On the moments of the scaling function psi /sub 0/

Abstract

The authors derive relationships between the moments of the scaling function psi /sub 0/(t) associated with multiplicity M, K-regular, compactly supported, orthonormal wavelet bases, which are extensions of the multiplicity 2, K-regular orthonormal wavelet bases constructed by I. Daubechies (1988). One such relationship is that the square of the first moment of the scaling function ( psi /sub 0/(t)) is equal to its second moment. This relationship is used to show that uniform sample values of a function provide a third order approximation of its scaling function expansion coefficients.