Chapters authored
Periodogram Analysis under the Popper-Bayes Approach
In this chapter, we discuss the use of the Lomb-Scargle periodogram, its advantages, and pitfalls on a geometrical rather than statistical point of view. It means emphasizing more on the transformation properties of the finite sampling – the available data – rather than on the ensemble properties of the assumed model statistical distributions. We also present a brief overview and criticism of recent literature on the subject and its new developments. The whole discussion is under the geophysical inverse theory point of view, the Tarantola’s combination of information or the so-called Popper-Bayes approach. This approach has been very successful in dealing with large ill-conditioned, or under-determined complex problems. In the case of periodogram analysis, this approach allows us to manage more naturally the experimental data distributions and its anomalies (uncorrelated noise, sampling artifacts, windowing, aliasing, spectral leakage, among others). Finally, we discuss the Lomb-Scargle-Tarantola (LST) periodogram: an estimator of spectral content existing in irregularly sampled time series that implements these principles.
Part of the book: Real Perspective of Fourier Transforms and Current Developments in Superconductivity