二阶谱理论及其在海浪研究中的应用 Ⅱ.估计方法与应用

BISPECTRUM THEORY AND ITS APPLICATION TO SEA WAVE STUDY Ⅱ. BISPECTRUM ESTIMATION AND APPLICATION

为了使人们能方便掌握、合理选择估计二阶谱的方法,对目前现有估计二阶谱的相关函数方法、周期图方法、TOR方法和CTOM方法作了较详尽地介绍,并比较了各种方法的优缺点,最后重点讨论二阶谱于海浪研究中的应用及已取得的成果。

Since bispectrum can provide information about random process that is suppressed in the ordinary power spectrum such as the degree of guadratic nonlinearity and deviation from normality, bispectrum analysis has been widely applied in diverse fields. But unfortunately, a few of the several methods of bispectrum estimation for practical use must be further improved. The existing approaches used for bispectrum estimation only can be classified into two broad classes: (1) a conventional method, which is based on Fourier transform, and may fall into the correlation function and periodgram approaches similar to the conventional method for power spectrum estimation; (2) a parametric method, which is based on a non-Gaussian white noise driven autoregrassive (AR) model, and may be divided into the third-order recursion (TOR) and the constrained third-order mean (CTOM) approaches. In present paper, the several approaches mentioned above are described in detail, and the statistical properties of bispectrum estimation are briefly reviewed. Finally, the application of bispectrum to the study of nonlinear waves is especially discussed. This paper can hopefully be helpful in choosing a rational approach for bispectrum estimation.