Abstract
Using a parameterization of the space of multiresolution analyses with compact support [− J, J + 1] and a maximum of J vanishing moments for the wavelet, this work investigates the general solution of the orthogonality conditions. More specifically, complex solutions up to J = 5 are presented. A classification of the solutions according to the degree of symmetry of the associated scaling function is proposed. Furthermore, symmetric but complex multiresolution analyses are described for a number of vanishing moments up to J = 8. Finally, a symmetric multiresolution analysis is constructed on [0, 1].
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