# An Efficient Teager Energy Operator-Based Automated QRS Complex Detection

Authors: Hamed Beyramienanlou; Nasser Lotfivand
Journal: Journal of Healthcare Engineering
 (2018)

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## Abstract

Database. The efficiency and robustness of the proposed method has been tested on Fantasia Database (FTD), MIT-BIH Arrhythmia Database (MIT-AD), and MIT-BIH Normal Sinus Rhythm Database (MIT-NSD). Aim. Because of the importance of QRS complex in the diagnosis of cardiovascular diseases, improvement in accuracy of its measurement has been set as a target. The present study provides an algorithm for automatic detection of QRS complex on the ECG signal, with the benefit of energy and reduced impact of noise on the ECG signal. Method. The method is basically based on the Teager energy operator (TEO), which facilitates the detection of the baseline threshold and extracts QRS complex from the ECG signal. Results. The testing of the undertaken method on the Fanatasia Database showed the following results: sensitivity (Se) = 99.971%, positive prediction (P+) = 99.973%, detection error rate (DER) = 0.056%, and accuracy (Acc) = 99.944%. On MIT-AD involvement, Se = 99.74%, P+ = 99.97%, DER = 0.291%, and Acc = 99.71%. On MIT-NSD involvement, Se = 99.878%, P+ = 99.989%, DER = 0.134%, and Acc = 99.867%. Conclusion. Despite the closeness of the recorded peaks which inflicts a constraint in detection of the two consecutive QRS complexes, the proposed method, by applying 4 simple and quick steps, has effectively and reliably detected the QRS complexes which make it suitable for practical purposes and applications.


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## Body

## 1. Introduction

Cardiovascular disease is the primary global cause of death. According to the World Health Organization, about 17.3 million people died of cardiovascular disease in 2008, which represented 30 percent of all global deaths. This number is predicted to grow to more than 23.6 million by 2030 [1, 2]. Heart diseases like cardiovascular disease, sudden death, ischemic heart disease, and cardiac arrhythmias are all diagnosed by analyzing the heart’s signal [3–5]. The electrocardiogram is a noninvasive method of recording signals of heart muscle contractions over a period of time. Therefore, the accurate analysis of these signals will result in a more accurate diagnosis of cardiovascular diseases [6, 7]. An ECG signal is a combination of QRS complex, P and T peaks, and sometimes includes U peak. The detection of the QRS complex also helps to detect and determine P and T peaks, QT interval, ST interval, and the respiratory rate, which are considered as the human’s vital signs. Therefore, the accurate recognition of QRS complex has a significant role in the accurate diagnosis of heart disease [8].During the past decades, a variety of QRS complex detection methods have been developed [9] such as Pan–Tompkins method of R-wave detection [10], support vector machine [11], and the wavelet method, which is an analytical technique based on time-frequency chromatography. The wavelet transform is widely used in medical signal analysis such as EEG or ECG. However, this has a drawback because by applying a fixed scale, the signal characteristics are ignored [3, 12, 13]. Kalman filters use a dynamic model derived from a dynamic system to predict the hidden state in a nonlinear approach [14]. Artificial neural networks are an ideal self-correcting nonlinear process used in a wide range of tasks [15]. Shannon energy computes the average signal energy in a signal spectrum. In other words, it reduces the high intensity to balance out with the low intensity [16–18]. The Adaptive Double Threshold Filter (ADTF) and Discrete Wavelet Transform (DWT) are used to reduce the noise in the ECG signal to improve the ECG signal filtering [19]. Hermit transformation, which is used as an alternative to the Fourier transformation, may by optimization, shows an improved performance [20]. Teager Energy Operator (TEO) mainly shows the frequency and instantaneous changes of the signal amplitude that is very sensitive to subtle changes. Although TEO was first proposed for modeling nonlinear speech signals, it was later widely applied in the audio signal processing. Using TEO can minimize the effects of P and T waves on QRS complex detection [21]. Remarkable research efforts have been developed to analyze the sensitive point of the ECG signal based on TEO [22, 23].The aim of this study is to propose a new approach based on an innovative viewpoint using TEO to detect QRS complex in the ECG signal. The recorded ECG signal may be affected by noise interference, such as power line interference, which must be eradicated for more accuracy. The Section2 of the study consists of a series of preprocessing measures to minimize the noises before QRS complex detection on the ECG signal. This includes low-pass filter which removes noises such as power line interference. Since P or T peaks may interfere with the TEO computation, the moving average technique is used to smoothen and envelope the spikes in the signal. Sensitivity, positive prediction, and accuracy of the proposed algorithm from Fantasia Database, MIT-AD, and MIT-NSD are evaluated in the Section 3 of this article. Finally, in Sections 4 and 5 of the study, a discussion and conclusions are presented.


