tailieunhanh - báo cáo hóa học:" Research Article New Inequalities and Uncertainty Relations on Linear Canonical Transform Revisit"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article New Inequalities and Uncertainty Relations on Linear Canonical Transform Revisit | Hindawi Publishing Corporation EURASIP Journal on Advances in Signal Processing Volume 2009 Article ID 563265 7 pages doi 2009 563265 Research Article New Inequalities and Uncertainty Relations on Linear Canonical Transform Revisit Xu Guanlei 1 2 Wang Xiaotong 1 2 and Xu Xiaogang2 3 1 Department of Navigation Dalian Naval Academy Dalian 116018 China 2 Institute of Photoelectric Technology Dalian of China Dalian 116018 China 3 Department of Automatization Naval Academy Dalian 116018 China Correspondence should be addressed to Xu Guanlei xgl_86@ Received 10 May 2009 Accepted 22 June 2009 Recommended by Ling Shao 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 a and b. 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 a and b. The reason why the three lower bounds are only associated with LCT parameters a and b and independent of c and d is presented. The results show it is possible that the bounds tend to zeros. Copyright 2009 Xu Guanlei et al. 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. 1. Introduction The uncertainty principle is one elementary principle in signal processing 1-10 and physics 11-13 . For one given function f t e L1 R n L2 R without loss of generalization assuming II f t 2 1 in the .