Cubic phase coupling estimation via trispectrum autorregresive modeling

In this communication the use of AR modelling in the estimation of cubic phase coupling is studied. After obtaining the trispectrum of an harmonic signal with cubic phase couplings, the parametric modelling is used to design a method that models this trispectrum and allows the location of the cubic couplings. This method is based on a twofold AR modelling of the data using their fourth-order cumulants, such as, after the extraction of the two sets of coefficients, called frequency and sum coefficients, the modelled trispectrum is built and the phase coupling are located as the peaks in this trispectrum. A frequency selection method is proposed to overcome the problems associated to the maximum-detection algorithms in the trispectral domain, which also reduces significantly the computational burden necessary to find these maxima. Practical conditions of implementation and the limitations of using this approach are showed and discussed in simulations.