CFWhitman

I'm not putting words in your mouth. The point is that if the Nyquist Shannon theorem is correct, then the audible frequencies are exactly reproduced. Thus when you upsample what you've captured to any higher rate, you don't have to guess the sample points of the higher rate for the audible part of the signal (the part intended to be captured). The theorem says that you have captured that part of the signal perfectly, and thus can predict any point on the captured sound waves with perfect accuracy (that's theoretically, anyway). If you can't predict those points, then the theory is incorrect.

The signals above 20kHz (or above wherever the Nyquist rate you're using limited you to) are not accurately captured at all. You don't have enough sample points to even guess at the missing ones (it would be like trying to recreate a straight line with only one endpoint). However, there is no reason to care about those missing parts. It is still possible to upsample the audible part of a 44.1kHz capture to 48 kHz with perfect accuracy (no guessing involved). Nobody cares about the missing (inaudible) parts. They were filtered out. The article linked indicates that you can't do that without "guessing" the missing sample points because they are in between the ones you've captured. That's not correct. Of course any article that puts up a stair step soundwave graph for purposes other than mocking it wasn't written by someone who understands the Nyquist Shannon theorem in the first place.

I don't want to go on forever on this, but I will try to make it more clear.

Regarding interpolation, I don't want to argue about semantics. I want to be clear on what's happening. Technically, any time you calculate data you didn't collect, that's interpolation from a mathematical point of view, just like technically all squares are rectangles even though referring to a square as a rectangle out of context would be misleading.

"In fact it is exactly and precisely linear interpolation."

No, that's not correct. a sine wave is not calculated linearly. There is more to trigonometry than linear interpolation. Sound waves are predictable. Missing data can be calculated accurately as long as you have enough data to accurately describe the wave.

"You can turn around and say 'bah but this is all above the human range of hearing,' but that's not the point. The point is that predicting the values between sample points is never accurate; it's an approximation to the original wave form and we never know how good it is going to be."

You just threw out modern digital recording theory, which has been in application for over thirty years. Sound waves above the range that we are trying to capture are irrelevant to the discussion. Why bring them in? You can capture them if you want to, but you need to go up to the Nyquist rate for those frequencies to do so (incidentally, in my last post I should have said Nyquist rate, not frequency, which is related but not really the term I meant). If you don't, then you can't even begin to calculate their waveform. For practical purposes the parts of a cymbal clash that you can't hear are different sound waves than the ones you are capturing.

Perhaps you should look further into what oversampling accomplishes.

I will sum it up. If you are correct, then digital recording theory, which has been in application for over thirty years, is complete rubbish. The Nyquist rate is meaningless, and people who claim that you need 192kHz files to get accurate sound are probably underestimating. If, on the other hand, digital recording theory is correct, then you only need as many sampling points as the Nyquist rate gives you to accurately predict all the ones in between.