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) detection 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-parameter calculation in the bispectrum estimation problem. This algorithm is based on the recursion-in-order minimization of appropriate squared errors with respect to the reflection coefficients, introduced by the Levinson recursion for Toeplitz and non-Hermitian matrices. The recursive nature in this method allows us to obtain the bispectrum of several orders up to the desired one, with significant computational savings. In computer simulations this method demonstrates its potential both in the estimation of signal bispectra and in QPC bispectral detection problems in noisy environments.