Symmetry exploitation in the design and implementation of recursive 2-D rectangularly sampled digital filters

It is well known that exploiting the symmetries existing in the frequency response of 2-D filters results in a reduction in design and implementation complexities. In this paper we explore how to exploit a general class of symmetries in the design and implementation of recursive two-dimensional (2-D) filters. Three types of filters are being studied, namely, causal, factorizable noncausal, and unfactorizable noncausal. The capability of each of these filters to exhibit symmetries is discussed. A method is then proposed to obtain the required form of the filter transfer function for exhibiting the different types of symmetries. Examples are solved both to illustrate the proposed method and to compare the performance of these filter types for the same implementation complexity.