Multiple oscillation frequencies separated by close to or less than the formal frequency resolution of a data set are a serious problem in the frequency analysis of time series data. We present a new and fully automated Bayesian approach that searches for close frequencies in time series data and assesses their significance by comparison to no signal and a mono-periodic signal. We extensively test the approach with synthetic data sets and apply it to the 156 days-long high-precision BRITE photometry of the SPB star HD 201433, for which we find a sequence of nine statistically significant rotationally split dipole modes.
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