Uncertainty principles for coupled fractional Wigner–Ville distribution

Abstract

The coupled fractional Wigner–Ville distribution is a more general version of the fractional Wigner–Ville distribution. Main properties including boundedness, Moyal’s formula and inversion formula are studied in detail for the transformation. Additionally, the relation of the coupled fractional Wigner–Ville distribution with the two-dimensional Fourier transform is studied. We also present the relationship between the coupled fractional Wigner–Ville distribution with the two-dimensional Wigner–Ville distribution. We show how the properties and relations allow us to derive several versions of the uncertainty inequalities related to the coupled fractional Wigner–Ville distribution.

Keywords

• coupled fractional Fourier transform
• uncertainty principle
• fractional Fourier transform