Symmetric Self-Hilbertian Wavelets via Orthogonal Lattice Optimization

Orthonormal Hilbert pairs of wavelets that are time-reverse (mirror image) versions of each are termed Symmetric Self-Hilbertian wavelets and are used in the dual-tree complex wavelet transform. Previous methods for constructing the corresponding scaling low-pass filter are based on optimizing the product filter. These methods are practical only when the number of free-parameters is small due to the high computational load otherwise. An alternative method that is based on the orthogonal lattice is presented here and is practical with any number of free-parameters. Higher analytic quality Hilbert pairs can be obtained when there are more free-parameters. An effective strategy for optimizing the lattice parameters to give high quality filters is presented here.