Universal Optimal Parameters of the Closed-Form Linear Canonical Wigner Distribution

The closed-form linear canonical Wigner distribution (CFLCWD), equipped with nine linear canonical transform (LCT) free parameters, is an effective time-frequency method suitable for extracting the principal features of linear frequency-modulated signals from an extreme strong stationary Gaussian noise background. However, the appropriate parameters for non-stationary non-Gaussian noise jamming nonlinear frequency-modulated signal processing are still unknown. To address this issue, we reveal the equivalence of the uncertainty product in CFLCWD domains and those in LCT domains, based on which we deduce the CFLCWD's uncertainty inequality, whose equality is achieved by a Gaussian signal. We further derive the universal optimal LCT free parameters with which the CFLCWD reaches the highest-resolution in time-frequency plane. In particular, the strong uncertainty inequality of the classical Wigner distribution is also revisited.