X-ray binaries (XRBs) are binary systems where a compact object, either a black hole or a neutron star, accretes matter from a stellar companion via an accretion disc. As this material spirals in, it heats up and emits X-rays, typically exhibiting transient outburst behaviour.

During these outbursts, XRBs often transition between hard states (dominated by inverse Comptonization in a hot-electron corona) and soft states (where thermal emission from the disc prevails). In the hard states, XRBs display strong variability across multiple timescales, frequently featuring quasi-periodic oscillations (QPOs).

To probe these fast dynamics, we employ spectral-timing Fourier techniques, which allow us to infer the geometry of the accretion flow and the mechanisms governing radiation propagation in the vicinity of the compact object, crucial information not directly accessible through the stationary spectrum alone.

In this talk, I will delve into the spectral-timing phenomenology of XRBs and present the insights gained from applying a time-dependent Comptonization model, aiming to deepen our understanding of the state transition and outburst evolution in these complex systems.