Abstract
Timely detection of cardiac abnormalities from an Electrocardiogram (ECG) signal is very essential. This requires its appropriate and efficient processing. In the literature, most of the researchers focussed on linear techniques that were applied on filtered ECG datasets leaving an ample scope for exploring the use of non-linear techniques in the presence and absence of natural noise-processes. Therefore, there is a need of supplementing the existing research on ECG signal interpretation by using non-linear techniques on noisy ECG data. Non-linear techniques are expected to yield supplementary clues about the non-linearities in the underlying cardiovascular system. One such promising non-linear technique, known as chaos theory (analysis), has been considered here to estimate reliable and robust thresholds for R-peak detection using fractal dimension, Approximate Entropy, Sample Entropy, correlation dimension, and Lyapunov exponent based on time-delay dimension (embedding). Also, time–frequency analysis techniques have shown their effectiveness for analyzing such types of non-linear and non-stationary signals due to simultaneous interpretation of the signal in both time and frequency domain. Among existing TFA techniques such as wavelet transform, short time Fourier transform, Hilbert transform, Auto-regressive Time Frequency Analysis (ARTFA) offers good time–frequency resolution. Therefore, Chaos theory and ARTFA have been considered in this paper. First, raw ECG signal was filtered using Savitzky Golay Digital Filtering (SGDF) because it retains all important signal features after filtering. Second, a novel optimal trajectory detection step was proposed on the basis of phase space reconstruction (attractors) in chaos theory. Third, ARTFA has been used to find the spectral components of the extracted features using chaos theory. Here, ARTFA has been used for finding the autoregressive coefficients in the first step and time–frequency description in the second step. Burg method has been considered for Auto-regressive modeling to fit an ARTFA model for analyzing ECG signal by minimizing (least squares) the forward and backward prediction errors. MIT-BIH arrhythmia database has been considered for validating the present research effort. Some real time signals were also tested to explore direct usage of the proposed technique in practical applications. The obtained results show that the proposed technique enhances sensitivity, positive predictive value and accuracy thereby improving the detection of arrhythmias. Computational cost of the proposed technique is reduced to a great extent by using the chaos theory (analysis) yielding efficient detection performance. All results have been obtained in MATLAB environment R2011a. Improved values viz. 99.96% SE, 99.97% PPV, and 99.93% ACC are obtained.
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Data Availability
Available on physionet website (https://physionet.org).
Code Availability
Software application which is developed by present authors.
Abbreviations
- BLW:
-
Base Line Wandering
- ECG:
-
Electrocardiogram
- SGDF:
-
Savitzky-Golay Digital Filtering
- HRV:
-
Heart Rate Variability
- ARTFA:
-
Auto-regressive Time Frequency Analysis
- FD:
-
Fractal dimension
- AE-χ:
-
Approximate Entropy
- SE-χ′:
-
Sample Entropy
- PCs:
-
Principal Components
- PSD:
-
Power Spectral Density
- MATLAB:
-
Matrix Laboratory
- MIT-BIH:
-
Massachusetts Institute of Technology-Beth Israel Hospital
- Arr:
-
Arrhythmia
- Hz:
-
Hertz
- FN:
-
False Negative
- FP:
-
False Positive
- TP:
-
True Postive
- KNN:
-
K-Nearest Neighbor
- DT:
-
Decision Tree
- YW:
-
Yule-Walker
- IFs:
-
Instantaneous frequencies
- CWT:
-
Continuous wavelet transform
- EMD:
-
Empirical mode decomposition
- CD:
-
Correlation dimension
- LE:
-
Lyapunov exponent
- TF:
-
Time–Frequency
- AR:
-
Auto-Regressive
- TFA:
-
Time–Frequency analysis
- BM:
-
Burg method
- AIC:
-
Akaike’s information criterion
- PCA:
-
Principal Component Analysis
- DSE :
-
Sensitivity
- DPPV :
-
Positive Predictive Value
- DACC :
-
Accuracy
- FFT:
-
Fast Fourier Transform
- dB:
-
Decibel
- LBBB:
-
Left Bundle Branch Block
- PVC:
-
Premature ventricular contraction
- AF:
-
Atrial fibrillation
- VF:
-
Ventricular fibrillation
- SSS:
-
Sick sinus syndrome
- STFT:
-
Short-time Fourier transform
- ST:
-
Synchrosqueezed transform
- IMFs:
-
Intrinsic mode functions
- SWT:
-
Synchrosqueezed wavelet transforms
References
Singhal, A., Singh, P., Fatimah, B., & Pachori, R. B. (2020). An efficient removal of power-line interference and baseline wander from ECG signals by employing Fourier decomposition technique. Biomedical Signal Processing and Control, 57, 101741. https://doi.org/10.1016/j.bspc.2019.101741.
