[SciPy-User] OT: Stats Q (educate me please)

David Goldsmith d.l.goldsmith@gmail....
Thu Jun 10 15:52:08 CDT 2010

I recently had cause to ponder moving averages, and given my general
interest in noise theory, it got me wondering: relative to the PS of the
signal, what's the PS of a n-width moving average.  After unsuccessfully
(though far from exhaustively) looking for some results in the literature, I
just started thinking about it myself, and came to realize, both based on
what the graphs are saying about the situation and then in light of that, in
retrospect, conceptually as well, since the moving average is a smoothing of
the signal, it's some kind of low-pass filter (removing power at higher
frequencies), which begs the question: what kind of low-pass filter?  In
particular, is it a truncation filter, completely removing any power from
windows smaller than n (the intuitive, though far from obvious, conclusion),
or is it an attenuation filter, applying some monotonically decreasing
envelope to the PS for frequencies corresponding to windows smaller than n?
(Or does it somehow influence even the power of frequencies corresponding to
windows larger than n?)  Reference/proof?  Thanks for the education.

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