Skip to main content

Advertisement

SpringerLink
Log in

Alexander fractional differential window filter for ECG denoising

  • Technical Paper
  • Published:
Australasian Physical & Engineering Sciences in Medicine Aims and scope Submit manuscript

Abstract

The electrocardiogram (ECG) non-invasively monitors the electrical activities of the heart. During the process of recording and transmission, ECG signals are often corrupted by various types of noises. Minimizations of these noises facilitate accurate detection of various anomalies. In the present paper, Alexander fractional differential window (AFDW) filter is proposed for ECG signal denoising. The designed filter is based on the concept of generalized Alexander polynomial and the R–L differential equation of fractional calculus. This concept is utilized to formulate a window that acts as a forward filter. Thereafter, the backward filter is constructed by reversing the coefficients of the forward filter. The proposed AFDW filter is then obtained by averaging of the forward and backward filter coefficients. The performance of the designed AFDW filter is validated by adding the various type of noise to the original ECG signal obtained from MIT-BIH arrhythmia database. The two non-diagnostic measure, i.e., SNR, MSE, and one diagnostic measure, i.e., wavelet energy based diagnostic distortion (WEDD) have been employed for the quantitative evaluation of the designed filter. Extensive experimentations on all the 48-records of MIT-BIH arrhythmia database resulted in average SNR of 22.014 ± 3.806365, 14.703 ± 3.790275, 13.3183 ± 3.748230; average MSE of 0.001458 ± 0.00028, 0.0078 ± 0.000319, 0.01061 ± 0.000472; and average WEDD value of 0.020169 ± 0.01306, 0.1207 ± 0.061272, 0.1432 ± 0.073588, for ECG signal contaminated by the power line, random, and the white Gaussian noise respectively. A new metric named as morphological power preservation measure (MPPM) is also proposed that account for the power preservance (as indicated by PSD plots) and the QRS morphology. The proposed AFDW filter retained much of the original (clean) signal power without any significant morphological distortion as validated by MPPM measure that were 0.0126, 0.08493, and 0.10336 for the ECG signal corrupted by the different type of noises. The versatility of the proposed AFDW filter is also validated by its application on the ECG signal from MIT-BIH database corrupted by the combination of the noises as well as on the real noisy ECG signals are taken from MIT-BIH ID database. Furthermore, the comparative study has also been done between the proposed AFDW filter and existing state of the art denoising algorithms. The results clearly prove the supremacy of our proposed AFDW filter.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Saritha C, Sukanya V, Murthy YN (2008) ECG signal analysis using wavelet transforms. Bulg J Phys 35:68–77

    Google Scholar 

  2. Khaing AS, Naing ZM (2011) Quantitative investigation of digital filters in electrocardiogram with simulated noises. Int J Inf Electron Eng 1:210–216

    Google Scholar 

  3. Jagannath DJ, Selvakumar AI (2014) Issues and research on foetal electrocardiogram signal elicitation. Biomed Signal Process Control 10:224–244

    Article  Google Scholar 

  4. Chen T, Mazomenos EB, Maharatna K et al (2013) Design of a low-power on-body ECG classifier for remote cardiovascular monitoring systems. IEEE J Emerg Sel Top Circuits Syst 3:75–85

    Article  Google Scholar 

  5. Tsouri GR, Ostertag MH (2014) Patient-specific 12-lead ECG reconstruction from sparse electrodes using independent component analysis. IEEE J Biomed Heal Inform 18:476–482. https://doi.org/10.1109/JBHI.2013.2294561

    Article  Google Scholar 

  6. Dima S, Panagiotou C, Mazomenos EB et al (2013) On the detection of myocadial scar based on ECG/VCG analysis. IEEE Trans Biomed Eng 60:3399–3409

