  Cygnus X-1, as the first discovered black hole binary, is a key source for
understanding the mechanisms of state transitions, and the scenarios of
accretion in extreme gravity fields. We present a spectral-timing analysis of
observations taken with the Insight-HXMT mission, focusing on the
spectral-state dependent timing properties in the broad energy range of 1--150
keV, thus extending previous RXTE-based studies to both lower and higher
energies. Our main results are the following: a) We successfully use a simple
empirical model to fit all spectra, confirming that the reflection component is
stronger in the soft state than in the hard state; b) The evolution of the
total fractional root mean square (rms) depends on the selected energy band and
the spectral shape, which is a direct result of the evolution of the power
spectral densities (PSDs); c) In the hard/intermediate state, we see clear
short-term variability features and a positive correlation between central
frequencies of the variability components and the soft photon index $\Gamma_1$,
also at energies above 15 keV. The power spectrum is dominated by red noise in
the soft state instead. These behaviors can be traced to at least 90 keV; d)
The coherence and the phase-lag spectra show different behaviors dependent on
different spectral shapes.
