NOVEL TECHNIQUES FOR THE DETECTION AND ESTIMATION OF THREE-WAVE COUPLING WITH APPLICATION TO HUMAN BRAIN WAVES

摘要: Composite linear and quadratic systems produce three-wave coupling when stimulated by random-phase input sinusoids. Due to the non-linearity of system output frequencies are arithmetically related input. Using third order cumulant statistics their associated bispectrum, techniques devised based on phaseinsensitive matrix structures for detection frequency estimation frequencies. The separation series into symmetric skew-symmetric portions allows us exploit characteristic eigendecompositions estimation. After symmetrization, biphases can be easily extracted as coefficients sequence. a generalized eigenvector representation, we relate bases subspace rotation algorithm. Biphases estimated directly from eigenvalues pencil formed matrices. dimensionality our matrices reduced through use projections which yield slice bispectrum. Radon transform procedure is bispectral processing an isotropic radial Volterra filter. compact Kronecker product formulation algorithms also converted in biphase Simulations showing performance above procedures presented both synthetic biomedical time series. These include specific exhibiting nonlinearities electroencephalographic (EEG) data.