SOME BASIC ASPECTS AND USES OF HIGHER-ORDER SPECTRA

被引:17
作者
BRILLINGER, DR
机构
[1] Statistics Department, University of California, Berkeley
基金
美国国家科学基金会;
关键词
BILINEAR PROCESS; BISPECTRUM; CUMULANT; NONLINEAR SYSTEM; NON-GAUSSIAN PROCESS; POINT PROCESS; SPECTRUM; VOLTERRA EXPANSION;
D O I
10.1016/0165-1684(94)90025-6
中图分类号
TM [电工技术]; TN [电子技术、通信技术];
学科分类号
0808 ; 0809 ;
摘要
Some fundamental probabilistic and statistical aspects of higher-order spectra are described. Emphasis is placed on the use of these spectra with non-Gaussian processes in the identification of nonlinear systems. Simple examples based on point processes and bilinear systems are presented to illustrate the ideas. Historical references are provided throughout.
引用
收藏
页码:239 / 249
页数:11
相关论文
共 34 条
[1]  
Banks, Mathematical Theories of Nonlinear Systems, (1988)
[2]  
Bhabha, On the stochastic theory of continuous parametric systems and its application to electron-photon cascades, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 202, pp. 301-332, (1950)
[3]  
Blanc-Lapierre, Fortet, Théorie des Fonctions Aléatorires, (1953)
[4]  
Blumich, Nichlineare Rauschanalyse in der magnetischen Kernresonanzspektropie, Dissertation, (1981)
[5]  
Bogoliubov, Problems of a Dynamical Theory in Statistical Physics, (1962)
[6]  
Brillinger, The non-linear regression of time series, Ann. Math. Statist., 34, (1963)
[7]  
Brillinger, An introduction to polyspectra, The Annals of Mathematical Statistics, 36, pp. 1351-1374, (1965)
[8]  
Brillinger, The identification of polynomial systems by means of higher order spectra, J. Sound Vibration, 12, pp. 301-313, (1970)
[9]  
Brillinger, The identification of a particular nonlinear time series system, Biometrika, 64, pp. 509-515, (1977)
[10]  
Brillinger, Parameter estimation for nonGaussian processes via second and third order spectra with an application to some endocrine data, Advanced Methods of Physiological System Modelling, 2, pp. 53-81, (1989)