Application Study On The RBF Neural Network Based Technique In FIR Digital Filter Design

In this thesis, the author investigates the design of FIR filters by the use of the neural network (NN) algorithm based on the RBF (radial basis functions) optimization technique. As is known that there have been a number of other neural network based optimal techniques in the research field of digital filter design, but some of them are suffered from high complexity causing time consuming iteration computations. This fact motivates us to develop more efficient NN-based optimization technique for designing digital filters.As RBF is publicly recognized as having good astringency, fast convergence speed and stability of computation, the author attempted to develop an RBF-based optimization algorithm for designing the FIR digital filters. Our contribution in this regard can be summarized as the following:i) By choosing a cosine radial neural network we derived the transfer function of the FIR filter, upon which the optimal algorithm is developed, also the condition for the astringency of our algorithm is derived as , where ? is the rate of the neural learning and N stands for the order of the FIR filter.ii) The training step of radial basis function is also given. By adopting the MSE (mean-square error) criteria it is easy to get , the transfer function of the FIR to be designed quickly. Further improvements can be obtained by properly distributing different weighted coefficients aq on sampling points both for the pass band and stop band.iii) The RBF based optimal design algorithm is testified by a number of FIR digital filter design examples. Computer simulation results show that the algorithm is able to yield competitive filter performance with a significant reduction of computation time. iv) Effectiveness of RBF based optimization technique is also verified by its application to other digital signal processing problems, such as the design of digital differentiator and the Hilbert transformer. Simulation results for such examples demonstrate that good results can also be obtained.