    Article  PubMed  Google Scholar 

  7. Mazomenos EB, Biswas D, Acharyya A, Chen T, Maharatna K, Rosengarten J, Morgan J NC (2013) A low-complexity ECG feature extraction algorithm for mobile healthcare applications. IEEE J Biomed Heal Inform 17:459–469

    Article  Google Scholar 

  8. M.Dennis JH (2004) Modern signal processing. Cambridge University Press, London

    Google Scholar 

  9. Vullings R, De Vries B, Bergmans JWM (2011) An adaptive Kalman filter for ECG signal enhancement. Biomed Eng IEEE Trans 58:1094–1103

    Article  Google Scholar 

  10. Sayadi O, Shamsollahi MB (2008) ECG denoising and compression using a modified extended Kalman filter structure. IEEE Trans Biomed Eng 55:2240–2248. https://doi.org/10.1109/TBME.2008.921150

    Article  PubMed  Google Scholar 

  11. Alfaouri M, Daqrouq K (2008) ECG signal denoising by wavelet transform thresholding. Am J Appl Sci 5:276–281. https://doi.org/10.3844/ajassp.2008.276.281

    Article  Google Scholar 

  12. El-fattah MAA, Dessouky MI, Diab SM, El-samie FEA (2008) Speech enhancement using an adaptive Wiener filtering approach. Prog Electromagn Res 4:167–184

    Article  Google Scholar 

  13. Christov II, Daskalov IK (1999) Filtering of electromyogram artifacts from the electrocardiogram. Med Eng Phys 21:731–736. https://doi.org/10.1016/S1350-4533(99)00098-3

    Article  PubMed  CAS  Google Scholar 

  14. Ferdjallah M, Barr R (1994) Adaptive digital notch filter design on the unit circle for the removal of powerline noise from biomedical signals. IEEE Trans Biomed Eng 41:529–536

    Article  PubMed  CAS  Google Scholar 

  15. Wang J, Ye Y, Pan X et al (2014) Fractional zero-phase filtering based on the Riemann–Liouville integral. Sig Process 98:150–157. https://doi.org/10.1016/j.sigpro.2013.11.024

    Article  Google Scholar 

  16. Sikkandar MY, Akshayaa V, Dinesh AD, Dinikshaa Sree L (2013) Analysis of cardiac abnormalities using Hilbert-Huang transform. Int J Biomed Eng Technol 13:69–86

    Article  Google Scholar 

  17. Tang G, Qin A (2008) ECG de-noising based on empirical mode decomposition. In: 9th international conference for young computer scientists, pp 903–906

  18. Elbuni A, Kanoun S, Elbuni M, Ali N (2009) ECG parameter extraction algorithm using (DWTAE) algorithm. In: International conference on computer technologies and development, pp 315–320

  19. Poornachandra S (2008) Wavelet-based denoising using subband dependent threshold for ECG signals. Digit Signal Process 18:49–55. https://doi.org/10.1016/j.dsp.2007.09.006

    Article  Google Scholar 

  20. Wang J, Ye Y, Pan X, Gao X (2015) Parallel-type fractional zero-phase filtering for ECG signal denoising. Biomed Signal Process Control 18:36–41. https://doi.org/10.1016/j.bspc.2014.10.012

    Article  Google Scholar 

  21. Artal-Bartolo E (1994) Sur les couples de Zariski. J Algebraic Geom 3:223–247

    Google Scholar 

  22. Jalab HA, Ibrahim RW (2015) Fractional Alexander polynomials for image denoising. Sig Process 107:340–354. https://doi.org/10.1016/j.sigpro.2014.06.004

    Article  Google Scholar 

  23. Krishna BT (2011) Studies on fractional order differentiators and integrators: a survey. Sig Process 91:386–426. https://doi.org/10.1016/j.sigpro.2010.06.022

    Article  Google Scholar 

  24. Hu J, Pu Y, Zhou J (2011) A novel image denoising algorithm based on riemann-liouville definition. J Comput 6:1332–1338. https://doi.org/10.4304/jcp.6.7.1332-1338

