Abstract
A joint empirical mode decomposition and optimal frequency band estimation approach is proposed to reduce the low-frequency noise adaptively. In each level of the decomposition, this paper considers the residue as the approximation of the low-frequency noise while the sum of the intrinsic mode functions is considered as the approximation of the denoised signal. Conventionally, the signal-to-noise ratio (SNR) of the denoised signal is used as a criterion for determining the optimal level of the decomposition. In particular, the level of the decomposition which achieves the highest SNR is defined as the optimal level of the decomposition. However, as the clean signal is unknown, it is difficult to find the optimal level of decomposition. To address this issue, the cutoff frequency of the residue in each level of the decomposition is estimated via an optimization problem. Here, the total energy of the difference between the energy spectrum of the residue and that of its corresponding matched filter is minimized subject to a constraint on the energy of the matched filter being equal to that of the residue. After finding the solution of the optimization problem for each level of the decomposition, the index corresponding to the global minimum of the absolute difference of the optimal cutoff frequency between two consecutive levels of the decomposition is defined as the optimal level of the decomposition. Since the optimal level of the decomposition is found automatically, our proposed method avoids the inappropriate selection of the parameter. Besides, the computer numerical simulation results show the superior performance yielded by our proposed method over the existing approaches on various test signals at different noise levels.
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Data availability
All the ECGs, the speeches and noises used in this paper are downloaded from the following databases: (1) https://archive.physionet.org/cgi-bin/atm/ATM. (2) http://spib.linse.ufsc.br/noise.html. (3) https://catalog.ldc.upenn.edu/LDC93S1
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Acknowledgements
This paper was supported partly by the National Natural Science Foundation of China (No. 62101130), the Guangdong Basic and Applied Basic Research Foundation (No. 2020A1515110289) and the Dongguan Sci-tech Commissioner Program (No.20201800500182).
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Kuang, W., Yang, P., Lai, Y. et al. Joint Empirical Mode Decomposition and Optimal Frequency Band Estimation for Adaptive Low-Frequency Noise Suppression. Circuits Syst Signal Process 42, 4170–4196 (2023). https://doi.org/10.1007/s00034-023-02309-2
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DOI: https://doi.org/10.1007/s00034-023-02309-2