Multivariate Linear Predictive Spectral Analysis Employing Weighted Forward and Backward Averaging: A Generalization of Burg's Algorithm

Abstract

A method for multivariate linear predictive spectral analysis, employing weighted forward and backward averaging, is presented and programmed in FORTRAN. The method constitutes a generalization of Burg's univariate algorithm to the multivariate case. The essential analytical procedure is to minimize the trace of the sum of the weighted forward and backward error matrices by choice of the partial correlation coefficients, subject to a linear matrix constraint which guarantees that the forward-extrapolated and backward- extrapolated correlation matrix estimates are Hermitians of each other. The choice of error weighting is important and is discussed. Solution of a bilinear matrix equation is required in the algorithm.

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Document Details

Document Type
Technical Report
Publication Date
Oct 13, 1976
Accession Number
ADA031755

Entities

People

  • Albert H. Nuttall

Organizations

  • Naval Underwater Systems Center

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Coefficients
  • Eigenvalues
  • Equations
  • Estimators
  • Extrapolation
  • Frequency
  • Guarantees
  • Noise
  • Numbers
  • Plastic Explosives
  • Procedures (Computers)
  • Residuals
  • Sequences
  • Signal Processing
  • Transfer Functions
  • White Noise

Readers

  • Approximation Theory.
  • Linear Algebra