Bispectrum estimation: A parametric approach

Higher order spectra contain information about random processes that is not contained in the ordinary power spectrum such as the degree of nonlinearity and deviations from normality. Estimation of the bispectrum, which is a third-order spectrum, has been applied in various fields to obtain information regarding quadratic phase coupling among harmonic components and non-Gaussianness of processes. Existing methods of bispectrum estimation are patterned after the conventional methods of power spectrum estimation which are known to possess certain limitations. The paper proposes a parametric approach to bispectrum estimation based on a non-Gaussian white noise driven autoregressive (AR) model. The AR parameter estimates are obtained by solving the third-order recursion equations which may be Toeplitz in form but not symmetric. It is shown that the method provides bispectral estimates that are far superior to the conventional estimates in terms of bispectral fidelity and that in the case of detecting phase coupling among sinusoids, the method provides significantly better resolution.