Chawla, M. P. S. (2011). PCA and ICA processing methods for removal of artifacts and noise in electrocardiograms: A survey and comparison. Journal of Applied Soft Computing, 11(2), 2216–2226. https://doi.org/10.1016/j.asoc.2010.08.001.
Kaur, I., Rajni, R., & Marwaha, A. (2016). ECG signal analysis and arrhythmia detection using wavelet transform. Journal of the Institution of Engineers Ind Series B, 97(4), 499–507. https://doi.org/10.1007/s40031-016-0247-3.
Dohare, A. K., Kumar, V., & Kumar, R. (2013). An efficient new method for the detection of QRS in electrocardiogram. Jounal of Computers and Electrical Engineering, 40(5), 1717–30. https://doi.org/10.1016/j.compeleceng.2013.11.004.
Li, Y. (2014). Heartbeat detection, classification and coupling analysis using electrocardiography data. Doctor of Philosophy. Department of Electrical Engineering & Computer Science, Case Western Reserve University. https://etd.ohiolink.edu/apexprod/rws_etd/send_file/ send?accession=case1405084050&disposition=inline
Shang, P., Li, X., & Kamae, S. (2005). Chaotic analysis of traffic time series. Journal of Chaos, Solitons and Fractals, 25(1), 121–128. https://doi.org/10.1016/j.chaos.2004.09.104.
Alhamdi, M. (2015). Analysis of human electrocardiogram for arrhythmia auto-classification and biometric recognition systems using analytic and autoregressive modeling parameters. Degree of Doctor of Engineering, University of Portsmouth. https://researchportal.port.ac.uk/portal/en /theses/analysis-of-human-electrocardiogram-for-arrhythmia-autoclassification-and-biometric-recognition-systems-using-analytic-and-autoregress ive-modeling-parameters(7bb302a7-cb94–4df2-b04a-aac1ade0beee).html
Duskalov, I. (1998). Developments in ECG acquisition, preprocessing, parameter measurement, and recording. IEEE Engineers in Medical and Biology Magazine, 7(2), 50–8. https://doi.org/10.1109/51.664031.
Fatimah, B., Singh, P., Singhal, A., & Pachori, R. B. (2020). Detection of apnea events from ECG segments using fourier decomposition method. Biomedical Signal Processing and Control, 61, 102005. https://doi.org/10.1016/j.bspc.2020.102005.
Vandeput, S. (2010). Heart rate variability: Linear and nonlinear analysis with applications in human physiology. Dissertation of Doctor in Engineering Sciences, Leuven (Belgium): Katholieke Universiteit Leuven. https://theses.eurasip.org/theses/542/heart-rate-variability-linear-and-nonlinear/
Rangayyan, R. M. (2001). Biomedical signal analysis: A case-study approach. . Wiley-Interscience.
Gupta, V., & Mittal, M. (2020). A novel method of cardiac arrhythmia detection in electrocardiogram signal. International Journal of Medical Engineering and Informatics, 12(5), 489–499. https://doi.org/10.1504/IJMEI.2020.109943.
Merino, M., Gomez, I. M., & Molina, A. J. (2015). Envelopment filter and K-means for the detection of QRS waveforms in the electrocardiogram. Journal of Medical Engineering and Physics, 37(6), 605–9. https://doi.org/10.1016/j.medengphy.2015.03.019.
