Some properties of generalized factorable 2-D FIR filters
نویسنده
چکیده
Factorable M{dimensional lters are interesting because they can be implemented e ciently: their computational complexity is O(Mn) instead of O(n ) (as in the case of generic non{factorable lters). Unfortunately, the pass{band support of a factorable lter can assume only very simple shapes (parallelepipeds with edges pairwise parallel to the axes), which are not adequate for most applications. In a recent paper, Chen and Vaidyanathan proposed a new class of non{factorable M-dimensional lters, whose pass{band support can be any parallelepiped, which can be realized with complexity O(Mn). In addition, they are designed starting from 1-D prototypes, which makes for a very simple design procedure. In this paper, we show that such lters belong to the class of Generalized Factorable (GF) lters (whose formal de nition we introduce here), and derive some properties of theirs relative to the 2{D case. Our review includes issues such as the relation between minimax frequency response parameters and lter size (which is nontrivial in the multidimensional case), symmetries, 2{D step response, and frequency response constraints.
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