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Journal of the Optical Society of America A

Relationships between the Radon–Wigner and fractional Fourier transforms

Adolf W. Lohmann, Bernard H. Soffer

Published Jun 1, 1994• 223 citations
Publisher

Abstract

Two recently described transforms are shown to be related. The Radon–Wigner transform is the squared modulus of the fractional Fourier transform. This new theorem may serve to translate signal and image processing results between different signal representations. Some consequences regarding moments are presented, including a new fractional-Fourier-transform uncertainty relation. Implications for processing are suggested.

DOI
10.1364/josaa.11.001798

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