Sellami, A., & Hwang, H. (2018). A robust deep convolutional neural network with batch-weighted loss for heartbeat classification. Expert System With Application. https://doi.org/10.1016/j.eswa.2018.12.037.
Moridani, M. K., & Pouladian, M. (2019). A novel method to ischemic heart disease detection based on non-invasive ECG imaging. Journal of Mechanics in Medicine and Biology, 19(1), 19500021–25. https://doi.org/10.1142/S0219519419500027.
Khalea, A. F., Owis, M. I., & Yassine, I. A. (2015). A novel technique for cardiac arrhythmia classification using spectral correlation and support vector machines. Expert System with Application, 42(21), 8361–8368. https://doi.org/10.1016/j.eswa.2015.06.046.
Acharya, U. R., Fujita, H., Adam, M., Lih, O. S., Sudarshan, V. K., Hong, T. J., Koh, J. E. W., Hagiwara, Y., Chua, C. K., Poo, C. K., & San, T. R. (2017). Automated characterization and classification of coronary artery disease and myocardial infarction by decomposition of ECG signals: A comparative study. Information Science, 377, 17–19. https://doi.org/10.1016/j.ins.2016.10.013.
Dliou, A., Latif, R., Laaboubi, M., Maoulainine, F. M. R., & Elouaham, S. (2013). Time-frequency analysis of a noised ECG signals using empirical mode decomposition and Choi-Williams techniques. International Journal of Systems, Control and Communications, 5(4), 231–245. https://doi.org/10.1504/IJSCC.2013.058177.
Huijun, W., Guizhong, L., Wunchun, F. (2003). A new time-frequency analysis based upon AR model. In: Proceedings of the IEEE International Conference on Neural Networks and Signal Processing. https://doi.org/https://doi.org/10.1109/ICNNSP.2003.1279358.
Singh, P., Srivastava, P.K., Patney, R.K., Joshi, S.D., Saha, K. (2013). Nonpolynomial spline based empirical mode decomposition, In: Proceedings of the Int Conf Signal Processing and Communication, pp. 435–440. https://doi.org/https://doi.org/10.1109/ICSPCom.2013.6719829.
Sharma, R., Pachori, R.B., Gautam, S. (2014). Empirical mode decomposition based classification of focal and non-focal EEG signals, In: Proceedings of the IEEE Int Conf on Medical Biometrics, 30 May-01 June, 2014, Shenzhen, China. https://doi.org/https://doi.org/10.1109/ICMB.2014.31.
Singh, P., Joshi, S. D., Patney, R. K., & Saha, K. (2016). Fourier-based feature extraction for classification of EEG signals using EEG rhythms. Circuits System Signal Processing, 35(10), 3700–3715. https://doi.org/10.1007/s00034-015-0225-z.
Gupta, A., Singh, P., & Karlekar, M. (2018). A novel signal modeling approach for classification of seizure and seizure-free EEG signals. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 26(5), 925–35. https://doi.org/10.1109/TNSRE.2018.2818123.
Daubechies, I., Lu, J., & Wu, H. T. (2011). Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool. Applied and Computational Harmonic Analysis, 30, 243–261. https://doi.org/10.1016/j.acha.2010.08.002.
Sharma, M., Pachori, R. B., & Acharya, U. R. (2017). A new approach to characterize epileptic seizures using analytic time-frequency flexible wavelet transform and fractal dimension. Pattern Recognitions Letters, 94, 172–179. https://doi.org/10.1016/j.patrec.2017.03.023.
Singh, P., & Joshi, S. D. (2019). Some studies on multidimensional fourier theory for Hilbert transform, analytic signal and AM–FM Representation. Circuits, Systems, and Signal Processing, 38, 5623–5650. https://doi.org/10.1007/s00034-019-01133-x.
Singh, P. (2020). Novel generalized Fourier representations and phase transforms. Digital Signal Processing, 106, 102830. https://doi.org/10.1016/j.dsp.2020.102830.
