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Continuous wavelet transforms based on classical orthogonal polynomials and functions of the second kind. (English) Zbl 1133.42313

Authors’ abstract: The aim of this paper is to promote the use of classical orthogonal polynomials to define useful continuous wavelet transforms. We present some applications in connection with the detections of isolated singularities and joint time-frequency analysis of a fractal via the representation of the corresponding wavelet coefficients.

MSC:

42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
65T60 Numerical methods for wavelets
68T10 Pattern recognition, speech recognition
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