Orthonormal Hilbert-Pair of Wavelets With (Almost) Maximum Vanishing Moments

An orthonormal Hilbert-pair consists of a pair of conjugate-quadrature-filter (CQF) banks such that the equivalent wavelet function of both banks are approximate Hilbert transforms of each other. We found that the celebrated orthonormal wavelets of Daubechies, which have maximum vanishing-moment (VM), cannot be used to construct good Hilbert-pairs. In this letter, we reduce the number of VM by one and construct a Hilbert-pair with almost maximum VM. Each pair of wavelets are time-reverse versions of each other, and the individual wavelets are of the least asymmetric type (i.e., approximate linear phase CQF)