SOME PROPERTIES OF GENERALIZED FACTORABLE 2-D FIR FILTERS

Factorable M-dimensional filters are interesting because they can be i mplemented efficiently: their computational complexity is O(Mn) instea d of O(n(M)) (as in the case of generic non-factorable filters), Unfor tunately, the passband support of a factorable filter can assume only very simple shapes (parallelepipeds with edges pairwise parallel to th e awes), which are not adequate for most applications, In a recent pap er, Chen and Vaidyanathan proposed a new class of non-factorable M-dim ensional filters, whose passband support can be any parallelepiped, wh ich can be realized with complexity O(Mn). In addition, they are desig ned starting from I-D prototypes, which makes for a very simple design procedure, In this paper, we show that such filters belong to the cla ss of generalized factorable (GF) filters (whose Formal definition we introduce here), and derive some properties of theirs relative to the 2-D case, Our review includes issues such as the relation between mini max frequency response parameters and filter size (which is nontrivial in the multidimensional case), symmetries, 2-D step response, and fre quency response constraints.