Generalized uncertainty relations of Tsallis entropy on FrFT

Abstract

As the generalization of Shannon entropy, the Tsallis entropy plays an important role in signal processing. In this paper, the generalized uncertainty relations with respect to Tsallis entropy associated with FrFT(fractional Fourier transform) are demonstrated for the first time to date. First, the Tsallis entropy-based continuous and sampled uncertainty principles are shown in terms of signal processing viewpoint based on a few mathematical inequalities. Second, the Tsallis entropy-based uncertainty relations with respect to FrFT with tighter bounds are derived in great detail with physical interpretation, whose refined uncertainty bounds are related to the FrFT parameters and sharper than the traditional counterparts. In addition, the relations between the Tsallis entropy and Shannon entropy and Rényi entropy are discussed as well. Finally, the numerical comparison is given to show the efficiency and the performance of the proposed uncertainty principles.

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Acknowledgements

This work is fully supported by NSFCs (61771020, 61471412) and 2019KD0AC02.

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Correspondence to Xu Guanlei.

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Guanlei, X., Xiaogang, X. & Xiaotong, W. Generalized uncertainty relations of Tsallis entropy on FrFT. SIViP 15, 9–16 (2021). https://doi.org/10.1007/s11760-020-01716-1

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Keywords

  • Tsallis entropy
  • Uncertainty principle
  • FrFT (fractional Fourier transform)