An Isserlis' Theorem for Mixed Gaussian Variables: Application to the Auto-Bispectral Density

被引：28

作者：

Michalowicz, J. V. ^{[1
,2
]}

Nichols, J. M. ^{[1
]}

Bucholtz, F. ^{[1
]}

Olson, C. C. ^{[1
]}

机构：

[1] USN, Res Lab, Div Opt Sci, Washington, DC 20375 USA

[2] SFA Inc, Crofton, MD USA

来源：

JOURNAL OF STATISTICAL PHYSICS | 2009年 / 136卷 / 01期

关键词：

Isserlis' theorem; Wick's theorem; Mixed-Gaussian distribution; Auto-bispectral density; NONLINEARITY; ORDER; SPECTRA; SYSTEMS; SERIES;

D O I：

10.1007/s10955-009-9768-3

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

This work derives a version of Isserlis' theorem for the specific case of four mixed-Gaussian random variables. The theorem is then used to derive an expression for the auto-bispectral density for quadratically nonlinear systems driven with mixed-Gaussian iid noise.

引用

页码：89 / 102

页数：14

共 19 条

[1] Generation of colored noise [J].

Bartosch, L .

INTERNATIONAL JOURNAL OF MODERN PHYSICS C, 2001, 12 (06) :851-855

[2] AN INTRODUCTION TO POLYSPECTRA [J].

BRILLINGER, DR .

ANNALS OF MATHEMATICAL STATISTICS, 1965, 36 (05) :1351-1374

[3]

CAILLEC JML, 2005, MULTIDIM SYST SIGN P, V16, P49

[4] Wick's theorem for nonsymmetric normal ordered products and contractions [J].

Evans, TS ;

Kibble, TWB ;

Steer, DA .

JOURNAL OF MATHEMATICAL PHYSICS, 1998, 39 (11) :5726-5738

[5] HIGHER-ORDER CUMULANTS AND CUMULANT SPECTRA [J].

HINICH, MJ .

CIRCUITS SYSTEMS AND SIGNAL PROCESSING, 1994, 13 (04) :391-402

[6]

Isserlis L, 1918, BIOMETRIKA, V12, P134, DOI 10.2307/2331932

[7] Second-order spectra for quadratic nonlinear systems by Volterra functional series: Analytical description and numerical simulation [J].

Marzocca, P. ;

Nichols, J. M. ;

Milanese, A. ;

Seaver, M. ;

Trickey, S. T. .

MECHANICAL SYSTEMS AND SIGNAL PROCESSING, 2008, 22 (08) :1882-1895

[8] On the use of the auto-bispectral density for detecting quadratic nonlinearity in structural systems [J].

Nichols, J. M. ;

Marzocca, P. ;

Milanese, A. .

JOURNAL OF SOUND AND VIBRATION, 2008, 312 (4-5) :726-735

[9] The trispectrum for Gaussian driven, multiple degree-of-freedom, non-linear structures [J].

Nichols, J. M. ;

Marzocca, P. ;

Milanese, A. .

INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 2009, 44 (04) :404-416

[10] BISPECTRUM ESTIMATION - A DIGITAL SIGNAL-PROCESSING FRAMEWORK [J].

NIKIAS, CL ;

RAGHUVEER, MR .

PROCEEDINGS OF THE IEEE, 1987, 75 (07) :869-891

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