Design of 2-D state-space digital filters with powers-of-two coefficients based on a genetic algorithm

This paper presents a new design method of 2-D state-space digital filters (2D-SSDFs) with powers-of-two coefficients based on a genetic algorithm (GA). The design problem is formulated in a state-space model. All coefficients of 2D-SSDF are then encoded to binary strings in order to apply the GA to the design problem. In addition, a stability test routine is embedded in the GA procedure to ensure the stability of the resulting 2D-SSDFs. The proposed method can obtain 2D-SSDFs with small approximation error in a nonuniform discrete space such as powers-of-two coefficients, which means that the designed 2D-SSDFs are attractive for high-speed operation and simple hardware architecture. The effectiveness of the proposed method is demonstrated by a design example.