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**To**:**Loopers-Delight@loopers-delight.com****From**:**Bill Fox <billyfox@soundscapes.us>****Subject**:**Re: sample rate****Date**:**Tue, 20 Dec 2005 02:53:37 -0500**

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. Cheers, Bill

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**References**:- Re:sample rate
*From:*a k butler <akbutler@tiscali.co.uk>

- Re:sample rate

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