Projeto de filtros digitais IIR com técnicas de computação evolucionária

Abstract

IIR digital filter design is classic problem in Electrical Engineering. Digital filter have many applications, and dozens of different behaviors. There are many specialist methods in literature, each with specific differences and characteristics. But most of these methods are not flexible, preventing one from fixing all parameters, because some of them are a sub-product of the calculation process. Therefore, this problem is also solved in literature with Evolutionary Computing techniques. Several works were found with this approach, but in almost all, the focus was in the evolutionary algorithm rather than on the filter problem, using this only as a benchmark function. Moreover, the filter stability - prerequisite for the filter application - is neglected in almost all of them. So, this work proposes a new fitness function, as well as a new codification, in order to obtain good filters, obedient to the specifications, with Evolutionary Computing algorithms in the canonic form, this is, without structural modifications. The proposed fitness function tries to correct distortions caused by the traditional one, which does not takes into account the filter gain specifications. The new coding maps the search space only to the stable solutions, not excluding any valid solution in the transformation. Moreover, a post-processing allows the filter phase equalization, this is, to make the pass band phase delay linear. This property is necessary in many types of applications, specially the telecommunication ones. The modifications performance is compared to the classic approaches found in the literature, and the most efficient set is use to compare the two most used Evolutionary Computing algorithms, GA and PSO. After this, extensive parameter tuning experiments were made, producing a final version of the method to compare with the specialist one. The chosen specialist method was the Elliptic filter, because the filter response has similarities with the one found by the proposed algorithm, and also because it is the most powerful one. Results showed excellent filters found with the proposed modifications, with a specification obedience rate well above the ones obtained with the classical approaches. Comparing with the specialist method, a similar performance was achieved, showing that IIR filter design with Evolutionary Computing can be used in real systems. Future work will address new modifications in the fitness function, and the performance of different EC algorithms in this problem. The application in online systems is promising, so the behavior of this approach with non-stationary specifications coming from channel estimation techniques should also be investigated.