Heuristic synthesis of low coefficient sensitivity second-order digital filters using genetic programming

The authors propose a new approach to the synthesis of low coefficient sensitivity second-order digital filter sections using genetic programming (GP). GP is applied to the synthesis problem by establishing a mapping between the filter structures and computer programs. Genetic operators change the computer programs in order to change the connections between the elements in the filter structures, and consequently change the coefficient sensitivities of those filter structures. The fitness measure that includes the coefficient sensitivities enables the selection operator to choose low sensitivity filter structures. In the paper, two coefficient sensitivity measures are used: the magnitude sensitivity and the relative sensitivity. A numerical example is presented to demonstrate that the sensitivity of the filter synthesised by GP is lower than that of other low coefficient sensitivity filter structures proposed so far.