Complex Daubechies Wavelets

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]. © 1995 Academic Press. All rights reserved.