## 2. Methodology

The details of the proposed method are illustrated in Figure1. The QRS complex detection procedure involves four steps.(i)
Most of the time, the recorded ECG signal is afflicted by noises [24]. The noise frequencies generated by the power lines’ interferences are in the range of 50 to 60 Hz. The noises generated by the muscle contractions and the electrodes placed on the body skin are in the range of 38 to 48 Hz. These greatly impede on the ECG signals. However, a notch filter is very effective in removing these noises. The maximum density of the QRS complex is between 5 to 20 Hz [17, 25]. Therefore, the IIR Butterworth digital filter is the best compromise for phase response and signal attenuation. It has no ripple in the band-pass and is more efficient than the FIR filter [26, 27]. To reduce the noises from the electrical (device) components in order to make a peak clearer for detection, a Butterworth low-pass digital filter, with order 4 and cut-off frequency of 15 Hz, was used.(ii)
TEO has various applications, especially in AM and FM signal processing such as speech signals. TEO can be driven from a second-order differential equation [28]. The total energy of oscillation (i.e., the sum of kinetic and potential energies) can be obtained from the following equation:(1)E=12kx2+12mx2,wherem is the mass of the oscillating body and k is the spring constant.Using the formula in (1), a periodic harmonic formula can be obtained:(2)xt=AcosΩt+ϕ,whereϕ is the phase shift, Ω is the oscillation frequency, A is the oscillation amplitude, and xt denotes the position of the oscillating body with respect to time. Using (1) and (2), the essential harmonic energy to generate signals can be calculated:(3)E=12mA2αA2Ω2.The following is a simplified form of TEO:(4)Ψcxt=ddtxt2−xtd2dt2xt,Ψcxt=x′t2−xtx″t.SubstitutingnT for t we will get the following equation:(5)Ψdxn=x2n−xn−1xn+1,whereΨcxt is the energy operator for continuous time t, xt is the tth signal component, x′t and x″t are the first and second derivatives of xt, respectively, T is the sample period, and n is the sample size [28, 29].The dynamicity of the heart beats creates an intermittent and nonlinear pattern for TEO. Since TEO itself is a nonlinear operator, it nonlinearly captivates the intermittent characteristics.(iii)
After computing TEO, in some signals, spikes of energies are observable and are attributed to P and T peaks in QRS complex. Although not wide in range, they hamper the accurate detection of the QRS complex. To resolve the situation, these spikes should be converted into energy envelopes. There are several methods for this such as Hilbert transform [6] or averaging method [30]. In the present study, moving average the following equation is used:(6)MA=filterh,j,TEO.Hereh defines a rectangle with L length, j is a constant and is equal to 1, and TEO defines Teager energy from previous steps. To increase the small amplitude, square root is used:(7)S=sqrtMA.HereMA is the moving average obtained from the previous step.To decrease the baseline signal’s value below zero, the following formula is used [16]:(8)BD=xn−μσ,where σ is the standard deviation and μ is defined as signal average.(iv)
The process of peak detection includes the following step:(9)signaln,baseline<signaln,notselect,signaln<baseline,n=2,3,4,…,where baseline (0) is the threshold level for peak detection and R peaks are found in an ECG signal by searching the maximum peak within ±50 samples (length of window = min (RR interval)) of the recognized location of the candidate R peak in the previous step (Equation (9)).Figure 1
The diagram block shows 4 steps of QRS complex detection.


## 3. Results

Under the supervision of the National Research Center, the PhysioBank database was developed by the National Institute of Health in order to do a clinical diagnosis and conduct research on complex cardiovascular physiologic signals [31]. The proposed method was tested on three different ECG databases [32] including Fantasia Database (FTD), MIT-BIH Arrhythmia Database (MIT-AD), and MIT-BIH Normal Sinus Rhythm Database (MIT-NSD).The suggested peak detection method based on TEO has been implemented with MATLAB R2016a on a minimum laptop with a 4 GB of memory and Intel core i3-4000M 2.4 GHz CPU on Windows 10. This algorithm takes less than 0.026 second.The following formulae were used to determine the performance, sensitivity, error rate detection, positive prediction, and the accuracy of the proposed method:(10)SensitivitySe=TPTP+FN×100%,DetectionerrorrateDER=FP+FNTP×100%,Positivepredictivityrate+P=TPTP+FP×100%,AccuracyAcc=TPTP+FP+FN×100%.TP is the number of R peaks, FN is the number of missed R peaks, and FP is the false positive prediction of R peak due to the existing noise with dispositioned true R peak.


