* "Danny-K" <[EMAIL PROTECTED]> on Wed, 30 May 2001
| I am curious to learn exactly how sampling at twice the highest frequency
| changes things. I'm trying to visualize it, but I can't grasp it.
Are you familiar with the term "jaggies" in regards to images displays?
Jaggies are the stair-stepping you see when the resolution of the image is
lower than the medium. The technical term for this is "aliasing". The
simplest (but most expensive) anti-aliasing technique is to increase the
resolution of the image to the resolution of the medium. This is just as
important for printed media as it is for CRTs and LCD panels.
The exact same aliasing phenomenon occours in digital audio, and the exact
same technique is used to eliminate it: increase the resolution, except in
digital audio it is called "frequency response" (resolution has a partially
different meaning). Aliasing occours when the sampling frequency is less
than twice the frequency, exactly as you describe. The math is moderately
complex, and a physics text book can do a better job of describing it than
I can, so I won't :).
Anyway, if the higest frequency in a sound is 20kHz, then a sampling
frequency of 40kHz will be able to record it with 100% fidelity, assuming
you allocate enough bits to store the data.
In practice, the top ~25% of the response curve is "wasted" for roll-off
and anti-aliasing filters. So for CD-DA with a sampling frequency of
44.1kHz, the maximum frequency it can sample is 22.01kHz, but the effective
high end is ~15kHz. DAT improves on this by increasing the sampling
frequency to 48kHz, for a top of 24kHz or an effective frequency response
of ~18kHz. And the various DVD-Video and DVD-Audio specs can crank up to a
whopping 96kHz sampling frequency, offering frequency response that is
indistinguishable from the analog source.
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