(λ,μ)-Wigner distribution via quadratic-phase Fourier transform: Uncertainty principle, application, and properties

The scaled Wigner distribution (SWD), a generalization of the celebrated Wigner distribution (WD), has become widely used in time-frequency analysis. This study extends further the notion of SWD to the WD associated with quadratic-phase Fourier transform (QFT), which is so-called [Formula: see text]-QWD. It can be said that [Formula: see text]-QWD can be received from the symplectic WD through the change of coordinates of the general symplectic matrix. Furthermore, this paper will disclose a new Heisenberg’s uncertainty principle in [Formula: see text]-QWD domain, which is a significant extension of uncertainty inequalities for SWD. Next, [Formula: see text]-QWD shows flexibility in cross-term reduction in detecting bi-component linear frequency modulation (LFM) signals. A significant strength of the proposed application lies in its capacity to enhance auto-terms resolution and diminish cross-terms concurrently, even increasing the angular resolution and time-frequency resolution of the auto-terms. Moreover, two examples are carried out to verify the correctness of the statements. Finally, some basic properties, including shifting properties, conjugation properties, QFT marginal properties, anti-derivative properties, and the relation with the short-time Fourier transform (STFT) will be also demonstrated.