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.
© 1994 Optical Society of America
Original Manuscript: October 25, 1993
Revised Manuscript: December 23, 1993
Manuscript Accepted: January 11, 1994
Published: June 1, 1994
Adolf W. Lohmann and Bernard H. Soffer, "Relationships between the Radon–Wigner and fractional Fourier transforms," J. Opt. Soc. Am. A 11, 1798-1801 (1994)