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

[Charles R Harris]

On Thu, Jun 10, 2010 at 3:41 PM, Anne Archibald
<aarchiba at physics.mcgill.ca>wrote:

> On 10 June 2010 16:52, David Goldsmith <d.l.goldsmith at gmail.com> wrote:
> > 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.
>
> An n-width moving average is (I'm assuming equally-spaced data points)
> convolution by a boxcar of width n.  So its effect on the power
> spectrum is multiplication by a sinc function whose first zero is at a
> period of n samples and whose amplitude at zero frequency is 1. (If
> you have a finite-length data set and are doing circular convolution,
> for "sinc" read the Dirichlet kernel.)
>
>
The sinc needs to be squared for the power spectrum... Chuck
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