Skip to main content

ECG signal denoising by fractional wavelet transform thresholding



The analysis of electrocardiogram (ECG) signals allows experts to diagnose several cardiac disorders. However, the accuracy of such diagnosis depends heavily on the signal quality. In this paper, an efficient method based on fractional wavelet decomposition coupled with thresholding techniques is proposed for noise removal.


The usual low-pass and high-pass filters of the wavelet transform are replaced by fractional-order ones. Thus, fractional wavelets are proposed, simulated, and compared to other wavelets for ECG denoising. The denoising process was made operational by the means of an appropriate choice of the wavelet transform coefficient thresholding and the wavelet decomposition level of the signal.


Considering the relative error metrics, the best wavelet function for efficient denoising is the fractional one. In our study, we have used eight real ECG signals from the Physionet MITBIH. In order to prove the effectiveness of our method, we investigated the filtering of two types of noises, namely Gaussian white noise and power-line interference (PLI) noise. The proposed method removed the Gaussian white noise completely and had better performance on the PLI noise. Considering classical metrics of assessment, results show the advantage of the proposed method compared to other types of wavelets.


The proposed method is the most suitable one for removing PLI and Gaussian white noise from ECG signals with superior performance than other wavelets. Also, it can be applied for high-frequency denoising even without a priori frequency knowledge.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29


  • Abdelliche F, Charef A. Fractional wavelet for R-wave detection in ECG signal. Crit Rev Biomed Eng. 2008;36(2):79–91.

    Article  Google Scholar 

  • Abdelliche F, Charef A. R-peak detection using a complex fractional wavelet. IEEE International Conference on Electrical and Electronics Engineering (ELECO 2009). 2009; 267–270.

  • Abdelliche F, Charef A, Talbi ML, Benmalek M. A fractional wavelet for QRS detection. IEEE International Conference on Information & Communication Technologies 0–7803–9521-2/06. 2006; 1186–1189.

  • Abdelliche F, Charef A, Ladaci S. complex fractional and complex Morlet wavelets for QRS complex detection. ICFDA'14 International Conference on Fractional Differentiation and Its Applications, (ieee Xplore) Catania, Italy. 2014.

  • Benmalek M, Charef A. Digital fractional order operators for R-wave detection in electrocardiogram signal. IET Signal Process. 2009;3(5):381–91.

    Article  Google Scholar 

  • Berman SM. Sojourns and extremes of stochastic processes. Reading, MA: Wadsworth; 1989.

    MATH  Book  Google Scholar 

  • Blanco-Velasco M, Weng B, Barner K. ECG signal denoising and baseline wander correction based on the empirical mode decomposition. Comput Biol Med. 2008;38(1):1–13.

    Article  Google Scholar 

  • Chang KM, Liu SH. Gaussian noise filtering from ECG by wiener filter and ensemble empirical mode decomposition. Journal Signal Processing System. 2011;64(2):249–64.

    Article  Google Scholar 

  • Chen S, Dong X, Xiong Y, Peng Z, Zhang W. nonstationary signal denoising using an envelope-tracking filter. IEEE/ASME Transactions on Mechatronics 2018; 23(4): 2004–2015.

  • Coifman R, Wickerhauser M. Adapted waveform de-noising for medical signals et images. IEEE Engineering in Medicine and Biomogy Magazine. 1995;14(5):578–86.

    Article  Google Scholar 

  • Coifman R, Wickerhauser M. Experiments with adapted wavelet de-noising for medical signals and images. IEEE Press Series in Biomedical Engineering. 1998;12:323–46.

    MATH  Google Scholar 

  • Donoho D. De-noising by soft thresholding. Technical report. IEEE Trans Inf Theory. 1995;41(3):1–37.

    MATH  Article  Google Scholar 

  • Donoho D, Johnstone I. Ideal spatial adaptation via wavelet shrinkage. Biometrika. 1994;81:425–55.

