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

► The Heisenberg Uncertainty Principles for the 2-D NSLCT are derived. ► The derived principles can be applied to 2-D FRFTs, 2-D LCTs, and gyrator transforms. ► The principles for the real input case and the case where det(B)=0 are also derived. ► The functions that can achieve the lower bound of the inequality are also found.