Uncertainty principle and orthogonal condition for the short-time linear canonical transform
The short-time linear canonical transform (STLCT) is a novel time–frequency analysis tool, which maps the time domain signal into the joint time and frequency domain. This short paper investigates its two theoretical problems. The first one relates to the uncertainty principle in one STLCT domain, and the other one is that coefficients of the short-time linear canonical expansion (STLCE) are of incompleteness. To solve these issues, first, we develop the uncertainty principle in one STLCT domain. Second, the orthogonal condition is proposed to guarantee the completeness of the STLCE coefficients.
KeywordsLinear canonical transform Short-time linear canonical transform Uncertainty principle Orthogonal condition
The authors would like to thank the editor and the anonymous referee for their valuable comments and suggestions. This work was supported by the National Natural Science Foundation of China (61374135 and 61203084), Basic Science and Advanced Technology Research Project (cstc2015jcyjA0480) and Chongqing University Postgraduates Innovation Project (CYB15051).
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