Spatial-domain design of a class of two-dimensional recursive digital filters

This paper presents a technique for designing a class of two-dimensional (2-D) recursive digital filters, and also proposes a new state-space model for the 2-D recursive digital filters. The technique is applicable to the design of both quarter-plane causal filters and 2-D weakly causal filters. The filter is designed in terms of a canonic form state-space model, as well as a transfer function. The design is based upon minimization of the sum of squared differences between the desired and actual 2-D impulse responses over a finite interval. The test of stability for such filters is easy.