Cross-Bispectrum Computation and Variance Estimation

Abstract

A method for the estimation of cross-bispectra of discrete real-tune series is developed. The asymptotic varmnce properties of the bispectrnm are reviewed, and a method for the dn'ect estLmation of bispectral variance is given. The symmetry properties that minimize the computatmns necessary to obtain a complete estimate of the cross-bispectrnm m the right half-plane are described. A procedure is given for computing the cross-blspectrum by subdividing the domain into rectangular averaging regmns that help reduce the variance of the estimates and allow easy appbcation of the symmetry relationships to minimize the computational effort. As an example of the procedure, the crossbispectrum of a numerically generated, exponentially distributed tune series is computed and compared wtth theory