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Period Search

Comparison of The New and Old Methods
  • Alex Schwarzenberg-Czerny
Conference paper
Part of the Astrophysics and Space Science Library book series (ASSL, volume 218)

Abstract

Period search can be viewed as attempts to fit data ξ with a model curve ξ|| at consecutive frequencies ω (e.g. Lomb, 1976). The plot of the measure of the fit quality, usually a function of the L 2 vector norm ||ξ — ξ||||2, called the χ2 statistic, against the frequency ω constitutes a periodogram. The norm is associated with the scalar product \(\langle \xi ,\eta \,\rangle = \sum\nolimits_{i = 1}^n {{\mu _i}} {\bar \xi _i}{\eta _i},\) where ||ξ||2 =< ξ,ξ < and are weights. A set of the orthogonal functions ∅(l), l = 1, ... ,d || < n, such that < ∅(l),∅(k) >=δ lk spans the d || dimensional model subspace in the n dimensional space of the observations. It can be demonstrated that the orthogonal projection of the observations ξ onto the model space constitutes the least squares fit in the sense of the χ2 norm and that the residuals ξ ≡ ξ—ξ|| are orthogonal to the model: Hence Pythagoras Theorem holds:
(1)

Keywords

Beta Distribution Input Signal Shape Period Search Fourier Model Pythagoras Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 1997

Authors and Affiliations

  • Alex Schwarzenberg-Czerny
    • 1
    • 2
  1. 1.Astronomical Observatory of Adam Mickiewicz UniversityPoznańPoland
  2. 2.Copernicus Astronomical CentreWarsawPoland

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