    Article  Google Scholar 

  25. Miller KS, Ross B (1993) An introduction to the fractional calculus and fractional differential equations. Wiley, Hoboken

    Google Scholar 

  26. Yang XS (2010) A new metaheuristic bat-inspired algorithm. In: Gonzlez J, Pelta D, Cruz C, Terrazas G, Krasnogor N (eds) Nature inspired cooperative strategies for optimization. Springer, Berlin, 65–74

    Chapter  Google Scholar 

  27. De Luca CJ (2002) Surface electromygraphy: detection and recording. DelSys, Natick

    Google Scholar 

  28. Kauav SS, Markam K (2014) Removal of artifacts from electrocardiogram using different Fir window techniques. J Res Electr Electron Eng 3:44–51

    Google Scholar 

  29. Martin V (2013) Adaptive wavelet Wiener filtering of ECG signals. IEEE Trans Biomed Eng 60:437–445

    Article  Google Scholar 

  30. El-Dahshan E-SA (2011) Genetic algorithm and wavelet hybrid scheme for ECG signal denoising. Telecommun Syst 46:209–215

    Article  Google Scholar 

  31. PhysioNet, MIT-BIH. Arrhythmia Database. http://www.physionet.org/. Accessed 15 May 2017

  32. Ramakrishnan AG, Saha S (1997) ECG coding by wavelet-based linear prediction. IEEE Trans Biomed Eng 44:1253–1261. https://doi.org/10.1109/10.649997

    Article  PubMed  CAS  Google Scholar 

  33. Manikandan MS, Dandapat S (2007) Wavelet energy based diagnostic distortion measure for ECG. Biomed Signal Process Control 2:80–96. https://doi.org/10.1016/j.bspc.2007.05.001

    Article  Google Scholar 

  34. Ye Y, Wang D (2005) Zero phase learning control using reversed time input runs. J Dyn Syst Meas Control 127:133–139. https://doi.org/10.1115/1.1849251

    Article  Google Scholar 

  35. Suyi L, Jun L (2009) The optimal de-noising algorithm for ECG using stationary wavelet transform. In: 2009 WRI World Congress on computer science and information engineering, pp 469–473

  36. Bao J, Longman RW (2008) Enhancements of repetitive control using specialized FIR zero-phase filter designs. Adv Astronaut Sci 129:1413–1432

    Google Scholar 

  37. Britanak V (2010) New fast computational structures for an efficient implementation of the forward/backward MDCT in MP3 audio coding standard. Sig Process 90:536–547. https://doi.org/10.1016/j.sigpro.2009.07.019

    Article  Google Scholar 

  38. Chung SH, Kennedy RA (1991) Forward-backward non-linear filtering technique for extracting small biological signals from noise. J Neurosci Methods 40:71–86. https://doi.org/10.1016/0165-0270(91)90118-J

    Article  PubMed  CAS  Google Scholar 

  39. The MIT-BIH ECG-ID Database. https://www.physionet.org/physiobank/database/ecgiddb/. Accessed 20 June 2017

Download references

Acknowledgements

The authors would like to thank J. Wang for providing the codes for the implementation of the FFB, GL, RL, FBB and FBA filters.

Author information

Authors and Affiliations

  1. Dr. B.R. Ambedkar National Institute of Technology, Jalandhar, India

    Atul Kumar Verma, Indu Saini & Barjinder Singh Saini

Authors
  1. Atul Kumar Verma
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Indu Saini
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Barjinder Singh Saini
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Atul Kumar Verma.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Research involving human and animal rights

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Verma, A.K., Saini, I. & Saini, B.S. Alexander fractional differential window filter for ECG denoising. Australas Phys Eng Sci Med 41, 519–539 (2018). https://doi.org/10.1007/s13246-018-0642-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13246-018-0642-y

Keywords

Search

Navigation