Open Access

New Inequalities and Uncertainty Relations on Linear Canonical Transform Revisit

EURASIP Journal on Advances in Signal Processing20092009:563265

https://doi.org/10.1155/2009/563265

Received: 10 May 2009

Accepted: 22 June 2009

Published: 6 August 2009

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 parameters and 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 parameters and The reason why the three lower bounds are only associated with LCT parameters and and independent of and is presented. The results show it is possible that the bounds tend to zeros.

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Authors’ Affiliations

(1)
Department of Navigation, Dalian Naval Academy
(2)
Department of Automatization, Naval Academy
(3)
Institute of Photoelectric Technology, Dalian of China

Copyright

© Xu Guanlei et al. 2009

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.