Symmetric and antisymmetric tight wavelet frames

For a given set of wavelets Psi, we provide a general, and yet simple, method to derive a new set of wavelets psi' such that each wavelet in psi' is either symmetric or antisymmetric. The affine system generated by psi' is a tight frame for the space L-2(R-d) whenever the affine system generated by psi is so. Further, when psi is constructed via a multiresolution analysis, psi' can also be derived from a, but possibly different, multiresolution analysis. If moreover the multiresolution analysis for constructing psi is generated by a symmetric refinable function, then psi' is obtained from the same multiresolution analysis. (C) 2005 Elsevier Inc. All rights reserved.