Authors: Jun Shi Xiaoping Liu Naitong Zhang
Publish Date: 2013/04/11
Volume: 8, Issue: 1, Pages: 85-93
Abstract
The linear canonical transform LCT has been shown to be a useful and powerful analyzing tool in optics and signal processing Many results of this transform are already known including its uncertainty principles UPs The existing UPs of the LCT for complex signals can only provide sharp bounds with LCT parameters satisfying a 1/b 1ne a 2/b 2 However in most cases we strive to find a lower bound but not a sharper bound since a lower bound often leads to optimization problems in signal processing applications In this paper we first present a much briefer and more transparent derivation to obtain a general uncertainty principle of the LCT for arbitrary signals via operator methods Then we derive lower bounds of three UPs of the LCT for complex signals which are tighter lower bounds than the existing ones We also prove that the derived results hold for arbitrary LCT parametersThis work was completed in parts while Shi J was visiting the Department of Electrical and Computer Engineering University of Delaware Newark DE 19716 USA The work was supported in part by the National Basic Research Program of China Grant No 2013CB329003 the National Natural Science Foundation of China Grant No 61171110 and the ShortTerm Overseas Visiting Scholar Program of Harbin Institute of Technology
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