Construction of Real-Valued Wavelets by Symmetry Original Research Article

A construction of orthogonal wavelet bases in L2(Rd) from a multiresolution analysis is given when the scaling function is skew-symmetric about an integer point. These wavelets are real-valued when the scaling function is real-valued. As an application, orthogonal wavelets generated by polyharmonic B-splines are obtained. We also present an example to show that the center of a skew-symmetric scaling function may not be in Zd/2.