On the Moments of the Scaling Function psi_0
Gopinath, Ramesh A.
Burrus, C. Sidney
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 [6, 5] 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.
wavelets; scaling functions; Wavelet based Signal/Image Processing; wavelets; scaling functions