Extracting oscillation frequencies from data: Various approaches

Asteroseismology depends absolutely on the detection of authentic pulsation signatures in stars. A variety of mathematical and statistical tools have been developed to extract such signatures from photometric and spectroscopic time series. The earliest tools were developed on the platform of Fourier analysis, and Fourier-based methodology still plays a major part in the detection of pulsation signatures in the present day. Alternative approaches have been gaining ground in recent years. This article offers a brief but broad review of the various methodologies for detecting authentic periodic signals that have been developed over the past few decades, including examples of their pitfalls and successes.