Design of recursive and nonrecursive fan filters with complex transformations

This paper develops a technique for designing recursive and nonrecursive two-dimensional digital filters by the application of a complex transformation to a one-dimensional low-pass filter. A set of transformed filters is presented. The appropriate combination of these filters produces zero-phase fan filters. The advantage of such an approach is that the resulting fan filters are inherently stable and no optimization is needed. Several examples are presented for both finite impulse response (FIR) and infinite impulse response (IIR) fan filters and quadrant fan filters. The paper also includes implementation techniques using the properties of finite area arrays which reduce both computational and storage requirements compared with conventional implementations.