Parameterization and implementation of orthogonal wavelet transforms

In this paper a method is presented that parameterizes orthogonal wavelet transforms with respect to their properties (i.e. compact support, vanishing moments, regularity, symmetry) and also takes into considerations a simple implementation of the transform. The parameter space is given by the rotation angles of the orthogonal 2 × 2 rotations used in the lattice filters that realize the different stages of the wavelet transform. The different properties of an orthogonal wavelet transform can be expressed in this parameter space. Then, restricting the parameter space to the rotation angles of simple CORDIC-based approximate rotations leads to a reduced parameter space. The wavelet transforms in this reduced parameter space are amenable to a very simple implementation (only a small number of shift & add operations).