Parametrization 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 22{ rotations used in the lattice lters realizing the stages of the wavelet transform. Diierent properties of orthogonal wave-let 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 wordlength). 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 edged multipliers are required.