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

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)

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1982
Accession Number
ADA116083

Entities

People

  • Thomas Kailath

Organizations

  • Stanford University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Computer Programs
  • Data Science
  • Electrical Engineering
  • Equations
  • Filters
  • Functional Analysis
  • Generators
  • Hilbert Space
  • Information Science
  • Information Systems
  • Network Science
  • New York
  • Random Variables
  • Signal Processing
  • Stationary Processes
  • Stochastic Processes

Fields of Study

  • Engineering
  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Calculus or Mathematical Analysis
  • Linear Algebra

Technology Areas

  • Space