Mehla, V. K., Singhal, A., & Singh, P. (2020). A novel approach for automated alcoholism detection using Fourier decomposition method. Journal of Neuroscience Methods, 346, 108945. https://doi.org/10.1016/j.jneumeth.2020.108945.
Singh, P., Joshi, S.D., Patney, R.K., Saha, K. (2017). The Fourier decomposition method for nonlinear and non-stationary time series analysis. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. A, 473, 20160871. http://dx.doi.org/https://doi.org/10.1098/rspa.2016.0871
Staszewski, W. J., & Robertson, A. N. (2007). Time–frequency and time–scale analyses for structural health monitoring. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 365(1851), 449–477. https://doi.org/10.1098/rsta.2006.1936.
Gupta, V., Kanungo, A., Kumar, P., Sharma, A. K., & Gupta, A. (2018). Auto-regressive time frequency analysis (ARTFA) of electrocardiogram (ECG) signal. International Journal of Applied Engineering Research, 13(6), 133–8.
Singh, P., & Pachori, R. B. (2017). Classification of focal and nonfocal EEG signals using features derived from Fourier-based rhythms. Journal of Mechanics in Medicine and Biology, 17(7), 1–16. https://doi.org/10.1142/S0219519417400024.
Gupta, V., & Mittal, M. (2019). A Comparison of ECG signal pre-processing using FrFT, FrWT and IPCA for improved analysis. Innovation and Research in Biomedical Engineering (IRBM), 40(3), 145–156. https://doi.org/10.1016/j.irbm.2019.04.003.
Jachan, M., Matz, G., & Hlawatsch, F. (2007). Time-frequency ARMA models and parameter estimators for underspread nonstationary random processes. IEEE Transactions on Signal Process, 55(9), 4366–4381. https://doi.org/10.1109/TSP.2007.896265.
Xiaolin, L. (2005). Time-varying autoregressive modeling of nonstationary signals. Master's Thesis, Knoxville: University of Tennessee.
Marple, S. L. J. (1982). Frequency resolution of Fourier and maximum entropy spectral estimates. Geophysics, 47(9), 1303–1307. https://doi.org/10.1190/1.1441390.
Gupta, V., & Mittal, M. (2018). ECG Signals Interpretation using Chaos Theory. Journal of Advanced Research in Dynamical and Control Systems. 10(9), 2392–2397.
Paiva, J. S., Cardoso, J., & Pereira, T. (2018). Supervised learning methods for pathological arterial pulse wave differentiation: A SVM and neural networks approach. Int Jour of Med Infor., 109, 30–8. https://doi.org/10.1016/j.ijmedinf.2017.10.011.
Ataulla, Y. M., & Alsoufi, M. S. (2016). Wavelets in the analysis of autoregressive conditional heteroskedasticity (ARCH) models using neural network. American Journal of Applied Mathematics, 4(2), 92–8. https://doi.org/10.11648/j.ajam.20160402.14.
Goldberger, A., Amaral, L., Glass, L., & Hausdorff, J. M. (2000). Components of a new research resource for complex physiologic signals. PhysioBank, PhysioToolkit, and PhysioNet, 101(23), 215–20. https://doi.org/10.1161/01.cir.101.23.e215.
Guiñón, J.L. (2007). Moving average and Savitzki-Golay smoothing filters using mathcad. In: Proceedings of the Inter Conf on Eng Education – (ICEE), Sep. 3–7, 2007, Coimbra, Portugal. Available: icee2007.dei.uc.pt/proceedings/papers/39.pdf
Bromba, M. U. A., & Ziegler, H. (1981). Application hint for Savitsky-Golay digital smoothing filters. Analytical Chemistry, 53(11), 1583–6. https://doi.org/10.1021/ac00234a011.
Baleanu, D. (2012). Wavelet transforms and their recent applications in biology and geoscience. InTechOpen: Rijeka, Croatia. https://www.intechopen.com/books/ Wavelet Transforms and Their Recent Applications in Biology and Geoscience.
