Relationships between Psi_B energy operator and some time-frequency representations

Abdel-Ouahab Boudraa (1)

1 IRENAV - Institut de Recherche de l'Ecole Navale

Psi_B operator is an energy operator that measures the interactions between two complex signals. In this letter, new properties of Psi_B operator are presented. Connections between Psi_B operator and some time-frequency representations (cross ambiguity function, short-time Fourier transform, Zak transform, and Gabor coefficients) are established. Link between Psi_B operator of two input signals and their cross-spectrum is also derived. For two equal input signals, we find that Fourier transform of Psi_B operator is proportional to the second derivative of the ambiguity function. The established links show the ability of Psi_B operator to analyze non stationary signals. A numerical example is provided for illustrating how to estimate the second order moment, of a FM signal, using Psi_B operator. We compare the result to the moment given by the Wigner-Ville distribution

Mots clés: Psi_B energy operator; Cross-ambiguity function; Short-time; Fourier transform; Gabor coefficients; Cross-spectrum; Opérateur d'énergie Psi_B; fonctiond'Ambiguïté croisée; Transformée de Fourier à Court terme; coefficients de Gabor; spectre croisé

Domaines: Traitement du signal et de l'image [eess.SP]

Abdel-Ouahab Boudraa. Relationships between Psi_B energy operator and some time-frequency representations. IEEE Signal Processing Letters, 2010, 17 (6), pp.527-530. ⟨10.1109/LSP.2010.2045548⟩. ⟨hal-01083621⟩