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Relationships between Psi_B energy operator and some time-frequency representations

Relations entre Psi_B et quelques représentations temps-fréquence

Article dans une revue avec comité de lecture
Author
ccBOUDRAA, Abdel-Ouahab
13094 Institut de Recherche de l'Ecole Navale [IRENAV]

URI
http://hdl.handle.net/10985/8916
DOI
10.1109/LSP.2010.2045548
Date
2010
Journal
IEEE Signal Processing Letters

Abstract

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

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