New Inequalities and Uncertainty Relations on Linear Canonical Transform Revisit. (6th August 2009)

• Record Type: Journal Article
• Authors: Guanlei, Xu; Xiaotong, Wang; Xiaogang, Xu
• Other Names: Shao Ling Academic Editor.
• Is Part Of: EURASIP journal on advances in signal processing. Volume 2009(2009)
• Publication Date: 2009-08-06
• Subjects: Signal processing -- Periodicals; Traitement du signal; Signal processing; Periodicals; 621.3822
• DOI: 10.1155/2009/563265
• Languages: English
• ISSNs: 1687-6172

Abstract

Abstract : The uncertainty principle plays an important role in mathematics, physics, signal processing, and so on. Firstly, based on definition of the linear canonical transform (LCT) and the traditional Pitt's inequality, one novel Pitt's inequality in the LCT domains is obtained, which is connected with the LCT parametersa andb. Then one novel logarithmic uncertainty principle is derived from this novel Pitt's inequality in the LCT domains, which is associated with parameters of the two LCTs. Secondly, from the relation between the original function and LCT, one entropic uncertainty principle and one Heisenberg's uncertainty principle in the LCT domains are derived, which are associated with the LCT parametersa andb. The reason why the three lower bounds are only associated with LCT parametersa andb and independent ofc andd is presented. The results show it is possible that the bounds tend to zeros.