AbstractThis paper proposes a technique for designing a large class of two‐dimensional recursive digital filters. A mapping technique is used to design weakly causal digital filters. the design is based upon minimization of the sum of squared differences between the desired and actual two‐dimensional impulse responses over a finite interval. the filter is designed in terms of a canonic form state‐space model. the proposed technique has the advantage of simplicity and is applicable to the design of quarter‐plane digital filters as well as symmetric half‐plane digital filters. the test of stability for such filter