Re: Digital Watermarks for copy protection in recent Billbo

["Perry E. Metzger" <perry@piermont.com>]

Timothy C. May writes:
> >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.

The Nyquist Theorem states you need exactly twice the samples, not
over twice. The magic number isn't something like 2.2, its exactly
2. Now, the reality is that low pass filters in the recording studio
aren't going to be perfect and such, being analog devices, and higher
frequencies making it in will cause aliasing artifacts, so you
probably want to sample at above twice your putative cutoff because it
won't be your real cutoff, but in principle you need exactly twice the
highest frequency.

Perry