Some properties and algorithms for fourth order spectral analysis of complex signals

In this paper, we give two algorithms for linear system blind identification based on the fourth order spectrum (or trispectrum). The first algorithm uses only N of the N³ data of the fourth order spectrum. The second algorithm uses all the information contained in the fourth order spectra, but gives an optimal solution. This solution needs a previous phase unwrapping step; we give different solutions to unwrap the trispectrum phase. Finally, we establish the link between the well-known kurtosis maximization method and the optimal solution presented here; they are equivalent in first approximation. It means that we give an analytic solution to the blind identification problem which is nearly equivalent to the kurtosis maximization solution