A quantitative method for choosing optimal Daubechies wavelets

Abstract

We develop a new method for calculating specific values of Daubechies wavelets in one dimension. The novelty of this approach is its ability to calculate exact values of the Daubechies scaling functions and, by extension, wavelets, without calculating values of the scaling function at other unnecessary dyadic rationals. We then provide a new quantitative method for choosing the best wavelet for applications by giving a rigorous error analysis of the wavelet transform for functions of various smoothness.