Parameterization of Orthogonal Wavelet Transforms and Their Implementation

In this paper, a method for parameterizing orthogonal wavelet transforms is presented. The parameter space is given by the rotation angles of the orthogonal 2 2 rotations used in the lattice filters realizing the stages of the wavelet transform. Different properties of orthogonal wavelet transforms can be expressed in this parameter space. Then, the parameter space is restricted to the set of rotation angles given by simple orthogonal -rotations, i.e., the set of rotation angles k = arctan 2 k (k 2 f0; 1; ; wg where w is the word length). An orthogonal -rotation is essentially one recursion step of the CORDIC algorithm. The wavelet transforms in the reduced parameter space are amenable to a very simple implementation. Only a small number of shift and add operations instead of fully fledged multipliers is required.