New simple proofs of uncertainty inequalities for linear canonical space-time transform

The linear canonical space-time transform (LCST) is an expanded version of the space-time Fourier transform (SFT). In the current work, we first define the LCST and the SFT. The direct relationship between the LCST and the SFT is presented. Hereafter, by means of the relation technique, we give the alternative proof of scalar Parseval's identity for the LCST. Further, by leveraging the relation, we give simple proofs of some uncertainty inequalities associated with the LCST. It is found that the principles differ from the existing literature. Simulation based on space-time Gabor filters is performed to verify the validity of the uncertainty principle. Finally, we derive a particular case of the sharp Hausdorff–Young inequality for the LCST that inherits Plancherel's formula for the LCST and the SFT.