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

Article type: Review Article

Authors: Smallwood, D. O.

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

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.

DOI: 10.3233/SAV-1996-3402

Journal: Shock and Vibration, vol. 3, no. 4, pp. 237-246, 1996