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Re: sample rate

this is where SOME info is worse than NO info.
dude think about it.
u have a wave at 1/2 the sample frequency. think about it like connect-the-dots.
the only ones u can plot are the max(positive) and min(negative) points of the wave. NOW connect the dots and what do u have. thats right a sawtooth wave. even if the original was a sine.
but at least u have the frequency. forget about phase what about shape or tone?
even if u sampled at a frequency high enough to give u three or even 4 points to connect, its STILL approximate, very far from the shape of the original and certainly not "all the information of the original signal".
Adrian Bartholomew
8439 Lee Blvd
Leawood, KS 66206
(913) 660-6918

On Dec 20, 2005, at 1:53 AM, Bill Fox wrote:

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.