Sharper Hardy Uncertainty Relations on Signal Concentration in Terms of Linear Canonical Transform

Abstract

Linear canonical transform is of much significance to optics and information science. Hardy uncertainty principle, like Heisenberg uncertainty principle, plays an important role in various fields. In this paper, four new sharper Hardy uncertainty relations on linear canonical transform are derived. These new derived uncertainty relations are connected with the linear canonical transform parameters and indicate new insights for signal energy concentration. Especially, for certain transform parameters, e.g. $b=0$ , these new proposed uncertainty relations break the traditional counterparts in signal energy concentration, as will result in new physical interpretation in terms of uncertainty principle. Theoretical analysis and numerical examples are given to show the efficiency of these new relations.