Wavelets and Frames Based on Walsh-Dirichlet Type Kernels

Yu. A. Farkov

Abstract


Using the Walsh-Dirichlet kernel and some of its modifications, we construct several examples of frames and periodic wavelets on the positive half-line. The corresponding algorithms for decomposition and reconstruction are also discussed. It is noted that similar results can be obtained for wavelets and frames on the Cantor and Vilenkin groups.

Keywords


Dirichlet kernel; Orthogonal polynomials; Periodic wavelets; Parseval frames; Walsh functions

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eISSN 0975-8607; pISSN 0976-5905