The SIGEST paper begins with a careful survey of the rational covariance extension problem, tracing its historical developments from the early twentieth-century work of Carathéodory, Toeplitz, and Schur to the present. Connections and applications abound: potential theory, stochastic realization, spectral estimation, trigonometric moments, circuit and systems theory, signal and speech processing, robust control, and mobile communication. The authors have gone out of their way to relate mathematical developments to practical consequences---and to bring theory to life through well-chosen examples. In one instance among many, the authors clearly explain why the easily computable maximum entropy solution cannot capture valleys in the speech spectrum and hence produces "flat" synthesized speech.
The scientific contributions of the paper are substantial, including new theoretical results as well as an efficient Newton-based interior method. Of particular interest is the formulation of appropriate spaces leading to an optimization problem that solves the rational covariance extension problem with degree constraints. Appearance of a barrier-like integral analogous to barrier terms in interior methods leads to existence of interior minimizers, a well-posed optimization problem, and a systems-theoretic consequence.
We are grateful indeed to the authors for their efforts in giving us
an impressive SIGEST paper of wide scope and fascinating content.