The design of maximally smooth wavelets

A method for designing more regular (more differentiable) scaling functions than the Daubechies (1992) wavelets is presented. The approach is to numerically minimize the Holder exponent (a measure of smoothness) subject to constraints on the autocorrelation sequence of the scaling filter. The "maximally smooth" wavelets which result have a Holder exponent which grows faster than that of the Daubechies orthogonal wavelets, as the filter length increases. This is achieved by relaxing some of the vanishing moment conditions.