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Title: Matrix Methods for Estimating the Coherence Functions from Estimates of the Cross-Spectral Density Matrix

Abstract

It is shown that the usual method for estimating the coherence functions (ordinary, partial, and multiple) for a general multiple-input! multiple-output problem can be expressed as a modified form of Cholesky decomposition of the cross-spectral density matrix of the input and output records. The results can be equivalently obtained using singular value decomposition (SVD) of the cross-spectral density matrix. Using SVD suggests a new form of fractional coherence. The formulation as a SVD problem also suggests a way to order the inputs when a natural physical order of the inputs is absent.

Authors:
 [1]
  1. Mechanical and Thermal Environments Department, 9735 Sandia National Laboratories Albuquerque, NM 87185-0557, USA
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1198213
Grant/Contract Number:  
AC04-94AL85000
Resource Type:
Published Article
Journal Name:
Shock and Vibration
Additional Journal Information:
Journal Name: Shock and Vibration Journal Volume: 3 Journal Issue: 4; Journal ID: ISSN 1070-9622
Publisher:
Hindawi Publishing Corporation
Country of Publication:
Egypt
Language:
English

Citation Formats

Smallwood, D. O. Matrix Methods for Estimating the Coherence Functions from Estimates of the Cross-Spectral Density Matrix. Egypt: N. p., 1996. Web. doi:10.1155/1996/963607.
Smallwood, D. O. Matrix Methods for Estimating the Coherence Functions from Estimates of the Cross-Spectral Density Matrix. Egypt. doi:10.1155/1996/963607.
Smallwood, D. O. Mon . "Matrix Methods for Estimating the Coherence Functions from Estimates of the Cross-Spectral Density Matrix". Egypt. doi:10.1155/1996/963607.
@article{osti_1198213,
title = {Matrix Methods for Estimating the Coherence Functions from Estimates of the Cross-Spectral Density Matrix},
author = {Smallwood, D. O.},
abstractNote = {It is shown that the usual method for estimating the coherence functions (ordinary, partial, and multiple) for a general multiple-input! multiple-output problem can be expressed as a modified form of Cholesky decomposition of the cross-spectral density matrix of the input and output records. The results can be equivalently obtained using singular value decomposition (SVD) of the cross-spectral density matrix. Using SVD suggests a new form of fractional coherence. The formulation as a SVD problem also suggests a way to order the inputs when a natural physical order of the inputs is absent.},
doi = {10.1155/1996/963607},
journal = {Shock and Vibration},
number = 4,
volume = 3,
place = {Egypt},
year = {1996},
month = {1}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1155/1996/963607

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