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Uncertainty Principle for the Short-time Special Affine Fourier Transform

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Abstract

The special affine Fourier transform (SAFT) generalizes a number of well known unitary transformations, signal processing transformations and optics related mathematical operations. For example, Fourier transform, fractional Fourier transform, linear canonical transform, etc. The short-time special affine Fourier transform (STSAFT) is a novel time-frequency analysis tool, which solve the limitation of SAFT in time-frequency signal description. In this paper, we generalize some different uncertainty principles (UPs) for the SAFT and STSAFT of complex signals. The UPs for the STSAFT of complex signals are obtained in both local and global cases. Then the uncertainty principle for two STSAFT time-frequency domains is discussed. Finally, we provide a class of signals to illustrate our results.

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The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

This manuscript has benefited greatly from the constructive comments and helpful suggestions of the anonymous referees; the authors would like to express their deep gratitude to them.

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Authors and Affiliations

  1. College of Science, Tianjin University of Technology, Tianjin, 300384, China

    Rui Li & Qingyue Zhang

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  1. Rui Li
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  2. Qingyue Zhang
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Correspondence to Qingyue Zhang.

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This work was supported partially by the National Natural Science Foundation of China (11601383, 11971348 and 12071230)

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Li, R., Zhang, Q. Uncertainty Principle for the Short-time Special Affine Fourier Transform . Circuits Syst Signal Process 40, 4594–4613 (2021). https://doi.org/10.1007/s00034-021-01685-x

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