Wavelet-Based Signal approximation with Genetic Algorithms

In this paper, the usability of genetic algorithms for signal approximation is discussed. Due to recent developments in the field of signal approximation by wavelets, this work concentrates on signal approximation by wavelet-like functions. Signals are approximated by a finite linear combination of elementary functions and a genetic algorithm is employed to find the coefficients to such an approximation. The algorithm maintains a population of different approximations, encoded in the form of ‘chromosomes’. From this population ‘parents’ are selected according to their ‘fitness’, and the ‘children’ that constitute the next generation are produced from these parents using mutation and crossover operators. Fitness functions employed to evaluate different approximations are the L1, L2, L4, and L1 norms. Experiments are carried out on several test signals, using Gabor and spline wavelets, both to evaluate the quality of different fitness functions, encoding schemes, and operators, and to assess the usefulness of genetic algorithms in the realm of signal approximation. Although other existing methods are faster while providing comparable approximation quality, the algorithm offers a great deal of flexibility in terms of different elementary functions, fitness criteria, etc.