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 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.

Simulation of Stochastic Processes and Fields for Monte Carlo Simulation Applications: Some Recent Developments

1995 ◽  
Author(s):  
George Deodatis ◽  
Radu Popescu ◽  
Jean H. Prevost
Keyword(s):  
Density Matrix ◽  
Spectral Density ◽  
Stochastic Processes ◽  
Spectral Representation ◽  
Distribution Functions ◽  
Spectral Density Matrix ◽  
Spectral Representation Method ◽  
Cross Spectral Density ◽  
Representation Method ◽  
Non Gaussian

Abstract Two of the latest developments concerning the spectral representation method (used to simulate stochastic processes and fields) are presented in this paper. The first one introduces an extension of the spectral representation method to simulate non-stationary stochastic vector processes with evolutionary power. The proposed simulation formula is simple and straightforward and generates sample functions of the vector process according to a prescribed non-stationary cross-spectral density matrix. The second development introduces another extension of the spectral representation method to simulate multi-dimensional, multi-variate, non-Gaussian stochastic fields. In this case, sample functions are generated according to a prescribed cross-spectral density matrix and prescribed (non-Gaussian) probability distribution functions. Numerical examples are provided for both developments.

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