Psi_B-energy operator and cross-power spectral density

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.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