## 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:

- 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}

}

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Publisher's Version of Record

DOI: 10.1155/1996/963607

DOI: 10.1155/1996/963607

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