### 3.1. MIT-BIH Arrhythmia Database

MIT-AD contains slightly over 30 minutes of recordings in 48 records. The sampling frequency was set to 360 Hz with 11-bit ADC resolution. The subjects who were chosen for this study were 22 women aged 23 to 89 years and 25 men aged 32 to 89 years [31, 33]. Table 1 depicts the details of detected QRS complex in channel 1. The results showed that sensitivity was at 99.74% with a 0.391% (detection) error and 99.97% positive prediction with an accuracy of 99.71%. Table 2 compares the proposed algorithm in this study with those of other studies. All the stages and the process of QRS detections are illustrated in Figures 2–4. The MIT-AD is available on [36].Table 1
Results of QRS detection in MIT-BIH Arrhythmia Database (MIT-AD).
Case
TP + FN
TP
FN
FP
DER%
Se%
P+
Acc%
Time (s)
100
2273
2272
1
0
0.044
99.956
100.000
99.956
0.842011
101
1865
1866
0
1
0.054
100.000
99.946
99.946
0.831718
102
2187
2187
0
0
—
100.000
100.000
100.000
0.800651
103
2084
2083
1
0
0.048
99.952
100.000
99.952
0.832546
104
2229
2232
0
3
0.134
100.000
99.866
99.866
0.819847
105
2572
2584
12
4
0.619
99.538
99.845
99.385
0.821659
106
2027
2023
4
0
0.198
99.803
100.000
99.803
0.826349
107
2137
2134
3
0
0.141
99.860
100.000
99.860
0.831685
108
1763
1758
5
0
0.284
99.716
100.000
99.716
0.828862
109
2532
2527
5
0
0.198
99.803
100.000
99.803
0.839979
111
2124
2123
0
0
—
100.000
100.000
100.000
0.808473
112
2539
2539
0
0
—
100.000
100.000
100.000
0.822048
113
1795
1794
1
0
0.056
99.944
100.000
99.944
0.818563
114
1879
1856
23
0
1.239
98.776
100.000
98.776
0.80345
115
1953
1953
0
0
—
100.000
100.000
100.000
0.818539
116
2412
2389
23
0
0.963
99.046
100.000
99.046
1.321399
117
1535
1535
0
0
—
100.000
100.000
100.000
0.795675
118
2278
2279
0
1
0.044
100.000
99.956
99.956
0.082806
119
1987
1988
0
0
—
100.000
100.000
100.000
0.827755
121
1863
1862
1
0
0.054
99.946
100.000
99.946
0.804042
122
2476
2476
0
0
—
100.000
100.000
100.000
0.833951
123
1518
1517
0
0
—
100.000
100.000
100.000
0.816707
124
1619
1617
2
0
0.124
99.876
100.000
99.876
0.832643
200
2601
2601
0
0
—
100.000
100.000
100.000
0.79576
201
1963
1952
11
0
0.564
99.440
100.000
99.440
0.805514
202
2136
2116
19
0
0.898
99.110
100.000
99.110
0.810542
203
2980
2911
69
0
2.370
97.685
100.000
97.685
0.805071
205
2656
2653
3
0
0.113
99.887
100.000
99.887
0.818077
207
1860
1863
1
3
0.215
99.946
99.839
99.786
0.809665
208
2955
2935
20
0
0.681
99.323
100.000
99.323
0.814803
209
3005
3008
0
3
0.100
100.000
99.900
99.900
0.789794
210
2650
2628
22
2
0.913
99.170
99.924
99.095
0.813432
212
2748
2748
0
0
—
100.000
100.000
100.000
0.797922
213
3251
3243
8
0
0.247
99.754
100.000
99.754
0.826331
214
2262
2256
6
0
0.266
99.735
100.000
99.735
1.04979
215
3363
3358
5
0
0.149
99.851
100.000
99.851
0.796735
217
2208
2205
3
0
0.136
99.864
100.000
99.864
0.816972
219
2154
2154
0
0
—
100.000
100.000
100.000
1.032321
220
2048
2047
1
0
0.049
99.951
100.000
99.951
0.806677
221
2427
2423
4
0
0.165
99.835
100.000
99.835
0.817536
222
2483
2475
8
0
0.323
99.678
100.000
99.678
0.837608
223
2605
2594
11
0
0.424
99.578
100.000
99.578
0.79572
228
2053
2065
1
12
0.630
99.952
99.422
99.374
0.808852
230
2256
2256
0
0
—
100.000
100.000
100.000
0.806291
231
1571
1571
0
0
—
100.000
100.000
100.000
0.815568
232
1780
1786
0
4
0.224
100.000
99.777
99.777
0.802255
233
3079
3070
9
0
0.293
99.708
100.000
99.708
0.795327
234
2753
2750
3
0
0.109
99.891
100.000
99.891
0.80702
Total
109494
109262
285
33
0.291
99.740
99.970
99.710
0.81952Table 2
Comparison of performance of our proposed method with other methods using MIT-BIH Arrhythmia Database (MIT-AD).
Ref.
Method
DER
Se
P+
Acc%
[10]
Low-pass filtering, high-pass filtering derivative filtering
0.675
99.762
99.565
99.329
[34]
Multiscale mathematical morphology
0.0039
99.81
99.80
99.621
[35]
Shannon energy envelope, Hilbert transform
0.205
99.93
99.86
99.79
[8]
Median filter, Savitzky–Golay, Kurtosis
0.93
99.50
99.56
99.08
[17]
Shannon energy
0.164
99.95
99.88
99.84
[18]
Wavelet transform, Shannon energy envelope
0.163
99.93
99.91
99.838
Proposed method
Teager energy operator
0.291
99.74
99.97
99.71Figure 2
Recognition of R peaks in 108 records. TheY-axis represents amplitude, and X-axis represents the samples.
(a)
(b)
(c)
(d)Figure 3
(a) Low-pass filter, (b) Teager energy operator, (c) moving average, and (d) recognition of R peaks in 232 record. TheY-axis represents amplitude, and X-axis represents the samples.
(a)
(b)
(c)
(d)Figure 4
Examples of the detected QRS Complex from various cases. (a) 104, (b) 203, (c) 228, and (d) 116. TheY-axis represents amplitude, and X-axis represents the samples.
(a)
(b)
(c)
(d)In Figures2 and 3, (a) reveals wandering signals. (b) shows that after calculating Teager energy, the amplitudes of the signals are very low and close to zero. Therefore, small values with low energy are reduced to zero, and the wandering signals (drift) are canceled.


