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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 ${|x|}^{s}{g\left(x/|x|}^{1+\beta }\right)$, where $g$ is an ${L}^{p}$ infinitely oscillating function like $sin\left(x\right)$. 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:
 94A11 Application of orthogonal and other special functions in communication 42C40 Wavelets and other special systems 94A12 Signal theory (characterization, reconstruction, filtering, etc.)