Uncertainty relations for signal concentrations associated with the linear canonical transform

Abstract

The linear canonical transform (LCT) has been shown to be a useful and powerful tool in optics and signal processing. In this paper, a new uncertainty relation in the LCT domain has been obtained at first. It shows that nonzero signal's energy in two arbitrary LCT domains cannot be arbitrarily large simultaneously, which is the generalization of the uncertainty principle for signal concentrations in the Fourier domain. Meanwhile, the signals which are the best in achieving simultaneous concentration in two arbitrary LCT domains are also proposed. In addition, some potential applications are presented to show the effectiveness of the theorems.