Multivariate Periodic Wavelets of de la Vallée Poussin Type

Ronny Bergmann*, Jürgen Prestin

*Corresponding author for this work
1 Citation (Scopus)


In this paper we present a general approach to multivariate periodic wavelets generated by scaling functions of de la Vallée Poussin type. These scaling functions and their corresponding wavelets are determined by their Fourier coefficients, which are sample values of a function, that can be chosen arbitrarily smooth, even with different smoothness in each direction. This construction generalizes the one-dimensional de la Vallée Poussin means to the multivariate case and enables the construction of wavelet systems, where the set of dilation matrices for the two-scale relation of two spaces of the multiresolution analysis may contain shear and rotation matrices. It further enables the functions contained in each of the function spaces from the corresponding series of scaling spaces to have a certain direction or set of directions as their focus, which is illustrated by detecting jumps of certain directional derivatives of higher order.

Original languageEnglish
JournalJournal of Fourier Analysis and Applications
Issue number2
Pages (from-to)342-369
Number of pages28
Publication statusPublished - 01.01.2015


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