ANN bandpass filters for electro-optical implementation

The design and simulation of a bandpass filter are described, and an electro-optical implementation is proposed. The neural network used in this filter has an architecture similar to the one suggested by Kolmogorov´s existence theorem and a data processing method based on Fourier series. The resulting system, called the orthonormal neural network, can approximate any L₂ mapping function between the input and output vectors without using the backpropagation rule or hidden layers. Because the transfer functions of the middle nodes are the terms of the Fourier series, the synaptic link values between the middle and output layers represent the frequency spectrum of the signals of the output nodes. As a result, by autoassociatively training the network with all the middle nodes and testing it with certain selected ones, it is easy to build a nonlinear bandpass filter. The system is basically a two-layer network consisting of virtual input nodes and output nodes. The transfer functions of the output nodes are linear. As a result, the network is free from the problems of local minima and has a bowl-shaped error surface. The sharp slopes of this surface make the system tolerant to loss of computational accuracy and suitable for electro-optical implementation