Derivation and discrete implementation for analytic signal of linear canonical transform

摘要

Analytic signal and Hilbert transform associated with linear canonical transform (LCT) have been developed [Opt. Commun. 281, 1468 (2008)]. However, the aforementioned paper has some drawbacks; for example, this kind of analytic signal cannot preserve the positive frequency bands of the original signal under LCT operations. In this paper, these drawbacks are pointed out, and a better definition for analytic signal associated with LCT is proposed. In addition, a discrete implementation for the analytic signal associated with discrete LCT is also provided. Several numerical examples, shown with both time and Wigner time-frequency domains, are demonstrated to illustrate the efficiency and accuracy of the proposed LCT analytic signal.