And so it came to pass, on 11-25-96 10:42,
   that Steve McTague spake unto Bonnie Goodwin:
 ->> > If you want state of the art, stay clear of CDs. 16 bit
 ->> > wordlength and low sampling frequencies just don't cut it for
 ->> > anything above about 4Khz.
 BG>> BS. Wordlength doesn't have a thing to do with frequency response,
 BG>> it has to do with potential dynamic range. While it can be argued
 BG>> that 16 bits isn't enough, it is sufficient for most purposes.
I'd say 96dB range is enough for 99.99% of real-world situations.  Most other 
electronics in the chain will max out at or around 96dB anyway, and since the 
final step (the speakers and the listening environment) will generally have 
significantly less range available, I don't think a bit one way or the other 
would be all that significant.
 BG>> It is sampling rate that determines total possible frequency
 BG>> resposne and is determined by the sampling frequency devided by
 BG>> the Nyquist theorem, which is a total of about .47 of the sampling
 BG>> frequency is the highest usable frequency, which at 44.1kHz should
 BG>> give about a  20k (OK, 20,727Hz for those with calculators to
 BG>> check my math!) potential top end limit, after which everything
 BG>> must be cut off sharply to prevent antialiasing.
 SM> I'm curious to hear what you have to say about this very topic.  Do
 SM> you think the Nyquiest theorem is fair in saying a sampling rate of
 SM> 44kHz can be used on 20kHz signals?
Yes.  Nyquist's theorum merely applies to the minimum sampling rate that must 
be used to reproduce a given frequency without aliasing (although I'd learned 
it was exactly a 2:1 ratio -- in other words, a 44.1k sample rate permits a 
maximum 22.05kHz frequency to be sampled).  It makes no assumptions about the 
"quality" or overall accuracy of the sample.
 SM> If you're sampling at 44k, measuring a 20k+ hz wave means you're
 SM> only gonna have around 2 points of reference digitally, right?
Right.
 SM> Well, I don't think connecting 2 dots can represent the original
 SM> wave.  However, this is where you come in, since you're closer to
 SM> recording techniques than I and I rarely listen to sine waves for
 SM> music  :), maybe you can shed some light on this.  
Analog filtering after the D/A conversion will smooth off the square waveform 
to approximate the original waveform.
The problem arises when the frequency to be sampled exceeds half the sample 
rate.  Without the advent of decent graphics (which would make it easy to 
show how this is a problem) in this medium, suffice to say, sampling a higher 
frequency would lead to "aliasing", or false readings.  A simple example: 
when sampling at 44kHz, a 22kHz signal would look the same to the A/D as a 
44kHz signal, as would an 88kHz signal, and so on.  The multiple peaks would 
all occur within the sample period, and be missed.  Thus, upon playback, any 
signal that was originally 44kHz or 88kHz would be reproduced as extra 22kHz 
signal.
 SM> Don't you just hate it when amateurs (me included!) think they know
 SM> enough to be dangerous?   :)
Heh, yup :)
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Love, luck, and lollipops...
Matt


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