### 3.2. Fantasia Database

Fantasia Database (FTD) contains 40 cases in both groups: the young group aged 21 to 34 years (f1y01 … f2y10 and f2y01 … f2y10) and the elderly group aged 68 to 85 years (f2o01 … f2o10 and f2y01 … f2y10), with an average of 5 men and 5 women in each group. The members of each group underwent 120 minutes of continuous supine resting with complete care. The sampling frequency was set at 250 Hz, with a 16- and 12-bit resolutions for ADC. The records included 2 or 3 channels, such as respiration, ECG signal, and blood pressure [31, 37]. Fantasia Database is available on [38].The QRS complex detection details for the channel 2 in Fantasia Database are presented in Table3. Here too, the results showed 99.971% sensitivity with 0.056% detection error, and 99.973% positive prediction with an accuracy of 99.944%. Table 4 shows the comparison of the proposed method with the other studies. Figures 5 and 6 illustrate another example of detection: QRS Complex in the Fantasia Database with both elderly and young subjects. As shown in this figure, the proposed method can remove drift noise and detect correct location beat.Table 3
Results of QRS detection in Fantasia Database (FTD).
Case
TP
FN
FP
DER%
Se%
P+
Acc%
Time (s)
f1o01m
3988
0
0
—
100.000
100.000
100.000
1.051548
f1o02m
3813
0
0
—
100.000
100.000
100.000
1.040927
f1o03m
4046
0
0
—
100.000
100.000
100.000
1.055944
f1o04m
3433
0
3
0.087
100.000
99.913
99.913
1.02246
f1o05m
3720
2
4
0.161
99.946
99.893
99.839
0.997257
f1o06m
3408
0
0
—
100.000
100.000
100.000
1.020774
f1o07m
4025
0
0
—
100.000
100.000
100.000
1.031825
f1o08m
4739
0
3
0.063
100.000
99.937
99.937
1.012155
f1o09m
2796
0
2
0.072
100.000
99.929
99.929
1.016363
f1o10m
4602
0
0
—
100.000
100.000
100.000
1.030248
f1y01m
4917
0
0
—
100.000
100.000
100.000
1.026809
f1y02m
3967
0
0
—
100.000
100.000
100.000
1.029854
f1y03m
4289
0
0
—
100.000
100.000
100.000
1.006034
f1y04m
2998
0
0
—
100.000
100.000
100.000
1.005517
f1y05m
3942
0
4
0.101
100.000
99.899
99.899
1.015047
f1y06m
3906
1
5
0.154
99.974
99.872
99.847
1.004932
f1y07m
3381
0
1
0.030
100.000
99.970
99.970
1.009606
f1y08m
4098
0
0
—
100.000
100.000
100.000
1.043768
f1y09m
4509
0
2
0.044
100.000
99.956
99.956
1.029059
f1y10m
4912
1
0
0.020
99.980
100.000
99.980
1.046556
f2o01m
4216
0
0
—
100.000
100.000
100.000
1.026018
f2o02m
3594
5
0
0.139
99.861
100.000
99.861
1
f2o03m
3765
1
0
0.027
99.973
100.000
99.973
1.063687
f2o04m
3857
0
0
—
100.000
100.000
100.000
1.006415
f2o05m
4926
7
4
0.223
99.858
99.919
99.777
1.014471
f2o06m
2987
0
1
0.033
100.000
99.967
99.967
1.024759
f2o07m
3373
0
0
—
100.000
100.000
100.000
1.066044
f2o08m
4151
0
0
—
100.000
100.000
100.000
1.520268
f2o09m
3335
1
1
0.060
99.970
99.970
99.940
1.037157
f2o10m
4996
2
1
0.060
99.960
99.980
99.940
1
f2y01m
4586
0
0
—
100.000
100.000
100.000
1.016468
f2y02m
2807
0
0
—
100.000
100.000
100.000
1.018488
f2y03m
3882
1
0
0.026
99.974
100.000
99.974
1.023054
f2y04m
4943
0
7
0.142
100.000
99.859
99.859
1.038463
f2y05m
5169
2
0
0.039
99.961
100.000
99.961
1
f2y06m
4017
0
0
—
100.000
100.000
100.000
1.017889
f2y07m
3717
0
0
—
100.000
100.000
100.000
1.031076
f2y08m
4014
4
3
0.174
99.900
99.925
99.826
1
f2y09m
4870
11
2
0.267
99.775
99.959
99.734
1
f2y010m
4032
8
1
0.223
99.802
99.975
99.777
1
Total
160726
46
44
0.056
99.971
99.973
99.944
0.86252Table 4
Comparison of the proposed method with other methods using Fantasia Database (FTD).
DER%
SE%
+P%
Acc%
Sharma and Sunkaria [8]
0.19
99.90
99.91
99.81
Proposed method
0.056
99.971
99.973
99.944Figure 5
The phases of QRS complex detection in f1o09 case. (a) Low-pass filter phase; (b) the Teager energy from the Equation (5); (c) the moving average; (d) the final detection of QRS complex on ECG signal. The Y-axis represents amplitude, and X-axis represents the samples.
(a)
(b)
(c)
(d)Figure 6
Signal processing steps of the proposed R-peak detector using the case f1y06m. (a) The recognition phases by applying a low-pass filtering, (b) the Teager energy, (c) decreased baseline after moving average and sqrt, and (d) the detection phases. TheY-axis represents amplitude, and X-axis represents the samples.
(a)
(b)
(c)
(d)


