
Accession Number : ADA116083
Title : TimeVariant and TimeInvariant 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 secondorder 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 socalled reflection coefficient parameter. For stationary processes, the reflection coefficient will be timeinvariant. For nonstationary processes we can use the displacement rank concept either to find a simple timeupdate formula for the reflection coefficients or to replace them by a timeinvariant 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 (Hilbertspace) 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