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




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Shock and Vibration - Volume 3 1996, Issue 4, Pages 237-246

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

Received 2 December 1995; Accepted 7 February 1996

Copyright © 1996 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.





Author: D.O. Smallwood

Source: https://www.hindawi.com/



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