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Title: Using singular value decomposition to compute the conditioned cross-spectral density matrix and coherence functions

It is shown that the usual method for computing 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 inputs and outputs. The modified form of Cholesky decomposition used is G{sub zz} = LCL{prime}, where G is the cross spectral density matrix of inputs and outputs, L is a lower; triangular matrix with ones on the diagonal, and C is a diagonal matrix, and the symbol {prime} denotes the conjugate transpose. If a diagonal element of C is zero, the off diagonal elements in the corresponding column of L are set to zero. It is shown that the results can be equivalently obtained using singular value decomposition (SVD) of G{sub zz}. The formulation as a SVD problem suggests a way to order the inputs when a natural physical order of the inputs is absent.
Authors:
Publication Date:
OSTI Identifier:
106476
Report Number(s):
SAND--95-1094C; CONF-9510195--3
ON: DE95016743
DOE Contract Number:
AC04-94AL85000
Resource Type:
Conference
Resource Relation:
Conference: 66. shock and vibration symposium, Biloxi, MS (United States), 31 Oct - 3 Nov 1995; Other Information: PBD: 7 Aug 1995
Research Org:
Sandia National Labs., Albuquerque, NM (United States)
Sponsoring Org:
USDOE, Washington, DC (United States)
Country of Publication:
United States
Language:
English
Subject:
99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; 42 ENGINEERING NOT INCLUDED IN OTHER CATEGORIES; RESPONSE FUNCTIONS; CALCULATION METHODS; SPECTRAL DENSITY; MATRICES; MATHEMATICS; VECTORS; MATRIX ELEMENTS; DYNAMICS