### 3.3. MIT-BIH Normal Sinus Rhythm Database

MIT-NSD contains 18 long-term two-channel ECG recordings. This database includes 5 men, aged 26 to 45 and 13 women, aged 20 to 50. Frequency sampling equals to 128 Hz with 12-bit ADC resolution [31]. The details of QRS complex detection of channel 1 of MIT-NSD is presented in Table 5. The obtained values showed that sensitivity was equal to 99.878%, with an error equal to 0.134, positive prediction was equal to 99.989%, and accuracy was equal to 99.867%. Table 6 includes a comparison of the proposed algorithm with the other studies. Figure 7 illustrates the QRS detection in record with Gaussian white noise. As shown in the figure, the proposed method removed Gaussian white noise, but T peak was detected as a beat. MIT-NSD Database is available on [39].Table 5
Results of QRS detection in MIT-BIH Normal Sinus Rhythm Database (MIT-NSD).
Case
TP
FN
FP
DER%
Se%
+P%
Acc%
Time (s)
16265
11497
1
0
0.009
99.991
100.000
99.991
1.035
16272
7992
2
7
0.113
99.975
99.912
99.888
1.3
16273
10431
2
0
0.019
99.981
100.000
99.981
1.01
16420
10687
20
2
0.206
99.813
99.981
99.795
1.3
16483
12157
5
0
0.041
99.959
100.000
99.959
1.02
16539
9130
7
8
0.164
99.923
99.912
99.836
1.04
16773
9679
1
0
0.010
99.990
100.000
99.990
1.04
16786
9510
2
0
0.021
99.979
100.000
99.979
1.029
16795
10386
0
0
—
100.000
100.000
100.000
1.31
17052
8851
4
0
0.045
99.955
100.000
99.955
1.049
17453
11258
0
1
0.009
100.000
99.991
99.991
1
18177
11907
5
0
0.042
99.958
100.000
99.958
1.32
18184
10888
13
1
0.129
99.881
99.991
99.872
1.023
19088
12360
3
0
0.024
99.976
100.000
99.976
1.04
19090
10481
65
1
0.630
99.384
99.990
99.374
1.33
19093
9111
0
0
—
100.000
100.000
100.000
1.028
19140
11316
39
0
0.345
99.657
100.000
99.657
1.03
19830
14811
66
2
0.459
99.556
99.986
99.543
1.047
Total
192452
235
22
0.134
99.878
99.989
99.867
1.108389Table 6
Comparison of the proposed method with other methods using MIT-BIH Normal Sinus Rhythm Database (MIT-NSD).
Method
DER%
SE%
+P%
Acc%
Sharma and Sunkaria [8]
1.21
99.36
99.43
98.81
Proposed method
0.134
99.878
99.989
99.867Figure 7
Signal processing steps of the proposed R-peak detector using case 16272 with Gaussian white noise. (a) Low-pass filter; (b) the Teager energy; (c) moving average for eliminated spikes and BD stage; (d) detection of R peak. FP is false-positive prediction when the noise is detected. TheY-axis represents amplitude, and X-axis represents the samples.


