Oversampled FIR filter banks and frames in l/sup 2/(Z)
Perfect reconstruction FIR filter banks are equivalent to a particular class of frames in l/sup 2/(Z). These frames are the subject of this paper. Necessary and sufficient conditions on a filter bank to implement a frame or a tight frame decomposition are given, as well as the necessary and sufficient condition for perfect reconstruction using FIR filters. Complete parameterizations of FIR filter banks satisfying these conditions are also given. Further, we study the condition under which the frame dual to the frame associated to an FIR filter bank is also FIR, and give a parameterization of a class of filter banks having this property.