Genetic Algorithms for Digital Signal Processing

Recursive digital filters are potentially less computationally expensive than their non-recursive counterparts. However, algorithms for adjusting the coefficients of recursive filters may produce biased or suboptimal estimates of the optimal coefficent values. In addition, recursive filters may become unstable if the adaptive algorithm updates a feedback coefficient so that one of the poles remains outside the unit circle for any length of time. This paper details an adaptive algorithm for optimizing the coefficients of recursive digital filters based on the genetic algorithm. Stability considerations are addressed by implementing the population of adaptive filters as lattice structures which allows the entire feasible, stable coefficient space to be searched whilst ensuring that crossover and mutation do not produce invalid (unstable) filters. Results are presented showing the application of this technique to the tasks of system identification and adaptive data equalization.

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