From: Harald Giese <giese@dkrz.de>
Subject: Re: What's the best acceleration approximation for discrete data?
Date: Fri, 23 Jul 1999 11:52:18 +0200
Newsgroups: sci.math.num-analysis
Keywords: time series analysis

Rob Jones wrote:
> 
> Hi,
> 
> Has anyone got any acceleration approximation methods, given a discrete
> position output, which are less prone to stochastic noise than the
> difference method which I'm currently employing? (I'm trying to damp down
>  resonance in a hyper-accurate postioning system using acceleration
> feedback,
>  but my acceleration approximation has too much noise riding on it)
> ...


Hi Rob,

have a look at books on time series analysis, esp. cosine filters. Using
a running-mean filter (i.e. a "square window": w(j) = 1/N, N: window
length ) in the time domain would give you sidelobes in the frequency
domain (the Gibbs phenomenon). Using a cosine window (w(j) = 1/2(1-Cos[2
\pi j/(N-1)]), j=0,..,N-1) reduces these sidelobes much better.

Best regards,
Harald


Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T. 1993:
Numerical Recipes in C. Cambridge Univ. Pr.
Hamming, R.W. 1977: Digital Filters. Prentice Hall, Englewood Cliffs,
N.J.
Lanczos, C. 1956: Applied Analysis. Prentice Hall (...), Reprinted in
1988, Dover, N.Y.

-- 
Harald Giese
Email: giese@dkrz.de
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