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Wavelet analysis and chirps. (English) Zbl 0960.94006

Summary: “The authors propose a general model for chirp-like signals. The analytical structure of these chirps is given in the form |x| s g(x/|x| 1+β ), where g is an L p infinitely oscillating function like sin(x). Under suitable assumptions, they achieve a characterization of the chirps by means of their wavelet transforms.”

Only the central theorems are proved here whereas for detailed and complete proofs the reader is referred to the second author’s thesis “Généralisation de la théorie des chirps à divers cadres fonctionnels et applications à leur analyse par ondelettes”, Thèse, l’Université Paris Dauphine.

MSC:
94A11Application of orthogonal and other special functions in communication
42C40Wavelets and other special systems
94A12Signal theory (characterization, reconstruction, filtering, etc.)