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Computationally Efficient Multiwavelets Construction Method with New Signal-Dependent-Multiplicity Determination Scheme

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Abstract

Multiwavelets, which possess more favorable mathematical properties than scalar-wavelets, are deemed a promising means for non-stationary signal analysis. Due to high computational-complexity incurred in the construction of multiwavelets with arbitrary multiplicities (MWAM), the multiplicity of the multiwavelets currently utilized in practice is usually restricted to two, which limits the signal-processing performance. In this paper, a new fast MWAM construction method based on the finite-element analysis is introduced. The four orthogonality equations for solving the filter-coefficient matrices in the construction of multiwavelet functions are simplified to two equations mathematically, so the computational-complexity of the MWAM construction is significantly reduced. Meanwhile, a new optimal multiplicity selection strategy is also proposed based on the comparison between the time-frequency bandwidth-products of the multiscaling function and the probed signal. Finally, our proposed new fast MWAM-construction method in tandem with the new multiplicity-determination scheme is tested by an application, namely mechanical-bearing fault-diagnosis. The corresponding performance is quite promising. Our proposed new MWAM construction method along with the associated multiplicity-determination scheme can be applicable for many time-frequency signal-approximation and feature-extraction applications.

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Acknowledgements

This paper was supported by the National Natural Science Foundation of China under Grant No. 61801093.

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Authors and Affiliations

  1. School of Aeronautics and Astronautics, University of Electronic Science and Technology of China, Chengdu, 611731, Sichuan, China

    Xiao Yan, Qian Wang, Chunyu Yin & Pengwei Li

  2. School of Electrical Engineering and Computer Science, Louisiana State University, Baton Rouge, Louisiana, 70803, USA

    Hsiao-Chun Wu

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  1. Xiao Yan
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  5. Pengwei Li
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Correspondence to Qian Wang.

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

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Hsiao-Chun Wu, Qian Wang, Chunyu Yin and Pengwei Li have equally contributed to this work.

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Yan, X., Wu, HC., Wang, Q. et al. Computationally Efficient Multiwavelets Construction Method with New Signal-Dependent-Multiplicity Determination Scheme. Circuits Syst Signal Process 41, 5084–5107 (2022). https://doi.org/10.1007/s00034-022-02022-6

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