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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.