Some properties of generalized factorable 2-D FIR filters

A paper by Chen and Vaidyanathan (1993) describes a method for designing multidimensional (MD) filters with spectral support in the shape of a parallelepiped, starting from M 1-D prototypes. Such filters require a number of elementary operations per input sample (OPS) that grows linearly with the size of each 1-D prototype. As a matter of fact, they belong to the general class of generalized factorable (GF) filters, which we define here. Beside the computational efficiency (in both the design and the implementation), we show in this work that GF filters share some interesting properties (relative to symmetry and frequency response constraints)