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"Different algorithms for periodogram analysis are reviewed. The mathematically strong definition is that, for a periodical signal
For regularly distributed discrete moments of time
For using all the (sparse) data, there is a large group of methods based on a determination of a maximum (or minimum) of some test function
These methods may be divided into two large subgroups. The first one is the so-called “Non-parametric” or “point-point” methods. The test function characterizes the “effective distance between the points, which are subsequent in phase (see a review 1997KFNT...13f..67A) or at least a group of points close in phase. No approximation is made, no parameters are determined. The second group of the methods, alternately, are called “parametric” or “point-curve” methods and are based on (generally, weighted) least squares approximation (LSQ). The approximations proposed range from a usual cosine to polynomial (or non-polynomial) splines (special functions/shapes/patterns).
We argue for using complete mathematical models, instead of over-simplified (“step-by-step) ones (like “mean/trend removal” (=”detrending”), “pre-whitening” etc.), to avoid possible large bias of the parameters.An effective tool for an analysis of (multi-periodic) (multi-) harmonic signals is the program MCV (“Multi-Column Viewer) at http://uavso.org.ua/mcv/MCV.zip .
Such approximations are called the “phenomenological” ones, as the number of determined parameters may be significantly larger than that needed for the “physical” modeling (which may need models of unstable stellar atmospheres with a huge number of physical parameters). They are effective for photometric data, especially, of a newly discovered variables, A recent review is in 2020kdbd.book..191A .
We illustrate these methods with applications to variable stars of different types - pulsating (of types M, SR, RV,