The cross-spectral density matrix of a planar, electromagnetic stochastic source as a correlation matrix

2008 ◽  
Vol 281 (9) ◽  
pp. 2393-2396 ◽  
Author(s):  
Miguel A. Alonso ◽  
Emil Wolf
Keyword(s):  
Density Matrix ◽  
Spectral Density ◽  
Correlation Matrix ◽  
Spectral Density Matrix ◽  
Cross Spectral Density ◽  
The Cross

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

1996 ◽  
Vol 3 (4) ◽  
pp. 237-246 ◽  
Author(s):  
D.O. Smallwood
Keyword(s):  
Density Matrix ◽  
Spectral Density ◽  
Multiple Input Multiple Output ◽  
Spectral Density Matrix ◽  
Multiple Input ◽  
Cross Spectral Density ◽  
Input Multiple Output ◽  
The Cross ◽  
Value Decomposition ◽  
Physical Order

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.

scholarly journals Generation of Stationary Non-Gaussian Time Histories with a Specified Cross-spectral Density

1997 ◽  
Vol 4 (5-6) ◽  
pp. 361-377 ◽  
Author(s):  
David O. Smallwood
Keyword(s):  
Density Matrix ◽  
Spectral Density ◽  
Probability Density ◽  
Complex Frequency ◽  
Spectral Density Matrix ◽  
Cross Spectral Density ◽  
Time Histories ◽  
The Cross ◽  
Non Gaussian ◽  
Skewness And Kurtosis

The paper reviews several methods for the generation of stationary realizations of sampled time histories with non-Gaussian distributions and introduces a new method which can be used to control the cross-spectral density matrix and the probability density functions (pdfs) of the multiple input problem. Discussed first are two methods for the specialized case of matching the auto (power) spectrum, the skewness, and kurtosis using generalized shot noise and using polynomial functions. It is then shown that the skewness and kurtosis can also be controlled by the phase of a complex frequency domain description of the random process. The general case of matching a target probability density function using a zero memory nonlinear (ZMNL) function is then covered. Next methods for generating vectors of random variables with a specified covariance matrix for a class of spherically invariant random vectors (SIRV) are discussed. Finally the general case of matching the cross-spectral density matrix of a vector of inputs with non-Gaussian marginal distributions is presented.

scholarly journals Modal Participation Estimated from the Response Correlation Matrix

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Rune Brincker ◽  
Sandro D. R. Amador ◽  
Martin Juul ◽  
Manuel Lopez-Aenelle
Keyword(s):  
Density Matrix ◽  
Spectral Density ◽  
Correlation Matrix ◽  
Analytical Form ◽  
Mode Shapes ◽  
Transformation Matrices ◽  
Spectral Density Matrix ◽  
Spectral Density Functions ◽  
Input Load ◽  
The Time Domain

In this paper, we are considering the case of estimating the modal participation vectors from the operating response of a structure. Normally, this is done using a fitting technique either in the time domain using the correlation function matrix or in the frequency domain using the spectral density matrix. In this paper, a more simple approach is proposed based on estimating the modal participation from the correlation matrix of the operating responses. For the case of general damping, it is shown how the response correlation matrix is formed by the mode shape matrix and two transformation matrices T1 and T1 that contain information about the modal parameters, the generalized modal masses, and the input load spectral density matrix Gx. For the case of real mode shapes, it is shown how the response correlation matrix can be given a simple analytical form where the corresponding real modal participation vectors can be obtained in a simple way. Finally, it is shown how the real version of the modal participation vectors can be used to synthesize empirical spectral density functions.

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