## 3.1. MIT-BIH Arrhythmia Database

MIT-AD contains slightly over 30 minutes of recordings in 48 records. The sampling frequency was set to 360 Hz with 11-bit ADC resolution. The subjects who were chosen for this study were 22 women aged 23 to 89 years and 25 men aged 32 to 89 years [31, 33]. Table 1 depicts the details of detected QRS complex in channel 1. The results showed that sensitivity was at 99.74% with a 0.391% (detection) error and 99.97% positive prediction with an accuracy of 99.71%. Table 2 compares the proposed algorithm in this study with those of other studies. All the stages and the process of QRS detections are illustrated in Figures 2–4. The MIT-AD is available on [36].Table 1
Results of QRS detection in MIT-BIH Arrhythmia Database (MIT-AD).
Case
TP + FN
TP
FN
FP
DER%
Se%
P+
Acc%
Time (s)
100
2273
2272
1
0
0.044
99.956
100.000
99.956
0.842011
101
1865
1866
0
1
0.054
100.000
99.946
99.946
0.831718
102
2187
2187
0
0
—
100.000
100.000
100.000
0.800651
103
2084
2083
1
0
0.048
99.952
100.000
99.952
0.832546
104
2229
2232
0
3
0.134
100.000
99.866
99.866
0.819847
105
2572
2584
12
4
0.619
99.538
99.845
99.385
0.821659
106
2027
2023
4
0
0.198
99.803
100.000
99.803
0.826349
107
2137
2134
3
0
0.141
99.860
100.000
99.860
0.831685
108
1763
1758
5
0
0.284
99.716
100.000
99.716
0.828862
109
2532
2527
5
0
0.198
99.803
100.000
99.803
0.839979
111
2124
2123
0
0
—
100.000
100.000
100.000
0.808473
112
2539
2539
0
0
—
100.000
100.000
100.000
0.822048
113
1795
1794
1
0
0.056
99.944
100.000
99.944
0.818563
114
1879
1856
23
0
1.239
98.776
100.000
98.776
0.80345
115
1953
1953
0
0
—
100.000
100.000
100.000
0.818539
116
2412
2389
23
0
0.963
99.046
100.000
99.046
1.321399
117
1535
1535
0
0
—
100.000
100.000
100.000
0.795675
118
2278
2279
0
1
0.044
100.000
99.956
99.956
0.082806
119
1987
1988
0
0
—
100.000
100.000
100.000
0.827755
121
1863
1862
1
0
0.054
99.946
100.000
99.946
0.804042
122
2476
2476
0
0
—
100.000
100.000
100.000
0.833951
123
1518
1517
0
0
—
100.000
100.000
100.000
0.816707
124
1619
1617
2
0
0.124
99.876
100.000
99.876
0.832643
200
2601
2601
0
0
—
100.000
100.000
100.000
0.79576
201
1963
1952
11
0
0.564
99.440
100.000
99.440
0.805514
202
2136
2116
19
0
0.898
99.110
100.000
99.110
0.810542
203
2980
2911
69
0
2.370
97.685
100.000
97.685
0.805071
205
2656
2653
3
0
0.113
99.887
100.000
99.887
0.818077
207
1860
1863
1
3
0.215
99.946
99.839
99.786
0.809665
208
2955
2935
20
0
0.681
99.323
100.000
99.323
0.814803
209
3005
3008
0
3
0.100
100.000
99.900
99.900
0.789794
210
2650
2628
22
2
0.913
99.170
99.924
99.095
0.813432
212
2748
2748
0
0
—
100.000
100.000
100.000
0.797922
213
3251
3243
8
0
0.247
99.754
100.000
99.754
0.826331
214
2262
2256
6
0
0.266
99.735
100.000
99.735
1.04979
215
3363
3358
5
0
0.149
99.851
100.000
99.851
0.796735
217
2208
2205
3
0
0.136
99.864
100.000
99.864
0.816972
219
2154
2154
0
0
—
100.000
100.000
100.000
1.032321
220
2048
2047
1
0
0.049
99.951
100.000
99.951
0.806677
221
2427
2423
4
0
0.165
99.835
100.000
99.835
0.817536
222
2483
2475
8
0
0.323
99.678
100.000
99.678
0.837608
223
2605
2594
11
0
0.424
99.578
100.000
99.578
0.79572
228
2053
2065
1
12
0.630
99.952
99.422
99.374
0.808852
230
2256
2256
0
0
—
100.000
100.000
100.000
0.806291
231
1571
1571
0
0
—
100.000
100.000
100.000
0.815568
232
1780
1786
0
4
0.224
100.000
99.777
99.777
0.802255
233
3079
3070
9
0
0.293
99.708
100.000
99.708
0.795327
234
2753
2750
3
0
0.109
99.891
100.000
99.891
0.80702
Total
109494
109262
285
33
0.291
99.740
99.970
99.710
0.81952Table 2
Comparison of performance of our proposed method with other methods using MIT-BIH Arrhythmia Database (MIT-AD).
Ref.
Method
DER
Se
P+
Acc%
[10]
Low-pass filtering, high-pass filtering derivative filtering
0.675
99.762
99.565
99.329
[34]
Multiscale mathematical morphology
0.0039
99.81
99.80
99.621
[35]
Shannon energy envelope, Hilbert transform
0.205
99.93
99.86
99.79
[8]
Median filter, Savitzky–Golay, Kurtosis
0.93
99.50
99.56
99.08
[17]
Shannon energy
0.164
99.95
99.88
99.84
[18]
Wavelet transform, Shannon energy envelope
0.163
99.93
99.91
99.838
Proposed method
Teager energy operator
0.291
99.74
99.97
99.71Figure 2
Recognition of R peaks in 108 records. TheY-axis represents amplitude, and X-axis represents the samples.
(a)
(b)
(c)
(d)Figure 3
(a) Low-pass filter, (b) Teager energy operator, (c) moving average, and (d) recognition of R peaks in 232 record. TheY-axis represents amplitude, and X-axis represents the samples.
(a)
(b)
(c)
(d)Figure 4
Examples of the detected QRS Complex from various cases. (a) 104, (b) 203, (c) 228, and (d) 116. TheY-axis represents amplitude, and X-axis represents the samples.
(a)
(b)
(c)
(d)In Figures2 and 3, (a) reveals wandering signals. (b) shows that after calculating Teager energy, the amplitudes of the signals are very low and close to zero. Therefore, small values with low energy are reduced to zero, and the wandering signals (drift) are canceled.


