a k butler wrote:
Bell Labs researcher Harry Nyquist develops Sampling Theory. It states provides that if a signal is sampled at twice its nominal highest frequency, the samples will contain all of the information in the original signal.
Which is clearly not true :-)
There's no way to keep the phase information for a signal sampled
at only twice it's frequency.
Only the amplitude.
I guess that the Nyquist Theorum is misquoted somewhat here
Although you might be correct for a frequency of f when the sampling frequency is 2f, the theorem correctly stated says that it will be good for frquencies UP TO f Hz, i.e. not including f. So while you're correct for one frequency, f, the theorem holds 100% true for all frequencies below f and no information is lost. The mathematics bear out. For shorthand, the bandwidth of a system is stated as f Hz, not (f - 1) Hz.
BTW, I dare anyone to tell me they can HEAR that 20kHz has a wrong phase relationship in a system sampled at 40kHz. Plus, in the real world, where there are no ideal filters, a guard band is built in. That's why an audio system that is designed to have a 20kHz bandwidth uses a sampling frequency of 44.1kHz. This also avoids the problem of 20kHz not having a proper phase relationship since it is less than half the sampling frequency, not exaclty half the sampling frequency.