General solutions are derived for least-squares fits of amplitude, phase shift and baseline shift of sinusoidal modulations to normally distributed time series. Four cases are compared: weighted and unweighted fit, with and without a baseline shift. Computer simulations have been performed of the statistical distribution of the amplitude resulting from fits to white noise. A normalised amplitude is defined which follows exactly a Rayleigh distribution, even for small, uneven-sampled data sets. Equations are provided for the width of the distribution and the cumulative probability function. A simple criterion for the statistical significance of the fitted amplitude to a time series is derived and compared for equivalence with the Lomb-Scargle criterion based on a power function.
POMME Stefaan;
2020-04-30
ELSEVIER SCIENCE BV
JRC120184
0168-9002 (online),
https://publications.jrc.ec.europa.eu/repository/handle/JRC120184,
10.1016/j.nima.2020.163933 (online),
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