ORTHONORMAL MRA WAVELETS: SPECTRAL FORMULAS AND ALGORITHMS

摘要

Spectral decompositions of translation and dilation operators are built in terms of suitablenorthonormal bases of L2(R), leading to spectral formulas for scaling functions andnorthonormal wavelets associated with multiresolution analysis (MRA). The spectral formulasnare useful to compute compactly supported scaling functions and wavelets. It isnillustrated with a particular choice of the orthonormal bases, the so-called Haar bases,nwhich yield a new algorithm related to the infinite product matrix representation ofnDaubechies and Lagarias.