Multipoint Multirate Signal Processing

This thesis provides a fundamentally new, systematic study of multipoint multirate signal processing systems. The multipoint multirate operators are analyzed via equivalent circuits comprised entirely of conventional multirate operators. Interconnections of the operators are demonstrated, and the multipoint noble identities are derived. The multipoint polyphase representation is presented, and the M channel multipoint multirate system with vector length N is presented as an MN channel multipoint polyphase system. The conditions sufficient for perfect reconstruction in the multipoint multirate system are derived. These conditions constrain the multipoint filter banks to be composed of comb filters generated from paraunitary sets of conventional filters. The perfect reconstruction multipoint multirate system is then combined with the multiresolution wavelet decomposition to form the generalized wavelet decomposition with varying vector decimation length at each level. The generalized wavelet decomposition is used as an algorithm to redistribute the energy of a signal throughout the levels of the decomposition. It is shown that, for band pass and high pass signals, significant improvements can be made in the energy distribution. It is recommended that this algorithm be studied as a front end to a vector quantizer for data compression applications