At 05:03 AM 7/24/96 -0700, Timothy C. May wrote:

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Not familiar with the Nyquist limit w/ regards to sampling rate vs frequency :(

Check any textbook, or even a good dictionary. Basically, it says that one must sample at more than twice the frequency of the highest frequency to be reconstructed. Thus, a 20 KHz top frequency needs at least 40 K samples per second. The exact number is, I think, about 2.2x the freqency, which is why CDs were standardized at 44 K samples per second per channel.

No, Tim, the minimum Nyquist sample frequency _is_ precisely 2.000 times the highest frequency to be recovered. However, what is somewhat less well-known is the fact that in order to keep higher frequencies from being "aliased" (reflected to lower frequencies by heterodyne processes) it is necessary to remove (by filtering) any frequency content above that maximum, before sampling is done. Real-world filters (at least, _economical_ ones) do not have instantaneous cutoffs, so it is necessary to provide a little margin, in this case about 10%. Fortunately, a play-only CD only needs output filters, and the input data (the CD disk itself) has already been limited to about 20 kilohertz, so its requirements are not so stringent. The reason so-called "oversampling" started to be done on CD players is that interpolating digitally between samples results in a far higher aliased noise frequencies, allowing either better performance with the same-quality of filters, or equal quality with lower-cost filters, or a combination of them both. Jim Bell jimbell@pacifier.com