Albuquerque, NM 87185-0557 Matrix Methods for Estimating the Coherence Functions from Estimates of the Cross-Spectral Density Matrix
David O. Smallwood · 1996
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 ofCholesky 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 offractional 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. © 1996 John Wiley & Sons, Inc.