ΨBΨB-energy operator and cross-power spectral density

In this paper we consider the hermitian extension of the cross-ΨBΨB-energy operator that we will denote by ΨHΨH. In addition, cross energy terms are formalized through multivariate signals representation. We investigate the connection between the interaction energy function of ΨHΨH and the cross-power spectral density (CPSD) of two complex valued signals. In particular, this link permits to use this operator for estimating the CPSD. We illustrate the interest of ΨHΨH as a similarity between a pair of signals in frequency domain on synthetic and real data.