Design and implementation of wavelet packet-based filter bank trees for multiple access communications

The relationship of filter bank trees to wavelet packet trees for subspaces, decimation operators, and coordinates of the projections of a function onto the subspaces is briefly explained. Two designs for the filter banks are summarized and the equations for the designs are provided. For one of these the prototype filters are all the same, and for the other they are the same at each level of the tree. The best method for spectral factorization of high-order polynomials, needed for the filter designs, is selected. Lattice structures preserving perfect reconstruction with finite word lengths are used in computer simulations to study quantization effects.