U-L block-triangular matrix and ladder realizations of subband coders

The Euclidean algorithm, applied to zero-phase filters in the variable w=(z+z/sup -1/)/2 is shown to provide a ladder structure realization of perfect reconstruction digital filter banks (DFBs) and wavelets. DFB matrices in the variable w are introduced and seen to have triangular factors corresponding to the ladder sections. Two-dimensional DFBs with diamond support are obtained from the McClellan transformation, and a related transform of a DFB in w to a two-dimensional DFB matrix is obtained. A design method based on augmenting a given DFB with ladder sections is described. The application to the decomposition of biorthogonal wavelets is illustrated.<>