Transformation of Shannon´s sampling points into Daubechies´ wavelet sampling points

Recently, diverse wavelet prefiltering algorithms have been developed to improve the approximation performance of transforming the uniform sampling points into the theoretic wavelet sampling points. Particularly for the orthogonal compactly supported wavelet bases, there is simple FIR prefilter, which consists of the values of the scaling function at integer points. Our focus in this paper is on the study of the performance of the transforming errors and the corresponding systematic error of the pyramidal algorithm. We obtain sharp estimations of the upper bounds of errors for bandlimited signals. The results show that the selection of the initial scaling factor depends not only on the wavelet base, but also on the degree of the dispersion or concentration in the frequency of a signal. With this one can determine the initial multiresolution subspace according to the error requirement. Finally, the experiments show that for bandlimited signals with normalized energy, the scaling function D₄ and J=2 may be generally selected to get accurate initial scaling coefficients to some degree