High Resolution Estimation of Quadratic Phase Coupling in Nonlinear Systems

A new approach for estimating phase coupling due to quadratic nonlinearity is developed. The method is different from the periodogram approaches to bicoherence estimation and can be used in situations where high resolution frequency and bifrequency estimation are required. Least squares fitting is done between expressions for the autocorrelation and third moment sequences of sinusoidal signals and corresponding estimates of autocorrelation and third moments from samples of the process under consideration. The fraction of the power contributed by quadratic nonlinearity to bifrequencies is then estimated from the result of the least squares fit. Simulation examples illustrating the approach are also presented.