Matrix Methods for Estimating the Coherence Functions from Estimates of the Cross-Spectral Density Matrix
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 res...
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| Format: | Article |
| Language: | English |
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Wiley
1996-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.3233/SAV-1996-3402 |
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| _version_ | 1832561110627123200 |
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| author | D.O. Smallwood |
| author_facet | D.O. Smallwood |
| author_sort | D.O. Smallwood |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-b86de2a546d94693a51ee734e35f1b65 |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 1996-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-b86de2a546d94693a51ee734e35f1b652025-02-03T01:26:00ZengWileyShock and Vibration1070-96221875-92031996-01-013423724610.3233/SAV-1996-3402Matrix Methods for Estimating the Coherence Functions from Estimates of the Cross-Spectral Density MatrixD.O. Smallwood0Mechanical and Thermal Environments Department, 9735 Sandia National Laboratories Albuquerque, NM 87185-0557, USAIt 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.http://dx.doi.org/10.3233/SAV-1996-3402 |
| spellingShingle | D.O. Smallwood Matrix Methods for Estimating the Coherence Functions from Estimates of the Cross-Spectral Density Matrix Shock and Vibration |
| title | Matrix Methods for Estimating the Coherence Functions from Estimates of the Cross-Spectral Density Matrix |
| title_full | Matrix Methods for Estimating the Coherence Functions from Estimates of the Cross-Spectral Density Matrix |
| title_fullStr | Matrix Methods for Estimating the Coherence Functions from Estimates of the Cross-Spectral Density Matrix |
| title_full_unstemmed | Matrix Methods for Estimating the Coherence Functions from Estimates of the Cross-Spectral Density Matrix |
| title_short | Matrix Methods for Estimating the Coherence Functions from Estimates of the Cross-Spectral Density Matrix |
| title_sort | matrix methods for estimating the coherence functions from estimates of the cross spectral density matrix |
| url | http://dx.doi.org/10.3233/SAV-1996-3402 |
| work_keys_str_mv | AT dosmallwood matrixmethodsforestimatingthecoherencefunctionsfromestimatesofthecrossspectraldensitymatrix |