Empirical Wavelet Transform; Stationary and Nonstationary Signals

Hesam Akbari (Biomedical Engineering Department, South Tehran Branch, Islamic Azad University, Tehran, Iran)
Sedigheh Ghofrani (Electrical Engineering Department, South Tehran Branch, Islamic Azad University, Tehran, Iran)

Abstract


Signal decomposition into the frequency components is one of the oldest challenges in the digital signal processing. In early nineteenth century, Fourier transform (FT) showed that any applicable signal can be decomposed by unlimited sinusoids. However, the relationship between time and frequency is lost under using FT. According to many researches for appropriate time-frequency representation, in early twentieth century, wavelet transform (WT) was proposed. WT is a well-known method which developed in order to decompose a signal into frequency components. In contrast with original WT which is not adaptive according to the input signal, empirical wavelet transform (EWT) was proposed. In this paper, the performance of discrete WT (DWT) and EWT in terms of signal decomposing into basic components are compared. For this purpose, a stationary signal including five sinusoids and ECG as biomedical and nonstationary signal are used. Due to being non-adaptive, DWT may remove signal components but EWT because of being adaptive is appropriate. EWT can also extract the baseline of ECG signal easier than DWT.


Keywords


Empirical wavelet transform;Discrete wavelet transform;Signal decomposition

Full Text:

PDF

References


[1] O. Rioul, M. Vetterli. Wavelets and signal processing.

[2] IEEE Signal Processing Magazine, 1991, 8: 14-38.

[3] R. X. Gao, R. Yan. In Wavelets: theory and applications for manufacturing. Springer, 2011: 17–32.

[4] Alfred Haar. Zur theorie der orthogonalen funktionensys- teme. Mathematische Annalen., vol. 69, 1910,69(1): 331–371.

[5] JE Littlewood, REAC Paley. Theorems on Fourier series and power series. Journal of the London Mathematical Society, 1931, 6(3): 161-240.

[6] Y. Meyer. Wavelets and Operators. Cambridge Univ.

[7] Press, 1992.

[8] N.E. Huang, Z. Shen, S.R. Long, M.L. Wu,H.H.Shih, Q. Zheng, N.C. Yen, C.C. Tung, H.H. Liu. The empirical mode decomposition and Hilbert spectrum for nonlinear and nonstationary time series analysis. Proceedings of the royal society a mathematical physical and engineering sciences, 1998, 454: 903–995.

[9] J. Gilles. Empirical wavelet transform. IEEE Trans.Signal Process., 2013, 61(16): 3999-4010.

[10] M. Kedadouche, M.Thomas, A.Tahan. A comparative study between Empirical Wavelet Transforms and Empirical Mode Decomposition Methods: Application to bearing defect diagnosis. Mechanical Systems and Signal Processing, 2016, 81: 88-107.

[11] H. Singh Rupal, Soumya R. Mohanty, Nand Kishor,Dushyant Kumar Singh. Comparison of Empirical Mode Decomposition and Wavelet Transform for Power Quality Assessment in FPGA. International Conference on Power Electronics, Drives and Energy

[12] Systems (PEDES), 2018: 18654777.

[13] I. Daubechies, J. Lu, Hau-Tieng Wu. Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool. Applied and Computational Harmonic Analysis, 2011, 30(2): 243-261.

[14] I. Daubechies. Ten lectures on wavelets. Society for

[15] Industrial and Applied Mathematics, 1992.

[16] MIT-BIH Noise Stress Test database - 118e12m:

[17] http://www.physionet.org/physiobank/database/

[18] nstdb/

[19] O. Singh, R. K. Sunkaria. ECG signal denoising via

[20] empirical wavelet transform. Australasian College of

[21] Physical Scientists and Engineers in Medicine, 2016:

[22] -11.



DOI: https://doi.org/10.30564/jeisr.v1i2.1008

Refbacks

  • There are currently no refbacks.
Copyright © 2020 Sedigheh Ghofrani


Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.