Parametrizing smooth compactly supported wavelets

Abstract:

In this paper a concrete parameter space for the compactly supported wavelet systems of Daubechies is constructed. For wavelet systems with $N$ (generic) nonvanishing coefficients the parameter space is a closed convex set in ${{\mathbf {R}}^{(N - 2)/2}}$, which can be explicitly described in the Fourier transform domain. The moment-free wavelet systems are subsets obtained by the intersection of the parameter space and an affine subspace of ${{\mathbf {R}}^{(N - 2)/2}}$.