The Journal of the Australian Mathematical Society. Series B. Applied Mathematics

Research Article

The fractional fourier transform and the wigner distribution

David Mustard1


The Wigner distribution and many other members of the Cohen class of generalized phase-space distributions of a signal all share certain translation properties and the property that their two marginal distributions of energy density along the time and along the frequency axes equal the signal power and the spectral energy density. A natural generalization of this last property is shown to be a certain relationship through the Radon transform between the distribution and the signal's fractional Fourier transform. It is shown that the Wigner distribution is now distinguished by being the only member of the Cohen class that has this generalized property as well as a generalized translation property. The inversion theorem for the Wigner distribution is then extended to yield the fractional Fourier transforms.

(Received July 06 1994)

(Revised January 18 1995)


1 School of Mathematics, University of New South Wales, Sydney, 2052, Australia