An improved method for bispectral analysis of nonlinear wave interaction system

Digital bispectral analysis is an effective means to study nonlinear system such as random sea-wave and edge plasma turbulence. In this paper, an improved digital bispectral method, the complete iterative method, is proposed to solve the three-wave coupling equation. The detailed comparisons are made between the previous estimation methods, Ritz's iterative method (Ritz and Powers 1986 Physica D 20 320) and Kim's method (Kim et al 1996 Phys. Plasmas 3 3998), and the complete iterative method. The results suggest that, employing the complete iterative method to compute the linear and quadratic nonlinear transfer functions, and linear and quadratic coupling coefficients, the resultant calculations are shown to be more accurate than those reconstructed by the first two methods. And different from the previous two methods, the complete iterative method is demonstrated to be more suitable for the study of ordinary 'black-box' fluctuating systems or turbulence system with 'ideal' power spectrum, i.e., all the output signals are limited to have the same power spectra as input signals. Finally, some further discussions are made briefly that address on the applications of the complete iterative method in the study of some specific nonlinear systems.