An Esprit-like Algorithm for the Estimation of Quadratic Phase Coupling

Two algorithms are proposed for estimating the quadratically coupled frequency pairs (QC pairs) in a signal consisting of complex sinusoids in white noise, which may be nongaussian in general. Three matrices are constructed from the complex third order moments of the noisy signal, the latter two being time shifted versions of the first. The list of coupled frequencies is obtained from the rank reducing numbers of the matrix pencil formed from the first matrix and either of the latter two. The first algorithm then pairs these components by relating quadratic coupling to the intersection of generalized eigenspaces corresponding to two of these frequencies. The coupling strengths are also obtained in terms of generalized eigenvectors in this intersection space. The second algorithm constructs a two parameter matrix pencil using all the three matrices. The rank reducing pairs of this pencil on the unit circle yield the QC pairs and the associated generalized eigenvector the coupling strength.