Quadratic-phase Wigner distribution: Theory and applications

The Wigner distribution one of the most celebrated time–frequency tool for analyzing non-transient signals and has been widely employed in signal processing and other allied fields. In this article, we introduce a novel quadratic-phase Wigner distribution (QWD) by intervening the advantages of quadratic-phase Fourier transforms and Wigner distribution. We initiate our investigation by studying the fundamental properties of the proposed distribution, including the marginal, shifting, conjugate-symmetry, anti-derivative, Moyal’s and inversion formulae by using the machinery of quadratic-phase Fourier transforms and operator theory. Moreover, the convolution and correlation theorems associated with QWD are derived. Finally, we broaden the scope of the proposed distribution by detecting the parameters of the linear frequency modulated signals.