Fourier Methods

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 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.