Narrow Results

The properties of a 2D discrete transfer function with degree of each variable being unity are discussed. The coefficients of the denominator polynomial contain a parameter k (having real values) whose bounds are determined by stability considerations. These bounds are obtained by testing the overall polynomial at only four points z₁=±1 and z₂=±1. Suitable numerator polynomial can be associated to get the overall transfer function. Such structures can be cascaded so that the overall magnitude response can be changed by altering the response of one or more sections.

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.