Issue |
Astron. Astrophys. Suppl. Ser.
Volume 125, Number 1, October I 1997
|
|
---|---|---|
Page(s) | 207 - 217 | |
DOI | https://doi.org/10.1051/aas:1997217 | |
Published online | 15 October 1997 |
Method of running parabolae: Spectral and statistical properties of the smoothing function
Department of Astronomy, Odessa State University, T.G. Shevchenko Park, 270014 Odessa, Ukraine
Received:
30
April
1996
Accepted:
13
December
1996
Analytic expressions in a general form are derived for the
expectation of functions related to the smoothing the astronomical
signals using local approximations with additional weights. No
restrictions are made on distribution of the times of the signal.
Applications are made for polynomial fits of orders 0 and 2 and weights
and
. These variable weights ensure that
the smoothing function will be both continuous and differentiable,
which is important for determining the extrema and the shape of the
variations. Special attention is paid to evenly spaced time series data,
which if their number is large enough will allow one to obtain analytic
expressions for the main functions.
Key words: methods: analytical; data analysis; numerical; statistical
© European Southern Observatory (ESO), 1997