don't know whether A is true or not - that is what undefined means.

In the case of sampling theorem, we actually do know that "A" is NOT true (in other words, the signal cannot be reconstructed with "arbitrary accuracy", but the error can be shown to be bounded).

I'm just simply calling out that neither of real_jj's statements are true. His/her first statement was that A is still true even if C is untrue (and the reference to dithering is just bizzare and completely irrelevant), which is clearly illogical and never implied by Shannon's paper. His/her second statement was that C is not a necessary precondition for A to be true. This is also incorrect, since it's stated directly in Shannon's paper and I have provided a quote.

real_jj's response is instructive in that it clearly shows he/she has no clue whatsoever. Since it's pointless to argue with fools, I won't bother replying.

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