There is a long history and wide variety in period finding algorithms, that can be used to study light curves of variable stars, exoplanets and asteroids. They can be divided into a number of types:


  • Algorithms based on discrete Fourier transforms


These methods attempt to represent a set of observations with a series of trigonometric functions (sines and cosines, with different periods, amplitudes and phases). They are one of the oldest forms of time-series analysis and are also quite flexible. Fourier methods supported by Peranso are : Discrete Fourier Transform (Deeming) DFT, Date Compensated Discrete Fourier Transform (Ferraz-Mello) DCDFT,  CLEANest, FALC (Harris) and Bloomfield. 


 

  • Algorithms that model a light curve via a least-squares fit to some set of (orthogonal) basis functions


  • Algorithms that minimize some measure of the dispersion of time series data in phase space

    This includes methods such as Jurkewich and ANOVA. The minimization can be done in various ways, including:

    • Binned means. They look for the period that produces the least observational scatter ("best phasing of data") around the mean light curve. Peranso implements PDM (Stellingswerf)
    • Variance, such as in Phase binned AoV, AoV Transit
    • Entropy, such as Conditional Entropy
    • Total distance between points, such as in Dworetsky
    • String lengths. These methods fold the observation data on a series of trial periods, and at each trial period the sum of the lengths of line segments joining successive points (the string-length) is calculated. Minima in a plot of string-length versus trial frequency indicate possible periods. Peranso includes Lafler-Kinman and Renson


  • New research in period finding algorithms is exploring still other approaches, such as Bayesian methods or Neural networks


  • Some algorithms have been specifically developed for exoplanet research

    An example is Edge Enhanced Box-fitting Least Squares (EEBLS), which analyses stellar photometric time series in search for periodic transits by exoplanets, looking for signals characterized by a periodic alternation between two discrete levels, with much less time spent at the lower level.