    MathSciNet  MATH  Article  Google Scholar 

  • Bouny L EL, Khalil M, Adib A. ECG signal denoising based on ensemble EMD thresholding and higher order statistics. IEEE International Conference on Advanced Technologies for Signal and Image Processing (ATSIP’2017), Morocco; 2017.

  • El-Sayed A, El-Dahshan. Genetic algorithm and wavelet hybrid scheme for ECG signal denoising. Telecommun Syst. 2011;46(3):209–15.

    Article  Google Scholar 

  • Ercelebi E. Electrocardiogram signals de-noising using lifting-based discrete wavelet transform. Comput Biol Med. 2004;34(6):479–93.

    Article  Google Scholar 

  • Fathi A, Naghsh-Nilchi AR. Efficient image denoising method based on a new adaptive wavelet packet thresholding function. IEEE Trans Image Process. 2012;21(9):3981–90.

    MathSciNet  MATH  Article  Google Scholar 

  • Feilner M, Jacob M and Unser M. Orthogonal quincunx wavelets with fractional orders. IEEE International Conference on Image Processing (ICIP'01). 2001; I: 606–609.

  • Gupta V, Mittal M. A comparison of ECG signal pre-processing using FrFT, FrWT and IPCA for improved analysis. IRBM Innovation and Research in BioMedical engineering. June 2019;40(3):145–56.

    Article  Google Scholar 

  • Hadjileontiadis L, Panas S. Separation of discontinuous adventitious sounds from vesicular sounds using a wavelet-based filter. IEEE Trans Biomed Eng. 1997;44(7):876–86.

    Article  Google Scholar 

  • Hadjileontiadis L, Liatsos L, Mavrogiannis C, Rokkas T, Panas S. Enhancement of bowel sounds by wavelet-based filtering. IEEE Trans Biomed Eng. 2000;47(12):1269–81.

    Article  Google Scholar 

  • Hesar HD, Mohebbi M. An adaptive particle weighting strategy for ECG denoising using marginalized particle extended Kalman filter: an evaluation in arrhythmia contexts. IEEE Journal of Biomedical and Health Informatics. 2017;21(6):1581–92.

    Article  Google Scholar 

  • Ignjatović A, Wijenayake C, Keller G. Chromatic derivatives and approximations in practice—part II: nonuniform sampling, zero-crossings reconstruction, and denoising. IEEE Trans Signal Process. 2018;66(6):1513–25.

    MathSciNet  MATH  Article  Google Scholar 

  • Jianhong W, Yongqiang Y, Xiang P, Xudong G. Parallel-type fractional zero-phase filtering for ECG signal denoising. Biomedical Signal Processing and Control. 2015;18:36–41.

  • Kabir MA, Shahnaz C. An ECG signal denoising method based on enhancement algorithms in EMD and wavelet domains. IEEE Region 10 Conference TENCON. 2011; 284–287.

  • Kopsinis Y, Laughlin SM. Development of EMD-based denoising methods inspired by wavelet thresholding. IEEE Trans Signal Process. April 2009;57:1351–62.

    MathSciNet  MATH  Article  Google Scholar 

  • Kruskal WH, Wallis WA. Use of ranks in one-criterion variance analysis. J Am Stat Assoc. 1952;260(17):583–621.

    MATH  Article  Google Scholar 

  • Le Lay L. Identification fréquentielle et temporelle par modèle non entier. Thèse de Doctorat, 1998.

    Google Scholar 

  • Maiti D, Konar A. Approximation of a fractional order system by an integer order model using particle swarm optimization technique. arXiv preprint arXiv. 2008; 0811.0077.

  • Mallat SG. A wavelet tour of signal processing. 2nd ed. Academic Press, 1999.

  • Mallat SG. A wavelet tour of signal processing: the sparse way. 3rd ed. Burlington: Elsevier; 2009.

    MATH  Google Scholar 

  • Maniruzzaman M, Kazi M, Billah S, Biswas U, Gain B. least-mean-square algorithm based adaptive filters for removing power line interference from ECG signal. IEEE International Conference on Informatics, Electronics & Vision (ICIEV'12). 2012; 410: 737–740.

