TIME-SHIFTS GENERALIZED MULTIRESOLUTION ANALYSIS OVER DYADIC-SCALING REDUGING SUBSPACES

摘要

A Generalized Multiresolution Analysis (GMRA) associated with a wavelet is a sequence of nested subspaces of the function space L{sup}2(R), with specific properties, and arranged in such a way that each of the subspaces corresponds to a scale 2{sup}m over all time-shifts n. These subspaces can be expressed in terms of a generating-wandering subspace - of the dyadic-scaling operator - spanned by orthonormal wavelet-functions - generated from the wavelet. In this paper we show that a GMRA can also be expressed in terms of sub-spaces for each time-shift n over all scales 2{sup}m. This is achieved by means of "elementary" reducing subspaces of the dyadic-scaling operator. Consequently, Time-Shifts GMRA associated with wavelets, as well as "sub-GMRA" associated with "sub-wavelets" will then be introduced.