Using the Walsh-Fourier transform, we give a construction of compactly supported nonstationary dyadic wavelets on the positive half-line. The masks of these wavelets are the Walsh polynomials defined by finite sets of parameters. Application to compression of fractal functions are also discussed.
Y. A. Farkov, A. Yu. Maksimov and S. A. Stroganov, “On Biorthogonal Wavelets Related to the Walsh Functions,” International Journal of Wavelets, Multiresolution and Information Processing, Vol. 9, No. 3, 2011, pp. 485- 499. doi:10.1142/S0219691311004195
Y. A. Farkov and E. A. Rodionov, “Algorithms for Wave- let Construction on Vilenkin Groups,” P-Adic Numbers, Ultrametric Analysis, and Applications, Vol. 3, No. 3, 2011, pp. 181-195. doi:10.1134/S2070046611030022
Ya. Novikov, “On the Construction of Nonstationary Orthonormal Infinitely Differentiable Compactly Supported Wavelets,” Proceedings of the 12th International Association for Pattern Recognition, Jerusalem, 9-13 Oc- tober 1994, pp. 214-215.