This Mathematica Library is an implementation of the periodic Wavelet Transform based on an integral regular matrix M and its factorization into dilation matrices. Introducing the multivariate de la Vallée Poussin means, this Library provides many scaling functions for the levels of decomposition.
The underlying theory of patterns, its generating groups and the fast Fourier transform on these patterns is also implemented in this Library yielding a fast Wavelet Transform, when computing in Fourier coefficients. Further, several functions to work with the translates of a function with respect to the pattern
For the dyadic case, i.e. |det J_k|=2 for all factor matrices, this Library also provides the construction of corresponding wavelets and an algorithm to decompose on several different factorizations at the same time.
Further, for the dyadic two-dimensional case, several visualization methods are given for the pattern, the wavelet and scaling functions and the obtained fractions of a function sampled on a pattern and decomposed with respect to the wavelets.
Several examples illustrate most of the implemented functions, each of which is equipped with an detailed ::usage command.
The project is also available on GitHub and published under the GPL 3.0. On GitHub, one branch also provides the precomputed coefficients for the examples, which especially for the Box spline spares computational times. Also each example is available as PDF.