  We build on a long-standing tradition in astronomical adaptive optics (AO) of
specifying performance metrics and error budgets using linear systems modeling
in the spatial-frequency domain. Our goal is to provide a comprehensive tool
for the calculation of error budgets in terms of residual temporally filtered
phase power spectral densities and variances. In addition, the fast simulation
of AO-corrected point spread functions (PSFs) provided by this method can be
used as inputs for simulations of science observations with next-generation
instruments and telescopes, in particular to predict post-coronagraphic
contrast improvements for planet finder systems. We extend the previous results
and propose the synthesis of a distributed Kalman filter to mitigate both
aniso-servo-lag and aliasing errors whilst minimizing the overall residual
variance. We discuss applications to (i) analytic AO-corrected PSF modeling in
the spatial-frequency domain, (ii) post-coronagraphic contrast enhancement,
(iii) filter optimization for real-time wavefront reconstruction, and (iv) PSF
reconstruction from system telemetry. Under perfect knowledge of wind
velocities, we show that $\sim$60 nm rms error reduction can be achieved with
the distributed Kalman filter embodying anti- aliasing reconstructors on 10 m
class high-order AO systems, leading to contrast improvement factors of up to
three orders of magnitude at few ${\lambda}/D$ separations
($\sim1-5{\lambda}/D$) for a 0 magnitude star and reaching close to one order
of magnitude for a 12 magnitude star.
