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Phase dispersion minimization
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Phase dispersion minimization : ウィキペディア英語版
Phase dispersion minimization

Phase dispersion minimization (PDM) is a data analysis technique that searches for periodic components of a time series data set. It is useful for data sets with gaps, non-sinusoidal variations, poor time coverage or other problems that would make Fourier techniques unusable. It was first developed by Stellingwerf in 1978 〔("Period Determination Using Phase Dispersion Minimization", Stellingwerf, R.F., Astrophysical.J. v224, p953, 1978. )〕 and has been widely used for astronomical and other types of periodic data analyses. Source code is available for PDM analysis. The current version of this application is available for download.〔("PDM2 Application, Technical Manual, and test data sets", Stellingwerf, R. F., 2006. )〕
== Background ==
PDM is a variant of a standard astronomical technique called data folding. This involves guessing a trial period for the data, and cutting, or "folding" the data into multiple sub-series with a time duration equal to the trial period. The data are now plotted versus "phase", or a scale of 0->1, relative to the trial period. If the data is truly periodic with this period a clean functional variation, or "light curve", will emerge. If not the points will be randomly distributed in amplitude.
As early as 1926 Whittiker and Robinson 〔"The Calculus of Observations", Whittiker, E. T., Robinson, G. (London: Blackie and Son) 1926.〕 proposed an analysis technique of this type based on maximizing the amplitude of the mean curve. Another technique focusing on the variation of data at adjacent phases was proposed in 1964 by Lafler and Kinman.〔("An RR Lyrae Star Survey with Ihe Lick 20-INCH Astrograph II. The Calculation of RR Lyrae Periods by Electronic Computer", Lafler, J., Kinman, T. D. Astrophysical J., v11, p216, 1965. )〕 Both techniques had difficulties, particularly in estimating the significance of a possible solution.

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