On signal moments and uncertainty relations associated with linear canonical transform

The linear canonical transform (LCT) has been shown to be a powerful tool for signal processing and optics. This paper investigates the signal moments and uncertainty relations in the LCT domain. Firstly, some important properties of signal moments in the LCT domain are derived. Then some new Heisenberg's uncertainty relations for complex signals are proposed. The tighter lower bounds are related to the covariance of time and frequency and can be achieved by complex chirp signals with Gaussian envelope. The previously developed Heisenberg's uncertainty principles are special cases of the achieved results.