A rapid learning orthonormal neural network for signal processing

The author describes a neural network 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 hidden layers or the backpropagation rule. 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 of auto-associatively training the network with all the middle nodes and testing it with certain selected ones, it is quite easy to build a nonlinear bandpass filter. A rapid learning algorithm is introduced that reduces the training time. Several systems built with this new network are discussed