-=> Quoting Steve Mctague to Bonnie Goodwin <=-
 SM> I'm curious to hear what you have to say about this very
 SM> topic.  Do you think the Nyquiest theorem is fair in saying
 SM> a sampling rate of 44kHz can be used on 20kHz signals?
        Absolutely.
 SM> If you're sampling at 44k, measuring a 20k+ hz wave means
 SM> you're only gonna have around 2 points of reference digitally,
 SM> right? Well, I don't think connecting 2 dots can represent
        It doesn't work the way you think.  Even though there are
20,000 distinct frequencies going on, there is only 1 octave between
10,000 and 20,000 Hz.  There is 1 octave between 20 and 40 Hz.
Nyquists theorem covers all octaves evenly.  That's a vast
simplification, but sufficive to say, the top octave is handled just
fine, except possibly for some phase variation caused by truncating
info above 22kHz.  But at that octave, it's not important and it has
nothing to do with Nyquist's theorem.  As Bonnie indicated, the
usable highest frequency isn't quite the .5 ideal, but it's close
enough for the following example.
        As an example, if you wanted to cover from 1Hz to 40Hz (3
octaves, only 1 of which is audible to the human ear), Nyquist's
theorem says you need twice the highest frequency covered, so a
sampling rate of 80Hz is needed.  If you'll notice that's 2 samples
per frequency.  Sound familiar?  In effect, with a 44kHz sampling rate
to digitize 22kHz worth of sound, you have 2 samples per frequency
across the board, not just for the 10Hz-20kHz region.  I'm a little
rusty on this material, but I believe the reason is for a sine wave
(each frequency represents a sine wave), you need to know the maximum
and minimum amplitude.  (Someone correct me if I'm wrong...I'm really
only thinking about this logically from my basic knowledge of sine
waves) Digitally, this represents a stair-step, but during D/A
conversion, a sine wave is reconstructed with those amplitudes for
every frequency recorded within the 1Hz-22kHz range.  This is easy to
do because a sine wave is THE fundamaental building block.  It only
needs to know the amplitude for a given frequency to recreate one.  By
combining frequencies, you can reconstruct the musical signal quite
easily.  So no, Nyquist's theorem works fine for all frequencies to
infinity.
        I hope this helps.
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