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<p>Empirical wavelet transform (EWT) is an adaptive signal decomposition method that employs an adaptive filter bank to decompose an input signal into a set of narrow band modes. However, the boundaries in the existing EWT and its variants are found based on the global frequency characteristics of the signal and these methods are failed to capture the local time varying characteristics of the signal. Therefore, the performances yielded by applying these methods to the nonstationary signals are very poor. To address this difficulty, this paper proposes a short time EWT (STEWT) based method for decomposing a nonstationary signal into a set of modes. In particular, it integrates the short time Fourier transform (STFT) and the EWT together to perform the signal decomposition. First, the STFT is applied to the given signal. Second, the boundaries of the modes are estimated in the STFT domain. Third, a time varying filter bank is constructed and the filtering is performed in the STFT domain to obtain the various modes. Finally, the Hilbert transform (HT) is applied to those modes to obtain the time frequency representation of the signal. The results decomposed by our proposed method are compared to those decomposed by the conventional EWT based method, the variational mode decomposition (VMD) based method and other nonlinear adaptive time frequency analysis based methods. Here, the quality of the reconstruction factor (QRF) is employed as an objective metric for evaluating the performance. It is found that our proposed method achieves the higher averages of the QRFs of the modes as well as the higher averages of the QRFs of the instantaneous amplitudes (IAs) and the instantaneous frequencies (IFs) of the modes compared to the existing methods. Compared to other methods, the proposed method enhances the QRF performance of the given mode by an average of 25&#xa0;dB. Also, our proposed method requires a less computational time compared to the variational nonlinear chirp mode decomposition (VNCMD) based method, the time varying filtering based empirical mode decomposition (EMD) (TVFEMD) method based method and the sliding singular spectrum analysis (SSSA) based method. This demonstrates that our proposed method is more effective for decomposing the nonstationary signals than the other methods.</p>

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Estimation of Time Varying Boundaries and Filtering of Empirical Wavelet Transform with Application to Adaptive Nonstationary Signal Decomposition

  • 期刊论文

  • 发表日期：

    2025年1月25日

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  • Zhaoheng Zhou,
  • Bingo Wing-Kuen Ling,
  • Yang Zhou

摘要

Empirical wavelet transform (EWT) is an adaptive signal decomposition method that employs an adaptive filter bank to decompose an input signal into a set of narrow band modes. However, the boundaries in the existing EWT and its variants are found based on the global frequency characteristics of the signal and these methods are failed to capture the local time varying characteristics of the signal. Therefore, the performances yielded by applying these methods to the nonstationary signals are very poor. To address this difficulty, this paper proposes a short time EWT (STEWT) based method for decomposing a nonstationary signal into a set of modes. In particular, it integrates the short time Fourier transform (STFT) and the EWT together to perform the signal decomposition. First, the STFT is applied to the given signal. Second, the boundaries of the modes are estimated in the STFT domain. Third, a time varying filter bank is constructed and the filtering is performed in the STFT domain to obtain the various modes. Finally, the Hilbert transform (HT) is applied to those modes to obtain the time frequency representation of the signal. The results decomposed by our proposed method are compared to those decomposed by the conventional EWT based method, the variational mode decomposition (VMD) based method and other nonlinear adaptive time frequency analysis based methods. Here, the quality of the reconstruction factor (QRF) is employed as an objective metric for evaluating the performance. It is found that our proposed method achieves the higher averages of the QRFs of the modes as well as the higher averages of the QRFs of the instantaneous amplitudes (IAs) and the instantaneous frequencies (IFs) of the modes compared to the existing methods. Compared to other methods, the proposed method enhances the QRF performance of the given mode by an average of 25 dB. Also, our proposed method requires a less computational time compared to the variational nonlinear chirp mode decomposition (VNCMD) based method, the time varying filtering based empirical mode decomposition (EMD) (TVFEMD) method based method and the sliding singular spectrum analysis (SSSA) based method. This demonstrates that our proposed method is more effective for decomposing the nonstationary signals than the other methods.