## 3.2. Fantasia Database

Fantasia Database (FTD) contains 40 cases in both groups: the young group aged 21 to 34 years (f1y01 … f2y10 and f2y01 … f2y10) and the elderly group aged 68 to 85 years (f2o01 … f2o10 and f2y01 … f2y10), with an average of 5 men and 5 women in each group. The members of each group underwent 120 minutes of continuous supine resting with complete care. The sampling frequency was set at 250 Hz, with a 16- and 12-bit resolutions for ADC. The records included 2 or 3 channels, such as respiration, ECG signal, and blood pressure [31, 37]. Fantasia Database is available on [38].The QRS complex detection details for the channel 2 in Fantasia Database are presented in Table3. Here too, the results showed 99.971% sensitivity with 0.056% detection error, and 99.973% positive prediction with an accuracy of 99.944%. Table 4 shows the comparison of the proposed method with the other studies. Figures 5 and 6 illustrate another example of detection: QRS Complex in the Fantasia Database with both elderly and young subjects. As shown in this figure, the proposed method can remove drift noise and detect correct location beat.Table 3
Results of QRS detection in Fantasia Database (FTD).
Case
TP
FN
FP
DER%
Se%
P+
Acc%
Time (s)
f1o01m
3988
0
0
—
100.000
100.000
100.000
1.051548
f1o02m
3813
0
0
—
100.000
100.000
100.000
1.040927
f1o03m
4046
0
0
—
100.000
100.000
100.000
1.055944
f1o04m
3433
0
3
0.087
100.000
99.913
99.913
1.02246
f1o05m
3720
2
4
0.161
99.946
99.893
99.839
0.997257
f1o06m
3408
0
0
—
100.000
100.000
100.000
1.020774
f1o07m
4025
0
0
—
100.000
100.000
100.000
1.031825
f1o08m
4739
0
3
0.063
100.000
99.937
99.937
1.012155
f1o09m
2796
0
2
0.072
100.000
99.929
99.929
1.016363
f1o10m
4602
0
0
—
100.000
100.000
100.000
1.030248
f1y01m
4917
0
0
—
100.000
100.000
100.000
1.026809
f1y02m
3967
0
0
—
100.000
100.000
100.000
1.029854
f1y03m
4289
0
0
—
100.000
100.000
100.000
1.006034
f1y04m
2998
0
0
—
100.000
100.000
100.000
1.005517
f1y05m
3942
0
4
0.101
100.000
99.899
99.899
1.015047
f1y06m
3906
1
5
0.154
99.974
99.872
99.847
1.004932
f1y07m
3381
0
1
0.030
100.000
99.970
99.970
1.009606
f1y08m
4098
0
0
—
100.000
100.000
100.000
1.043768
f1y09m
4509
0
2
0.044
100.000
99.956
99.956
1.029059
f1y10m
4912
1
0
0.020
99.980
100.000
99.980
1.046556
f2o01m
4216
0
0
—
100.000
100.000
100.000
1.026018
f2o02m
3594
5
0
0.139
99.861
100.000
99.861
1
f2o03m
3765
1
0
0.027
99.973
100.000
99.973
1.063687
f2o04m
3857
0
0
—
100.000
100.000
100.000
1.006415
f2o05m
4926
7
4
0.223
99.858
99.919
99.777
1.014471
f2o06m
2987
0
1
0.033
100.000
99.967
99.967
1.024759
f2o07m
3373
0
0
—
100.000
100.000
100.000
1.066044
f2o08m
4151
0
0
—
100.000
100.000
100.000
1.520268
f2o09m
3335
1
1
0.060
99.970
99.970
99.940
1.037157
f2o10m
4996
2
1
0.060
99.960
99.980
99.940
1
f2y01m
4586
0
0
—
100.000
100.000
100.000
1.016468
f2y02m
2807
0
0
—
100.000
100.000
100.000
1.018488
f2y03m
3882
1
0
0.026
99.974
100.000
99.974
1.023054
f2y04m
4943
0
7
0.142
100.000
99.859
99.859
1.038463
f2y05m
5169
2
0
0.039
99.961
100.000
99.961
1
f2y06m
4017
0
0
—
100.000
100.000
100.000
1.017889
f2y07m
3717
0
0
—
100.000
100.000
100.000
1.031076
f2y08m
4014
4
3
0.174
99.900
99.925
99.826
1
f2y09m
4870
11
2
0.267
99.775
99.959
99.734
1
f2y010m
4032
8
1
0.223
99.802
99.975
99.777
1
Total
160726
46
44
0.056
99.971
99.973
99.944
0.86252Table 4
Comparison of the proposed method with other methods using Fantasia Database (FTD).
DER%
SE%
+P%
Acc%
Sharma and Sunkaria [8]
0.19
99.90
99.91
99.81
Proposed method
0.056
99.971
99.973
99.944Figure 5
The phases of QRS complex detection in f1o09 case. (a) Low-pass filter phase; (b) the Teager energy from the Equation (5); (c) the moving average; (d) the final detection of QRS complex on ECG signal. The Y-axis represents amplitude, and X-axis represents the samples.
(a)
(b)
(c)
(d)Figure 6
Signal processing steps of the proposed R-peak detector using the case f1y06m. (a) The recognition phases by applying a low-pass filtering, (b) the Teager energy, (c) decreased baseline after moving average and sqrt, and (d) the detection phases. TheY-axis represents amplitude, and X-axis represents the samples.
(a)
(b)
(c)
(d)


