Recursive Construction of Multichannel Transmission Lines with a Maximum Entropy Property

J. P. Burg gave a now-famous solution of the problem of finding the maximum-entropy extension of a section {c o, c 1,…, c n } of a scalar (stationary) covariance sequence, with a nice interpretation in terms of the reflection coefficients of an associated discrete transmission line: namely, that the maximum-entropy extension is obtained by adding trivial sections with zero reflection coefficients. This work inspired various extensions and generalizations, mostly without any associated physical interpretation. In this paper we shall use the generalized transmission lines associated with the basic triangular matrix factorization algorithms of the Displacement Structure Theory to obtain several interesting maximum entropy extension results. One is the perhaps surprising fact that Burg’s zero-reflection-coefficient extension solution may not always hold when the coefficients {c i } are matrix-valued.