GA-based design of 2D state-space digital filters with linear phase characteristics

This paper proposes a GA-based design method for two-dimensional (2D) state-space digital filters which satisfy simultaneously the magnitude response and constant group delays. The design problem of 2D state-space digital filters is formulated subject to the constraint that the resultant filters are stable. To apply the genetic algorithm to the design problem, all coefficients of 2D state-space digital filters are encoded into the Gray code representation demonstrating the superior performance to the standard binary one. In addition, a stability test routine is embedded in the design procedure in order to ensure the stability for the resultant filters. A numerical example is given to demonstrate the effectiveness of the proposed method.