Decoupling higher order cumulant sequences resulting from three wave coupling processes

Abstract

Using cumulant projections, the authors reduce the complexity of the frequency estimation problem for quadratically coupled sinusoids. The bispectrum is viewed along a single radial slice whose defining frequencies are related by a simple ratio. This procedure of taking projections along lines orthogonal to projection axes corresponding to those slices decouples the sinusoids. The projected cumulants contain one-dimensional sinusoids. Projections comprise frequency decoupling. Separating the projected cumulants into symmetric and skew-symmetric cumulants, phase decoupling is achieved. Sinusoidal frequency estimation can be derived from a purely autoregressive (AR) modeling of the skew-symmetric and symmetric cumulants. The predictor polynomials derived from this scheme combine both causal and non-causal components.<>