Quadratic phase coupling detection in harmonic vibrations via an order-recursive AR bispectrum estimation

The paper proposes a bispectral scheme for quadratic phase-coupling (QPC) d etection in harmonic signals in white and colored noise, possibly generated by non-linear vibrations. This scheme is carried out via an autoregressive bispectrum (AR) using several criteria to fix an optimum order for the AR model used. First, we propose a recursive-in-order algorithm for AR model-p arameter calculation in the bispectrum estimation problem. This algorithm i s based on the recursion-in-order minimization of appropriate squared error s with respect to the reflection coefficients, introduced by the Levinson r ecursion for Toeplitz and non-Hermitian matrices. The recursive nature in t his method allows us to obtain the bispectrum of several orders up to the d esired one, with significant computational savings. In computer simulations this method demonstrates its potential both in the estimation of signal bi spectra and in QPC bispectral detection problems in noisy environments.