Bogunovic, N., Jovic, A. (2010). Processing and analyisis of biomedical nonlinear signals by data mining methods. In: Proceedings of the 17th Inter Conf on Syst, Sig and Image Process. https://www.researchgate.net/publication/228549925
Zhai, X., & Tin, C. (2018). Automated ECG classification using dual heartbeat coupling based on convolutional neural network. IEEE Access, 6, 27465–72. https://doi.org/10.1109/ACCESS.2018.2833841.
Chawla, M. P. S., Verma, H. K., & Kumar, V. (2008). A new statistical PCA-ICA algorithm for location of R-peaks in ECG. International Journal of Cardiology, 129(1), 146–8. https://doi.org/10.1016/j.ijcard.2007.06.036.
Chillemi, S., Barbi, M., Di Garbo, A., Balocchi, R., Michelassi, C., Carpeggiani, C., & Emdin, M. (1997). Detection of nonlinearity in the healthy heart rhythm. Methods of Information in Medicine, 36(4–5), 278–81. https://doi.org/10.1055/s-0038-1636860.
Katz, M. J. (1988). Fractals and the analysis of waveforms. Computers in Biology and Medicine, 18(3), 145–56. https://doi.org/10.1016/0010-4825(88)90041-8.
Pincus, S.M. (1991). Approximate entropy as a measure of system complexity. Proceedings of the National Academy of Sciences, 88(6), 2297–301.
Richman, J. S., & Moorman, R. J. (2000). Physiological time-series analysis using approximate entropy and sample entropy. American Journal of Physiology-Heart and Circulatory Physiology, 278(6), 2039–49. https://doi.org/10.1152/ajpheart.2000.278.6.H2039.
Bogaert, C., Beckers, F., Ramaekers, D., & Aubert, A. E. (2001). Analysis of heart rate variability with correlation dimension method in a normal population and in heart transplant patients. Autonomic Neuroscience: Basic and Clinical, 90(1–2), 142–7. https://doi.org/10.1016/S1566-0702(01)00280-6.
Kennel, M. B., Brown, R., & Abarbanel, H. D. I. (1992). Determining embedding dimension for phase-space reconstruction using a geometrical construction. Physical Review A, 45(6), 3403–3411. https://doi.org/10.1103/PhysRevA.45.3403.
Ghoraani, B. (1998). Time-frequency feature analysis. Doctor of Philosophy. . Sharif University of Technology Department of Electrical and Computer Engineering.
Sejdic, E., Djurovic, I., & Jiang, J. (2009). Time–frequency feature representation using energy concentration: An overview of recent advances. Digital Signal Processing, 19(1), 153–183. https://doi.org/10.1016/j.dsp.2007.12.004.
Yaroslavsky, L. (1999). Time-frequency domain signal filtering: A next step forward. In: Proceedings of the Second International Workshop on Transforms and Filter Banks. Available: Signal.ee.bilkent.edu.tr/Nsip99/papers/62.pdf
Xiao, X., Mullen, T. J., & Mukkamala, R. (2005). System identification: a multi-signal approach for probing neural cardiovascular regulation. Physiological Measurement., 26(3), 41–71. https://doi.org/10.1088/0967-3334/26/3/R01.
Gill, I. S., & Ukimura, O. (2009). Contemporary interventional ultrasonography in urology. . Springer.
Burg, J. P. (1968). A new analysis technique for time series data. . NATO Advanced Study Institute on Signal Processing.
Melton, R. B. (1983). Classification of NDE waveforms with autoregressive models. Review of Progress in Quantitative Nondestructive Evaluation, 2A, 1117–26. https://doi.org/10.1007/978-1-4613-3706-5_72.
Zhang, L., Xiong, G., Liu, H., Zou, H., & Guo, W. (2010). Time-frequency representation based on time-varying autoregressive model with applications to non-stationary rotor vibration analysis. Sadha, 35(2), 215–32. https://doi.org/10.1007/s12046-010-0016-y.
