  Observations suggest that accretion discs in many X-ray binaries are likely
flared. An outer edge of the disc intercepts radiation from the central X-ray
source. Part of that radiation is absorbed and reemitted in the optical/UV
spectral ranges. However, a large fraction of that radiation is reflected and
appears in the broad-band X-ray spectrum as a Compton reflection bump. This
radiation is delayed and variability is somewhat smeared compared with the
intrinsic X-ray radiation. We compute response functions for flat and flared
accretion discs and for isotropic and anisotropic X-ray sources. A simple
approximation for the response function which is valid in the broad range of
the disc shapes and inclinations, inner and outer radii, and the plasma bulk
velocity is proposed. We also study the impact of the X-ray reprocessing on
temporal characteristics of X-ray binaries such as the power spectral density,
auto- and cross-correlation functions, and time/phase lags. We propose a
reprocessing model which explains the secondary peaks in the phase lag Fourier
spectra observed in Cyg X-1 and other Galactic black hole sources. The position
of the peaks could be used to determine the size of the accretion disc.
