Lossless Cascade Networks: The Crossroads of Stochastic Estimation, Inverse Scattering and Filter Synthesis

摘要

A correspondence is established between a family of inverse scattering problems, including filter synthesis and seismic exploration, and a family of matrix factorization problems, including stochastic filtering, stability testing, partial/stochastic realization and model order reduction. This correspondence originates from the notion of energy (i.e., losslessness), and it involves computational procedures whose signal-flow-graph representation is a lossless cascade network. Our analysis of recent results on efficient triangular factorization of Hermitian matrices indicates a possible extension of the network-theoretic notion of losslessness. (Reprints)