Neural network-based recognition of stability regions of two-dimensional discrete recursive filters
S.M. Aghili · 1991
There are many areas in which Two-Dimensional Discrete Recursive Filtering (TDDRF) is of significant importance (1), (2), (3), (4), (23). Implementation of this type of filter is usually by one of the two methods (i) Convolution Algorithm, or (ii) The Two-Dimensional Fast Fourier Transforms. Stability regions of these filters are determined by the locations of the poles of the transfer function. The order and separability of the denominator will influence the difficulty of determining the stability regions. In this dissertation, a new technique is presented for obtaining the stability regions of these filters with and without separable denominators using Artificial Neural Networks (ANN). The ANN stability testing technique enables the adaptive algorithms (i.e. recursive prediction error technique) to obtain the stability state without factorization of the denominator polynomial. In this research, the three phases of implementation of an ANN; search, training, and testing are presented. The dissertation introduces Piece-wise Linear Multiple Slopes (PLMS) activation functions as an alternative to the sigmoid activation function for implementation in the modified back propagation learning algorithm. The results of a number of simulations of artificial neural networks with different architectures and activation functions under various conditions using the modified back propagation learning algorithm are analyzed.