FOURIER SUPPORTS OF SCALING FUNCTIONS DETERMINE CARDINALITIES OF WAVELETS

摘要

It is well-known that the different kinds of multiresolution analysis (MRA) structures generate different wavelets. In this paper, we give two uniform formulas on the number of mother functions for various wavelets associated with MRA structures. These formulas show that the number of mother functions of wavelets is determined by the support of the Fourier transform of the scaling function in MRA structure.