  The strong variability of blazars can be characterized by power spectral
densities (PSDs) and Fourier frequency-dependent time lags. In previous work,
we created a new theoretical formalism for describing the PSDs and time lags
produced via a combination of stochastic particle injection and emission via
the synchrotron, synchrotron self-Compton, and external Compton (EC) processes.
This formalism used the Thomson cross section and simple $\delta$-function
approximations to model the synchrotron and Compton emissivities. Here we
expand upon this work, using the full Compton cross section and detailed and
accurate emissivities. Our results indicate good agreement between the PSDs
computed using the $\delta$-function approximations and those computed using
the accurate expressions, provided the observed photons are produced primarily
by electrons with energies exceeding the lower limit of the injected particle
population. Breaks are found in the PSDs at frequencies corresponding to the
cooling timescales of the electrons primarily responsible for the observed
emission, and the associated time lags are related to the difference in
electron cooling timescales between the two energy channels, as expected. If
the electron cooling timescales can be determined from the observed time lags
and/or the observed EC PSDs, then one could in principle use the method
developed here to determine the energy of the external seed photon source for
EC, which is an important unsolved problem in blazar physics.
