I am very leary about getting involved in this thread online as the nature of this discussion might get into a mathematics area that is outside of the scope of the typical discussion on a music related website thread.
There are several problems with this paper, all of which can be wrapped up into the quote of Shannon's theorem. The conclusion is drawn in the paper that Shannon's theorem requires an infinite sum and therefore renders the reconstruction process incomplete and inaccurate, thereby requiring higher sample frequencies.
The problem with this is that an infinite sum is only required if we sample at only double the highest frequency in the system. As you write:
Well it means at least one thing:
If we sample as slow as twice the highest frequency, in the real world, we never - and I say never - get back to the original signal!"
Of course this is correct, but you have left the crucial detail out that if we sample 1/infinity greater than this frequency then reconstruction is perfect with finite time systems. If we sample higher than double the highest frequency present then we no longer require an infinite sum in the reconstruction process and Shannon and Nyquist both work properly - in other words, higher sample frequencies are not required if we simply sample at greater than twice the highest frequency present.
We can see in Shannon's theorem that his theorem deals with infinite time. Shortening that to a finite amount of time no longer requires infinite sampling to create accuracy. Try it. I guarantee it works.
Also, the quote ascribed to Nyquist is not the Nyquist theorem - I'm sure it is something he wrote, but it is not the crux of his famed paper, "Certain Topics on Telegraph Transmission Theory."
Charles, I find your paper very frustrating. It is clearly very erroneous and allows the populous that reads it to draw incorrect conclusions about the nature of digital audio reconstruction. I think you are doing a great disservice to the market at large by publishing such information. I think you should pull the paper down and rewrite it factually and then re-post it. Your writing style is good and you are effective at getting a point across, but this point is simply false. It is simply incorrect that a higher FS system can reconstruct a 14kHz system more accurately than a base rate system, and it is simply inaccurate that modulation occurs on reconstruction of a properly sampled waveform. That is simply, absolutely erroneous and it is totally discouraging to see you peddleing such bunk.
Remember that Shannon only works either with infinite time at 2N or less than infinite time at >2N, and that ANY amount of time less than infinite is acceptable and ANY sample frequency greater than 2N works.
Nika.
