The design of multidimensional FIR perfect reconstruction filter banks for arbitrary sampling lattices

Summary form only given. The design of multidimensional perfect reconstruction filter banks (PRFBs) for arbitrary sampling lattices has been addressed. Necessary and sufficient conditions have been formulated for perfect reconstruction within this general context, and the design of multidimensional finite-impulse-response (FIR) PRFBs has been shown using a method that optimizes directly over the impulse response coefficients of the analysis and synthesis filters, expressing the perfect reconstruction condition as a set of equality constraints involving the impulse response coefficients. Symmetries among various filters in the filter bank or within a single filter not only serve to reduce the number of variables in the design problem, but also manifest themselves in the form of automatically satisfied constraints and redundancies among the constraints. In both cases, the total number of constraints in the design problem is reduced. The multidimensional filter banks share some desirable properties with their one-dimensional counterparts: the analysis and synthesis filters are equal complexity FIR filters, and it is possible to design systems with any number of channels.<>