Equivalence between the two-dimensional real and analytic signal Wigner distributions

Manuel Soares, Olivier Vallée, Charles de Izarra

Amalia Torre

Martin J. Bastiaans

Piotr Kazimierczyk, Arkadiusz Orłowski

P.J. Oonincx, H. G. ter Morsche

Applying the fractional Fourier transform (FRFT) and the Wigner distribution on a signal in a cascade fashion is equivalent with a rotation of the time and frequency parameters of the Wigner distribution. In this paper an integral representation formula is presented that yields affine transformations on the spatial and frequency parameters of the n-dimensional Wigner distribution if it is applied on a signal with the Wigner distribution as for the FRFT. This representation formula is used to solve certain energy localization problems in phase space.

David H. Hughes, Bruce W. Suter

The frequency operator, Ω equivalent to i (partial derivative) δ/δt, is not necessarily Hermitian when acting on nonstationary signals. Central moment densities of Ω and its conjugate, temporal operator Τ, are proportional to the real parts of local central moments derived from the Wigner distribution. A nonrelativistic space-time-frequency Wigner distribution forms the backdrop and motivation for the present investigation.