PARAMETERIZATION OF ORTHOGONAL WAVELET TRANSFORMS AND THEIR IMPLEMENTATION

In this paper, a method for parameterizing orthogonal wavelet transfor ms is presented, The parameter space is given by the rotation angles o f the orthogonal 2 x 2 rotations used in the lattice filters realizing the stages of the wavelet transform. Different properties of orthogon al 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 mu-rotations, i.e., the set of rotation angles a( k) = arctan 2(-k) (k is an element of {0, 1, ... , w} where w is the w ord length). An orthogonal mu-rotation is essentially one recursion st ep of the CORDIC algorithm. The wavelet transforms in the reduced para meter space are amenable to a very simple implementation. Only a small number of shift and add operations instead of fully fledged multiplie rs is required.