FRACTIONAL FOURIER-TRANSFORMS, WAVELET TRANSFORMS, AND ADAPTIVE NEURAL NETWORKS

A new optical architecture is developed, based on fractional Fourier t ransforms, that compromises between shift-invariant (frequency) and po sition-dependent filtering. The analogy of this architecture to wavele t transforms and adaptive neural networks is also presented. The ambig uity and Wigner distribution functions are obtainable from special cas es of the filter. The filter design corresponds to the training of the neural networks, and an adaptive learning algorithm is developed base d on gradient-descent error minimization and error back propagation. T he extension to multilayer architecture is straightforward.