  In the Markov and covariance interpolation problem a transfer function $W$ is
sought that match the first coefficients in the expansion of $W$ around zero
and the first coefficients of the Laurent expansion of the corresponding
spectral density $WW^\star$. Here we solve an interpolation problem where the
matched parameters are the coefficients of expansions of $W$ and $WW^\star$
around various points in the disc. The solution is derived using input-to-state
filters and is determined by simple calculations such as solving Lyapunov
equations and generalized eigenvalue problems.