  • MIT-BIH Arrhythmia Database at Accessed 4 Jan 2018.

  • Muduli PR, Mandal AK, Mukherjee A. An antinoise-folding algorithm for the recovery of biomedical signals from noisy measurements. IEEE Trans Instrum Meas. 2017;66(11):2909–16.

    Article  Google Scholar 

  • Nguyen P, Kim JM. Adaptive ECG denoising using genetic algorithm-based thresholding and ensemble empirical mode decomposition. Inf Sci. 2016;373:499–511.

    Article  Google Scholar 

  • Oliveira BR, Duarte MAQ, Abreu CCE, Vieira FJ. A wavelet-based method for power-line interference removal in ECG signals. Res Biomed Eng. 2018;34(1):73–86.

    Article  Google Scholar 

  • Oustaloup A, Cois O, Le Lay L. Représentation et identification par modèle non entier. Hermès Lavoisier. 2005.

  • Pham DH, Meignen S, Dia N, Jallon JF, Rivet B. Phonocardiogram signal denoising based on nonnegative matrix factorization and adaptive contour representation computation. IEEE Signal Processing Letters. 2018;25(10):1475–9.

    Article  Google Scholar 

  • Rioul O. Regular wavelets: a discrete-time approach. IEEE Trans on Signal Proc December. 1993;41(12):3572–8.

    MATH  Article  Google Scholar 

  • Sharma LN, Dandapat S, Mahanta A. ECG signal denoising using higher order statistics in wavelet subbands. Biomedical Signal Processing Control, Elsevier. 2010;5:214–22.

    Article  Google Scholar 

  • Shen H, Chen YQ, Qiu TS. Fractional processes and fractional order signal processing. Berlin: Springer Verlag; 2012.

    Book  Google Scholar 

  • Tseng CC. Design of fractional order digital FIR differentiators. IEEE Signal Process. 2001;8(3):77–9.

    Article  Google Scholar 

  • Tseng CC, Lee SL. Design of linear phase FIR filters using fractional derivative constraints. Signal Process. 2012;92:1317–27.

    Article  Google Scholar 

  • Üstündağ M, Gökbulut M, Sengür A, Ata F. Denoising of weak ECG signals by using wavelet analysis and fuzzy thresholding. Netw Model Anal Health Inform Bioinform. 2012;1(4):135–40.

    Article  Google Scholar 

  • Van Alste JA, Schilder TS. Removal of base-line wander and power-line interference from the ECG by an efficient FIR filter with a reduced number of taps. IEEE Transactions on Biomedical Engineering. 1985; BME– 32(12): 1052–1060.

  • Vargas VACP. Electrocardiogram signal denoising by clustering and soft thresholding Regis Nunes. IET Signal Processing. 2018;12(9):1165–71.

    Article  Google Scholar 

  • Vullings R, Vries B, Bergmans JWM. An adaptive Kalman filter for ECG signal enhancement. IEEE Trans Biomed Eng. April 2011;58(4):1094–103.

    Article  Google Scholar 

  • Zibulski M, Zeevi Y. Frame analysis of the discrete Gabor-scheme analysis. IEEE Trans Signal Proc April. 1994;42:942–5.

    Article  Google Scholar 

Download references


This study was done by mitdb/101, 105, 117, 119, 121, 215, 223, and 230 of the MIT-BIH Database.

The authors would like to thank LAAAS Laboratory (Laboratoire d’Automatique Avancée et d'Analyse des Systèmes) staff for their support and assistance throughout the work.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Ibtissem Houamed.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Houamed, I., Saidi, L. & Srairi, F. ECG signal denoising by fractional wavelet transform thresholding. Res. Biomed. Eng. 36, 349–360 (2020).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • ECG
  • Fractional wavelet
  • Denoising
  • Soft thresholding
  • Hard thresholding