Heisenberg's uncertainty principles for the 2-D nonseparable linear canonical transforms

摘要: The uncertainty principles of the 1-D Fourier transform (FT), fractional (FRFT), and linear canonical (LCT) have already been derived. In this paper, we extend previous works derive for two-dimensional nonseparable (2-D NSLCT), including complex input case, real case where det(B)=0 B is a parameter subset 2-D NSLCT. Since NSLCT generalization many operations, with derived principles, uncertain such as Fresnel transform, FT, FRFT, LCT, gyrator can also be found. Moreover, find that rotation, scaling, chirp multiplication Gaussian function minimize product variances in space domains. graphical abstractDisplay Omitted Highlights? Heisenberg Uncertainty Principles are ? applied to FRFTs, LCTs, transforms. functions achieve lower bound inequality