Accession Number : AD0436818

Title :   ESTIMATES OF THE BISPECTRUM OF STATIONARY RANDOM PROCESSES,

Corporate Author : BROWN UNIV PROVIDENCE R I DIV OF APPLIED MATHEMATICS

Personal Author(s) : Rosenblatt,M. ; VAN Ness,J. W.

Report Date : MAR 1964

Pagination or Media Count : 83

Abstract : Recently interest has arisen in applications of higher order spectra and in particular in the bispectrum. Various nonlinear effects in random phenomena are studied. The bispectrum has been in Connection with oceanographic problems, among which a number of interesting phenomena such as surf beats, wave breaking, and the energy transfer between wave components can be explained only by the nonlinearity of the wave motion. The present paper discusses the bispectrum itself, some of its properties, and some assumptions on it and on the process. Intuitive reasons for choosing an estimate of the form discussed here are then given along with some convenient expressions for this estimate. Further explanation is given for the concept of cumulant functions of the process, and the statistical properties of various estimates; that is with the asymptotic bias, second-order moments, and distribution of three estimates: (1) the thirdorder moment estimate, (2) the weighted bispectral density (the bispectral distribution function) estimate, and finally (3) the estimate of the bispectral density itself. (Author)

Descriptors :   (*HARMONIC ANALYSIS, SET THEORY), (*STATISTICAL FUNCTIONS, SEQUENCES(MATHEMATICS)), TABLES(DATA), STATISTICAL ANALYSIS, SERIES(MATHEMATICS), FOURIER ANALYSIS, INTEGRAL TRANSFORMS, PROBABILITY, STOCHASTIC PROCESSES, STATISTICAL PROCESSES

Distribution Statement : APPROVED FOR PUBLIC RELEASE