Accession Number : ADA116083

Title :   Time-Variant and Time-Invariant Lattice Filters for Nonstationary Processes.

Descriptive Note : Technical rept.,

Corporate Author : STANFORD UNIV CA INFORMATION SYSTEMS LAB

Personal Author(s) : Kailath,T

PDF Url : ADA116083

Report Date : May 1982

Pagination or Media Count : 50

Abstract : The structure of second-order processes is exposed by specification of whitening filters and modeling filters, or equivalently by Cholesky decompositions of the covariance matrix and its inverse. We shall show that these filters can be obtained as a cascade of lattice sections, each specified by a single so-called reflection coefficient parameter. For stationary processes, the reflection coefficient will be time-invariant. For nonstationary processes we can use the displacement rank concept either to find a simple time-update formula for the reflection coefficients or to replace them by a time-invariant vector reflection coefficient of size governed by the displacement rank of processes. These results are obtained in a quite direct way by using a geometric (Hilbert-space) formulation of the problem, combined with old results of Yule (1907) on update formulas for partial correlation coefficients and of Schur (1917) and Szego (1939) on the classical moment problem. (Author)

Descriptors :   *Mathematical filters, *Digital filters, *Signal processing, Rank order statistics, Stochastic processes, Covariance, Coefficients, Parameters, Algorithms, Displacement, Stationary, Simplification, Moments, Matrices(mathematics), Invariance

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE