Application of Coevolutionary Algorithm for Wavelet Filter Design
Keywords:
Evolutionary algorithm, filter design, waveletAbstract
Designing wavelets using analytic methods often
needs to solve complicated systems of equations that cannot be solved easily. This paper proposed a new wavelet filter design methods using a coevolutionary algorithm. Each wavelet is made up of low and high-pass finite impulse response (FIR) filters so we separate our design into two parts: the first part produce low-pass high resolution filter using GA with a two
parameters fitness function that minimize the Uncertainty rectangle diameter and low-pass bandwidth, in the second part we take some of the best individuals from the first population in each generation and combine them with population of the second part and generate a new population then find best individuals using the fitness function which is derived from Heisenberg Uncertainty Principle and moment cancellation property. Then combine these new individuals with the population of the first group and repeat the optimization using GA and the new generated population. With these methods we
optimize two filters in a parallel way. The reason that we cannot optimize filters independently is that uncertainty rectangle diameters in a function of both of the filters.
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