Spectral analysis with cubic splines

In 1993, a new method was developed for finding the periodicity of stellar light curves using cubic splines. The technique is similar in philosophy to the "minimum string length" approach and is therefore insensitive to the actual light curve shape. This work was described extensively in an article published in The Astrophysical Journal 436, pages 787-794 (1994 December 1).

The program source code for implementing the cubic spline spectral analysis can be found in two directories accessible with a web browser:

Spline subroutine library:  http://www.physics.lsa.umich.edu/akerlof/Spline/Spline/

Sample main programs: http://www.physics.lsa.umich.edu/akerlof/Spline/Samples/

Both of these directories contain ".doc" text files which should be read first. The /Spline directory contains all of the source code required to create a library of spline routines. /Spline/Samples contains the source code for various main programs which use the spline library to find the periodicity of unequally sampled light curves. A brief description can be found by clicking "poster paper".

 

For more information, contact Carl Akerlof, akerlof@mich.physics.lsa.umich.edu  


(from The Astrophysical Journal)

Application of cubic splines to the spectral analysis of unequally spaced data

C. Akerlof, C. Alcock, R. Allsman, T. Axelrod, D.P. Bennett, K.H. Cook, F. Freeman, K. Griest, S. Marshall, H-S. Park, S. Perlmutter, B. Peterson, P. Quinn, J. Reimann, A. Rodgers, C.W. Stubbs, and W. Sutherland

In the absence of a priori information, nonparametric statistical techniques are often useful in exploring the structure of data. A least-squares fitting program, based on Cubic B-splines has been developed to analyze the periodicity of variable star light curves. This technique takes advantage of the limited domain within which a particular B-spline is nonzero to substantially reduce the number of calculations needed to generate the regression matrix. By using simple approximations adapted to modern computer workstations, the computational speed is competitive with most other common methods that have been described in the literature. Since the number of arithmetic operations increases as N2, where N is the number of data points, this method cannot compete with the FFT modification of the Lomb-Scargle algorithm. However, for data sets with N < 10**4, it should be quite useful. Examples are shown, taken from the MACHO experiment.


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