Phase Dispersion Minimization

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PDM2 analysis for the double mode Cepheid variable TU Cas, primary period
Raw data set for the analysis shown above. The large gaps are often found in ground based observations.

Phase Dispersion Minimization (abbreviated PDM ) is a data analysis technique that determines periodic components from a time series measurement. It is mainly used when the data sets have missing time segments, non-sinusoidal oscillations, unfavorable time coverage or other disadvantages that prevent a Fourier analysis . The method was primarily described by Stellingwerf (1978). PDM is widely used in astronomy and physics .

Procedure

The Dispersion Minimization phase is a variant of data convolution. The core of the method is a repeated trying out or estimation of a period duration and subsequent superimposition of the data in sections according to the length of this estimation period. The data are thus folded into a phase plot. If the estimation period corresponds to the true period of the data, a measured value distribution according to a relatively simple function results in the phase diagram. If this is not the case, however, the measured values ​​are distributed arbitrarily.

In order to be able to carry out this form of result analysis, PDM divides the phase diagram into several subsections and calculates the variance of the measured values ​​within these subsections. These subsections can optionally overlap one another in order to get better coverage of the phase. The variances are added up and set in relation to the variance of the total measurement. If the estimation period agrees with the real one, the quotient of the variances is minimal. Inconsistent periods result in a quotient of approximately one. A graph in which these quotients are plotted over the estimation period provides the positions of probable periods.

An alternative approach to subdividing into subsections is to consider the differences between neighboring measured values. If the estimation period agrees with the true one, the ordinate values ​​of the measurements are adjacent and the summation of the differences is minimal.

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