Psi-B energy operator and cross-power spectral density

International audience; In this paper we consider the hermitian extension of the cross-Psi-B energy operator, that we will denote by Psi-H . In addition, cross energy terms are formalized through multivariate signals representation. We investigate the connection between the interaction energy function of Psi-H 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 Psi-H as a similarity between a pair of signals in frequency domain on synthetic and real data.