Multirate filters and filter banks

The design of narrowband filters using multirate structures often involves the choice of one structure from a very large set. This choice may be made to optimize any of a number of cost criteria, including coefficient storage, multiplication rate, and throughput. The properties of structures optimized under different criteria vary significantly. We have investigated these properties both experimentally and theoretically. Experimentally, we have optimized a large number of structures under three different criteria. Theoretically, we have developed lower bounds on the cost of structures, which yield insight into their properties. We have also developed a branch-and-bound algorithm to efficiently search for the optimum structure. In our test, this algorithm yielded improvements of up to nearly two orders of magnitude in search time. In the second phase of this research, we have investigated the theory and design of one- and multi-dimensional perfect reconstruction filter banks. In the 1-D case, we have developed a new approach to the design of equal-complexity FIR PRFB\u27s, which incorporates the necessary and sufficient conditions for perfect reconstruction directly in the numerical design procedure, as a set of nonlinear equality constraints. This approach permits the design of filter banks which perform more general functions than flat-passband band splitting. In addition, any symmetry inherent in a particular application may be readily incorporated to reduce the number of independent variables and constraints. We have also analyzed the effect that imposing such symmetry has on the possibility of perfect reconstruction. In the multi-dimensional case, we have extended the analysis of perfect reconstruction filter banks to arbitrary multi-dimensional downsampling lattices. We have also applied the above-mentioned PRFB design procedure to 2-D PRFB design