From: jim bell <jimbell@pacifier.com>
Date: Wed, 24 Jul 1996 16:02:05 +0800
To: Alan Horowitz <alanh@infi.net>
Subject: Re: Digital Watermarks for copy protection in recent Billbo
Message-ID: <199607240531.WAA21163@mail.pacifier.com>
MIME-Version: 1.0
Content-Type: text/plain


At 08:08 PM 7/23/96 -0400, Alan Horowitz wrote:
>> 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.
>
>   Well, fudge sticks. That sounds like this thing called an "image" in 
>heterodyne analog RF receivers. I know how those work.

Sampling produces essentially the same effect.

>What is the physical basis for "aliasing" as you describe, in the 
>sampling theater of operations?

Sampling a signal of frequency f1 at a rate of f2 produces two mixes, f1+f2 
and f1-f2.  The sum is sufficiently high that it isn't a concern, the 
difference could be.  If you have an input containing frequencies up to 25 
Khz, and you sample it at a rate of 40 kilosamples per second, the input 
frequency of 25 kilohertz gets mirrored down to 15 kilohertz, which is far 
lower than its original frequency.  This is a problem!  

Some of the early voice-scramblers used this effect, heterodyning the audio 
band with a higher-frequency signal and reversing it, changing higher 
frequencies to lower and vice versa.  Not particularly "secure" by today's 
standards, but it probably kept a few people from understanding what's going 
on.  I've heard, however, that with practice you could learn to understand 
such frequency-inverted speech, as odd as it sounds.

Jim Bell
jimbell@pacifier.com