Re: sample rate

[Adrian Bartholomew <adrian@bartholomusic.com>]

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.

Cheers,

Bill