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Properties and convergence analysis of FMmlet transform

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Abstract

The linearity, time shifting, time scaling, and time inversion properties of FMmlet transform are proved, and the frequency shifting property of one of the subspaces of FMmlet transform, namely the chirplet transform is presented. Moreover, it is proved that in the process of FMmlet based atomic signal decomposition, the residual signals decay exponentially.

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References

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Authors and Affiliations

  1. Department of Automation, Tsinghua University, 100084, Beijing, China

    Qionghai Dai, Zou Hongxing & Li Yanda

  2. Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, China

    Liu Zhixin & Wang Dianjun

Authors
  1. Qionghai Dai
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  2. Zou Hongxing
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  3. Liu Zhixin
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  4. Wang Dianjun
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  5. Li Yanda
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Correspondence to Qionghai Dai.

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Dai, Q., Hongxing, Z., Zhixin, L. et al. Properties and convergence analysis of FMmlet transform. Sci. China Ser. E-Technol. Sci. 45, 152–159 (2002). https://doi.org/10.1360/02ye9019

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  • DOI: https://doi.org/10.1360/02ye9019

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