  We present the most extensive analysis of Fourier-based X-ray timing
properties of the black hole binary Cygnus X-1 to date, based on 12 years of
bi-weekly monitoring with RXTE from 1999 to 2011. Our aim is a comprehensive
study of timing behavior across all spectral states, including the elusive
transitions and extreme hard and soft states. We discuss the dependence of the
timing properties on spectral shape and photon energy, and study correlations
between Fourier-frequency dependent coherence and time lags with features in
the power spectra. Our main results are: (a) The fractional rms in the
0.125-256 Hz range in different spectral states shows complex behavior that
depends on the energy range considered. It reaches its maximum not in the hard
state, but in the soft state in the Comptonized tail above 10 keV. (b) The
shape of power spectra in hard and intermediate states and the normalization in
the soft state are strongly energy dependent in the 2.1-15 keV range. This
emphasizes the need for an energy-dependent treatment of power spectra and a
careful consideration of energy- and mass-scaling when comparing the
variability of different source types, e.g., black hole binaries and AGN. PSDs
during extremely hard and extremely soft states can be easily confused for
energies above ~5 keV in the 0.125-256 Hz range. (c) The coherence between
energy bands drops during transitions from the intermediate into the soft state
but recovers in the soft state. (d) The time lag spectra in soft and
intermediate states show distinct features at frequencies related to the
frequencies of the main variability components seen in the power spectra and
show the same shift to higher frequencies as the source softens. [...abridged]
In particular, we discuss how the timing properties of Cyg X-1 can be used to
assess the evolution of variability with spectral shape in other black hole
binaries. [...abridged]
