Evolutionary synthesis of digital filter structures using genetic programming

This paper presents a synthesis method for infinite-impulse response (IIR) digital filter structures using genetic programming with automatically defined functions (GP-ADF). In the proposed method, digital filter structures are represented as Sexpressions with subroutines, which are written directly from the set of difference equations. This paper also shows the condition for the constructing the S-expressions that represent the filter structures without delay-free loops. Numerical examples synthesize two-filter structures: the low-coefficient sensitivity fourth-order filter structure and the low-output roundoff noise second-order filter structure.