On the Moments of the Scaling Function \psi_0
		 R. A. Gopinath C. S. Burrus

       Department of Electrical and Computer Engineering
		Rice University, Houston, TX-77251

		 	    ABSTRACT

This paper derives relationships between the moments of the scaling
function $\psi_0(t)$ associated with multiplicity $M$, $K$-regular,
compactly supported, orthonormal wavelet bases that are extensions of
the multiplicity $2$, $K$-regular orthonormal wavelet bases
constructed by Daubechies. One such relationship is that the square of
the first moment of the scaling function ($\psi_0(t)$) is equal to its
second moment. This relationship is used to show that uniform sample
values of a function provides a third order approximation of its
scaling function expansion coefficients. For the special case of
$M=2$, the results in this paper have been reported earlier.