Sampling Theorem

In a previous thread several posters commented concerning the
advantages of (continuous) tachometers in addition to encoders in
servo systems. A fair bit of this discussion exceeded my nameplate
headspace rating, but it seemed like the general idea was that low
speed, or worse low speed and small, events would yield estimates of
motor speed with unacceptably large confidence bounds.

A course called Discrete Time Systems was about as close to real EE
as I ever got. Anyway, about all that stuck was a theorem called the
Sampling Theorem, which at the time seemed elegant, cosmic, profound,
etc. Bascially it said there's no loss in digital vs continuous
measurement so long as you sample at twice the intensity of the
finest level of detail you want to measure. (The statement was
actually in terms of frequencies; sample twice as fast as the
briefest event you want to measure.)

So maybe this means with enough encoder lines and good FPU's tachs
would be redundant?

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IMHO the only way the sampling theorem could be any deeper would be
if the min sampling rate turned out to be e times as fast.

There is a (somehow) related theoretical result in economics: Under a
very plausible set of assumptions, _and in spite of repeated
disappointment_ everything takes e times as long to finish as
originally estimated.

--Jack