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Re: sample rate

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
> (and generally).

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.