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

Document Type

Article

Publication Date

9-1-2022

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.

Publication Source (Journal or Book title)

Circuits, Systems, and Signal Processing

First Page

5084

Last Page

5107

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