From: mpd@netcom.com (Mike Duvos)
Date: Thu, 25 Jul 1996 14:42:07 +0800
To: cypherpunks@toad.com
Subject: Re: Digital Watermarks for copy protection in recent Billbo
In-Reply-To: <199607241517.LAA18088@jekyll.piermont.com>
Message-ID: <199607250438.VAA02125@netcom6.netcom.com>
MIME-Version: 1.0
Content-Type: text/plain


"Perry E. Metzger" <perry@piermont.com> writes:

 > 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.

The Sampling Theorem states that equally spaced instantaneous
samples must be taken at a rate GREATER THAN twice the highest
frequency present in the analog signal being sampled.  If this is
done, the samples contain all the information in the signal, and
faithful reconstruction is possible.

Exactly twice the highest frequency won't do, and it should be
obvious that sampling a sine wave at twice its frequency yields
samples of constant magnitude and alternating sign which convey
nothing about its phase and little useful about its amplitude
either.  (Drawing a little picture might be helpful here.)

Although anything over twice the highest frequency will work in a
theoretical sense, a small fudge factor does wonders for digital
signal processing, if only to reduce to a reasonable value the
width of the window into the sample stream needed for various
signal manipulations.

--
     Mike Duvos         $    PGP 2.6 Public Key available     $
     mpd@netcom.com     $    via Finger.                      $