At 08:08 PM 7/23/96 -0400, Alan Horowitz wrote:

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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