Extracting oscillation frequencies from data: various approaches

Abstract

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.

Radial velocity data analysis with compressed sensing techniques

“…A large part of those methods consists in computing the autocorrelation function or folding the data at a certain period and look for correlation. See Engelbrecht (2013) for a survey or Zucker (2015Zucker ( , 2016 in the context of radial velocity measurements. Finally, we point out that the use of the sparsity of the signal is not specific to Compressed Sensing.…”