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Re: sample rate

> 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 
> for one frequency, f, the theorem holds 100% true for all frequencies 
> below f and no information is lost.  The mathematics bear

Hi Bill, unfortunately, that's just not correct.   Most of the information 
is lost even for a input frequency of 20KHz in a 44.1KHz digital system. 
The fact is, the ONLY information that is preserved is the frequency.  The 
volume level is somewhat preserved.  The phase information is completely 
lost.  Its not until you get down closer to 1/4 of the sampling frequency 
until you start preserving the phase and volume rather faithfully.

> 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,

I agree with you here Bill.   I doubt that _I_ could hear the difference 
phase.  This is especially true when you consider the equipment we have to 
work with these days (amplifiers, speakers, ect).    However, maybe 
we're going to have some kind of really incredible sound recreation 
available to the common man, and when that day comes I might want to 
to the stuff I've recorded right now with extremely high quality.  That's 
why a lot of people favor 192KHz 24bit recording.

One more thing - there is so much confusion abounding about digital audio 
that I have decided to make an excel spreadsheet which anyone can play 
to "see" firsthand how a sine wave might get captured in a digital system. 
Just email me, and I'll send it to you - its only 92Kb but I don't think I 
can attach this to Looper's Delight.