Fourier Domain

Abstract

The changes in brightness of an astronomical source as a function of time are key probes into that source's physics. Periodic and quasi-periodic signals are indicators of fundamental time (and length) scales in the system, while stochastic processes help uncover the nature of turbulent accretion processes. A key method of studying time variability is through Fourier methods, the decomposition of the signal into sine waves, which yields a representation of the data in frequency space. With the extension into \textit{spectral timing} the methods built on the Fourier transform can not only help us characterize (quasi-)periodicities and stochastic processes, but also uncover the complex relationships between time, photon energy and flux in order to help build better models of accretion processes and other high-energy dynamical physics. In this Chapter, we provide a broad, but practical overview of the most important relevant methods.

arXiv comment51 pages, 13 figures. Published In: Bambi, C., Santangelo, A. (eds) Handbook of X-ray and Gamma-ray Astrophysics. Springer, Singapore. This revised version adds a Conclusions section, corrects a few typos (including equations) and rewrites a few sentences for clarity. Acknowledgements include a few more people who contributed comments and discussions on the previous version

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