Akar, S. A., Kara, S., Latifoglu, F., & Biggic, V. (2013). Spectral analysis of photoplethysmographic signals: The importance of preprocessing. Biomedical Signal Processing and Control, 8(1), 16–22. https://doi.org/10.1016/j.bspc.2012.04.002.
Bianchi, A. M., Mainardi, L. T., & Cerutti, S. (2000). Time–frequency analysis of biomedical signals. Transactions of the Institute of Measurement and Control, 22(3), 215–230. https://doi.org/10.1177/014233120002200302.
Baselli, G., Cerutti, S., Civardi, S., Lombardi, F., Malliani, A., Merri, M., Pagani, M., & Rizzo, G. (1987). Heart rate variability signal processing: a quantitative approach as an aid to diagnosis in cardiovascular pathologies. International Journal of Bio-Medical Computing, 20(1–2), 51–70. https://doi.org/10.1016/0020-7101(87)90014-6.
Zetterberg, L. H. (1969). Estimation parameters for a linear difference equation with application to EEG analysis. Mathematical Bioscience, 5(3–4), 227–75. https://doi.org/10.1016/0025-5564(69)90044-3.
Akaike, H. (1970). Statistical predictor identification. Annals of the Institute of Statistical Mathematics., 22, 137–151. https://doi.org/10.1007/978-1-4612-1694-0_11.
Gupta, V., Mittal, M. (2018). Dimension reduction and classification in ECG signal interpretation using FA and PCA: A comparison. In: Proceedings of the Jangjeon Mathematical society, South Korea. 1542050872-pjms21–4–18.pdf (jangjeonopen.or.kr)
Gupta, V., Mittal, M. (2018). ECG signal analysis: Past, present and future. In Proceedings of the 8th IEEE Power India International Conference, NIT Kurukshetra. https://doi:https://doi.org/10.1109/POWERI.2018.8704365
Beniteza, D., Gaydeckia, P. A., Zaidib, A., & Fitzpatrick, A. P. (2001). The use of the Hilbert transform in ECG signal analysis. Computer in Biology and Medical, 31(5), 399–406. https://doi.org/10.1016/S0010-4825(01)00009-9.
Kaur, H., & Rajni, R. (2017). Electrocardiogram signal analysis for R-peak detection and denoising with hybrid linearization and principal component analysis. Turkish Journal of Electrical Engineering and Computer Sciences, 25, 2163–75. https://doi.org/10.3906/elk-1604-84.
Aletti, F., Bassani, T., Lucini, D., Pagani, M., & Baselli, G. (2009). Multivariate decomposition of arterial blood pressure variability for the assessment of arterial control of circulation. IEEE Transactions on Biomedical Engineering, 56(7), 1781–90. https://doi.org/10.1109/TBME.2009.2016845.
Orini, M. (2011). Time-frequency analysis for the dynamic quantification of the interactions between signals related to the cardiovascular system. Degree of Doctor in philosophy, Politecnico di Milano, Italy: Universidad de Zaragoza Instituto de Investigaci´ıon en Ingenier´ıa de Arag´on. https://doi:https://doi.org/10.1007/978-3-319-58709-7_9.
Kohler, B. U., Hennig, C., & Orglmeister, R. (2002). TheprinciplesofsoftwareQRS detection:Reviewingandcomparingalgorithmsfor detecting this important ECG waveform. IEEE Engineering in Medicine and Biology Magazine, 21(1), 42–57.
Pan, J., & Tompkins, W. L. (1985). Areal-timeQRS detection algorithm. IEEE Transactions on Biomedical Engineering, 32(3), 230–6.
Kaya, Y., Pehlivan, H., & Tenekeci, M. E. (2017). Effective ECG beat classification using higher order statistic features and genetic feature selection. Biomedical Research, 28(17), 7594–603.
Vuksanovic, B., & Alhamdi, M. (2013). AR-based method for ECG classification and patient recognition. International Journal of Biometrics and Bioinformatics, 7(2), 74–92.
