Uncertainty principles and the linear canonical transform

Abstract

In this chapter some uncertainty principles for the linear canonical transform (LCT) have been introduced. For the Heisenberg’s principles there exist different bounds for real and complex signals. Based on the LCT moments properties the lower bounds related to the covariance of time and frequency have been derived, which can reduce to different bounds for real and complex signals because real signals have zero covariance. Furthermore, some extensions of uncertainty principles including the logarithmic, entropic and Renyi entropic uncertainty principles are deduced based on the relationship between the LCT and the Fourier transform.