  In this paper we present a general approach to multivariate periodic wavelets
generated by scaling functions of de la Vall\'ee 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 Vall\'ee 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.