LabVIEW. (2013). Advanced signal processing toolkit help: Introduction to time frequency analysis (advanced signal processing toolkit), https://forums.ni.com/t5/NI-Labs-Toolkits/LabVIEW-2013-64-bit-Advanced-Signal-Processing-Toolkit/ta-p/3500458 [accessed 27 May 2019].
Gupta, V., Mittal, M. (2016). Respiratory signal analysis using PCA, FFT and ARTFA. In: Proceedings of the 2016 International Conference on Electrical Power and Energy Systems (ICEPES), Bhopal India.
Acharya, R., Kumar, A., Bhat, P. S., Lim, C. M., Lyengar, S. S., Kannathal, N., & Krishnan, S. M. (2004). Classification of cardiac abnormalities using heart rate signals. Medical and Biological Engineering and Computing, 42(3), 288–293. https://doi.org/10.1007/BF02344702.
Ubeyli, E. D. (2007). ECG beats classification using multiclass support vector machines with error correcting output codes. Digital Signal Processing, 17, 675–84. https://doi.org/10.1016/j.dsp.2006.11.009.
Gupta, V., & Mittal, M. (2018). KNN and PCA classifier with autoregressive modelling during different ECG signal interpretation. Journal of Procedia Computer Science-Els, 125, 18–24. https://doi.org/10.1016/j.procs.2017.12.005.
Thakor, N. V., Webster, J. G., & Thompkins, W. J. (1984). Estimation of QRS complex power spectra for design of a QRS filter. IEEE Transactions on Biomedical Engineering, 31(11), 702–5. https://doi.org/10.1109/TBME.1984.325393.
Kaya, Y., & Pehlivan, H. (2015). Classification of premature ventricular contraction in ECG. International Journal of Advanced Computer Science and Applications, 6(7), 34–40. https://doi.org/10.14569/IJACSA.2015.060706.
Swapna, G., Acharya, U. R., VinithaSree, S., & Suri, J. S. (2013). Automated detection of diabetes using higher order spectral features extracted from heart rate signals. Intelligent Data Analysis, 17(2), 309–26. https://doi.org/10.3233/IDA-130580.
Kora, P., Annavarapu, A., Yadlapalli, P., Krishna, K. S. R., & Somalaraju, V. (2017). ECG based atrial fibrillation detection using sequency ordered complex hadamard transform and hybrid firefly algorithm. Journal of Engineering Science and Technology, 20(3), 1084–1091. https://doi.org/10.1016/j.jestch.2017.02.002.
Kora, P. (2017). ECG based myocardial infarction detection using hybrid firefly algorithm. Computer Methods and Programs in Biomedicine, 152, 141–9. https://doi.org/10.1016/j.cmpb.2017.09.015.
Acharya, U. R., Sudarshan, V. K., Koh, J. E. W., Tan, J. H., Oh, S. L., Muhammad, A., Hagiwara, Y., Mookiah, M. R. K., Chua, K. P., Chua, C. K., Martis, R. J., & Tan, R. S. (2017). Application of higher-order spectra for the characterization of coronary artery disease using electrocardiogram signals. Biomedical Signal Processing and Control, 31, 31–43. https://doi.org/10.1016/j.bspc.2016.07.003.
Nanjundegowda, R., & Meshram, V. (2018). Arrhythmia recognition and classification using kernel ICA and higher order spectra. International Journal of Engineering and Technology, 7(2), 256–62. https://doi.org/10.14419/ijet.v7i2.9535.
Tary, J. B., Herrera, R. H., & Vander, B. M. (2018). Analysis of time-varying signals using continuous wavelet and synchrosqueezed transforms. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. https://doi.org/10.1098/rsta.2017.0254.
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Gupta, V., Mittal, M. & Mittal, V. Chaos Theory and ARTFA: Emerging Tools for Interpreting ECG Signals to Diagnose Cardiac Arrhythmias. Wireless Pers Commun 118, 3615–3646 (2021). https://doi.org/10.1007/s11277-021-08411-5
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DOI: https://doi.org/10.1007/s11277-021-08411-5