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

Smallwood, D. O.

doi:10.1155/1996/963607

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

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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:

Smallwood, D. O. ^[1]

Mechanical and Thermal Environments Department, 9735 Sandia National Laboratories Albuquerque, NM 87185-0557, USA

Publication Date:: Mon Jan 01 00:00:00 EST 1996

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

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                    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.

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                    Smallwood, D. O. Matrix Methods for Estimating the Coherence Functions from Estimates of the Cross-Spectral Density Matrix.  Egypt.  https://doi.org/10.1155/1996/963607

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                    Smallwood, D. O. Mon .  
"Matrix Methods for Estimating the Coherence Functions from Estimates of the Cross-Spectral Density Matrix".  Egypt.  https://doi.org/10.1155/1996/963607.

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@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         = {Mon Jan 01 00:00:00 EST 1996},

  month        = {Mon Jan 01 00:00:00 EST 1996}

}

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