The Optimal Closed-Form Linear Canonical Wigner Distribution

This study devotes to Heisenberg's uncertainty inequalities under the closed-form instantaneous cross-correlation function Wigner distribution (CICFWD), whose generalizability enables it to be a representative Wigner distribution (WD) in the linear canonical transform (LCT) domain. A relation between the spread in the time-CICFWD domain and the spreads and moments in LCT domains is established. We then obtain two versions of lower bounds on the uncertainty product of spreads in time-CICFWD and LCT-CICFWD domains. The first is the tightest universal lower bound for all signals, and the other is a lower bound for complex-valued signals. As a result, uncertainty principles for the traditional WD are revisited. The optimal LCT free parameters selection problems of the CICFWD are also well-addressed from the perspectives of the highest time-frequency resolution and its best estimation accuracy, respectively.