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Shock and Vibration
Volume 4, Issue 5-6, Pages 361-377

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

David O. Smallwood

Mechanical and Thermal Environments Department, Sandia National Laboratories, P.O. Box 5800, MS-0865 Albuquerque, NM 87185-0865, USA

Revised 3 September 1997

Copyright © 1997 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.