Relationships between Psi_B energy operator and some timefrequency representations
Relations entre Psi_B et quelques représentations tempsfréquence
Type
Articles dans des revues avec comité de lectureDate
2010Journal
IEEE Signal Processing LettersAbstract
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 timefrequency representations (cross ambiguity function, shorttime Fourier transform, Zak transform, and Gabor coefficients) are established. Link between Psi_B operator of two input signals and their crossspectrum 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 WignerVille distribution
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