Frequency analysis with Hopfield encoding neurons

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Abstract
A three-layer network that utilizes Hopfield encoding neurons [J. J Hopfield, Nature 376, 33 (1995)], is designed to compute the Fourier spectrum of an analog input signal of duration T. Each of the 2M (integer M≳0) Hopfield neurons in the input layer, is linked to an exclusive decoder with its output connected to all the 4M neurons present in the output layer. The connection strength between a decoder and a target neuron in the output layer (hereby called the output neuron), is characterized by a coupling constant which attenuates the decoder output that reaches the output neuron. All the attenuated 2M decoder signals reaching an output neuron are summed up within an integration time given by the period of the oscillatory drive of the Hopfield neuron. The frequency resolution and bandwidth of the analyzer network are given by 1/T and 2M/T, respectively. The first 2M output neurons yield the amplitudes of the real components of the Fourier spectrum, while the next 2M output neurons give the amplitudes of the corresponding imaginary components. Experiments show that the network exhibits an exponentially decaying learning error, and is capable of learning the general properties of Fourier transform from a limited set of examples. © 1996 The American Physical Society.