Synthesis of low-sensitivity second-order digital filters using genetic programming with automatically defined functions

This letter proposes a synthesis method for low coefficient sensitivity second-order IIR digital filter structures using genetic programming with automatically defined functions (GP-ADF). In this letter, digital filter structures are represented as S-expressions with subroutines. It is easy to generate syntactically valid S-expressions and perform the genetic operations, because the representation is suitable for GP. A numerical example uses the fitness measure, including the magnitude sensitivity, and demonstrates that the proposed method can synthesize efficiently very low coefficient sensitivity filter structures.