The optimal [formula omitted]-Wigner distribution

Abstract

This study devotes to the optimal parameter of the k-Wigner distribution (kWD) in terms of the highest time-frequency resolution. We first disclose a relation between spreads in time-kWD and time domains, as well as those in Fourier transform (FT)-kWD and FT domains. Then we use them to set up an equivalence relation between the uncertainty product in time-kWD and FT-kWD domains and that in time and FT domains. Finally we separately deduce Heisenberg’s uncertainty inequalities of all signals and complex-valued signals for the kWD. As a result, the optimal kWD is none other than the ordinary Wigner distribution. Examples are carried out to verify the correctness of the theoretical result. An application of the derived uncertainty inequalities in the estimation of bandwidths in kWD domains is also given.