Fractional Fourier transforms, wavelet transforms, and adaptive neural networks

Soo-Young Lee; Harold H. Szu

doi:10.1117/12.172793

1 July 1994 Fractional Fourier transforms, wavelet transforms, and adaptive neural networks

Soo-Young Lee, Harold H. Szu

Author Affiliations +

Optical Engineering, Vol. 33, Issue 7, (July 1994). https://doi.org/10.1117/12.172793

Abstract

A new optical architecture is developed, based on fractional Fourier transforms, that compromises between shift-invariant (frequency) and position-dependent filtering. The analogy of this architecture to wavelet transforms and adaptive neural networks is also presented. The ambiguity and Wigner distribution functions are obtainable from special cases of the filter. The filter design corresponds to the training of the neural networks, and an adaptive learning algorithm is developed based on gradient-descent error minimization and error back propagation. The extension to multilayer architecture is straightforward.

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Soo-Young Lee and Harold H. Szu "Fractional Fourier transforms, wavelet transforms, and adaptive neural networks," Optical Engineering 33(7), (1 July 1994). https://doi.org/10.1117/12.172793

Published: 1 July 1994

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