The Spectral-Timing Toolbox

X-ray spectral-timing analysis seeks to investigate how matter behaves in the strong gravitational fields around compact objects. By simultaneously examining the spectral and temporal properties of the emission, we can deduce underlying causal relationships between the different emitting components. Spectral-timing analysis is founded in the understanding that photon arrival time and photon energy should not be analyzed separately, since they are intrinsically connected by the underlying physics. Techniques like energy-dependent time lags of X-ray variability and phase-resolved spectroscopy of rapid quasi-periodic oscillations have led to breakthroughs in our understanding of corona geometry, disk-jet interactions, and the possible origin of QPOs. In this talk, I will review the Fourier underpinnings of spectral-timing analysis and showcase examples of spectral-timing techniques with data from RXTE, XMM, NuSTAR, and NICER.