Wavelets and Frames Based on Walsh-Dirichlet Type Kernels - Farkov, Yu. A. (Communications in Mathematics and Applications, 2010)
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