Wind/Solar Electrics ???

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Joel Kolstad wrote:

(I can't tell you how many times I've seen people stating something like,
'The Nyquist theorem requires sampling at at least twice the highest
frequency present in the signal," when of course it says no such thing.)

What do you think it means?


Nyquist figured out that higher frequency components of the input signal
will 'alias' and you will lose the ability to tell them from lower frequency
components. In order to avoid 'losing information' and not being able to
tell whether a particular sample stream was from a low or high frequency
component, Nyquist's theorem states you must sample at least twice as fast
as the highest component present.
http://www.cs.cf.ac.uk/Dave/Multimedia/node149.html
http://www.efunda.com/designstandard...sp_nyquist.cfm

A lot of folks mistake it to think you need to sample at least twice as fast
as the 'signal of interest' also, and try to ignore high frequency
components of the input because they're 'not interested in that noise'. But
what Nyquist proved was that any frequency in the sampled signal that is
more than 1/2 the sample frequency will 'alias' and 'wrap around' and be
*indistinguisable* from a frequency component that is less than 1/2 the
sample frequency.

For example, if sampling at 1000 hz, and the sampled signal is a 900 hz
'pure sine wave', the sampled data would look *exactly* the same as if you
had sampled a 100 hz 'pure sine wave'. They would be 'indistinguisable'.
So if/when you try to convert the sampled data back to analog, how do you
know whether it should reconstruct a 100 hz wave, or 900 hz? You don't, so
you have a conundrum.

So, to avoid losing this 'information' of being able to tell if you had a
100 hz or 900 hz input, the standard thing to do is filter the input so that
there is *no* 900 hz input. Then, the resulting sample data must have come
from the 100 hz component. And if/when you want to reconstruct it, you
*know* it should form a 100 hz signal because no 900 hz signal could
possibly been present (you eliminated it before sampling).

And as Joel mentioned earlier, since most low-pass filters do not have
perfect 'cutoff' (IIRC, simple first-orders 'roll off' at something like 3
db/decade), it is more common to eliminate any frequency component that is
more than about 40% of the sampling frequency.

daestrom