## 3.3. MIT-BIH Normal Sinus Rhythm Database

MIT-NSD contains 18 long-term two-channel ECG recordings. This database includes 5 men, aged 26 to 45 and 13 women, aged 20 to 50. Frequency sampling equals to 128 Hz with 12-bit ADC resolution [31]. The details of QRS complex detection of channel 1 of MIT-NSD is presented in Table 5. The obtained values showed that sensitivity was equal to 99.878%, with an error equal to 0.134, positive prediction was equal to 99.989%, and accuracy was equal to 99.867%. Table 6 includes a comparison of the proposed algorithm with the other studies. Figure 7 illustrates the QRS detection in record with Gaussian white noise. As shown in the figure, the proposed method removed Gaussian white noise, but T peak was detected as a beat. MIT-NSD Database is available on [39].Table 5
Results of QRS detection in MIT-BIH Normal Sinus Rhythm Database (MIT-NSD).
Case
TP
FN
FP
DER%
Se%
+P%
Acc%
Time (s)
16265
11497
1
0
0.009
99.991
100.000
99.991
1.035
16272
7992
2
7
0.113
99.975
99.912
99.888
1.3
16273
10431
2
0
0.019
99.981
100.000
99.981
1.01
16420
10687
20
2
0.206
99.813
99.981
99.795
1.3
16483
12157
5
0
0.041
99.959
100.000
99.959
1.02
16539
9130
7
8
0.164
99.923
99.912
99.836
1.04
16773
9679
1
0
0.010
99.990
100.000
99.990
1.04
16786
9510
2
0
0.021
99.979
100.000
99.979
1.029
16795
10386
0
0
—
100.000
100.000
100.000
1.31
17052
8851
4
0
0.045
99.955
100.000
99.955
1.049
17453
11258
0
1
0.009
100.000
99.991
99.991
1
18177
11907
5
0
0.042
99.958
100.000
99.958
1.32
18184
10888
13
1
0.129
99.881
99.991
99.872
1.023
19088
12360
3
0
0.024
99.976
100.000
99.976
1.04
19090
10481
65
1
0.630
99.384
99.990
99.374
1.33
19093
9111
0
0
—
100.000
100.000
100.000
1.028
19140
11316
39
0
0.345
99.657
100.000
99.657
1.03
19830
14811
66
2
0.459
99.556
99.986
99.543
1.047
Total
192452
235
22
0.134
99.878
99.989
99.867
1.108389Table 6
Comparison of the proposed method with other methods using MIT-BIH Normal Sinus Rhythm Database (MIT-NSD).
Method
DER%
SE%
+P%
Acc%
Sharma and Sunkaria [8]
1.21
99.36
99.43
98.81
Proposed method
0.134
99.878
99.989
99.867Figure 7
Signal processing steps of the proposed R-peak detector using case 16272 with Gaussian white noise. (a) Low-pass filter; (b) the Teager energy; (c) moving average for eliminated spikes and BD stage; (d) detection of R peak. FP is false-positive prediction when the noise is detected. TheY-axis represents amplitude, and X-axis represents the samples.


## 4. Discussion

The aim of the present research is to use a novel algorithm based on the Teager energy operator in ECG signal to detect QRS complex. The main findings of the study indicated the high reliability and accuracy of this method in QRS complex detection. In spite of applying zero-phase digital filter to maintain QRS complex location, the zero-phase filter is anticausal, and the results showed that the present method had faced a little lag which was less than 0.026 second. Only a detection shift of less than 0.05 second is acceptable [40].In testing the present method on MIT-AD, some records such as 203 and 210 are main sources of error. The error rate is higher than 1%, which is equal to 0.291. Record 203 has a great number of QRS complexes with multiform ventricular arrhythmia. The TEO phase revealed that the amplitudes are very low and close to zero. Due to this fact, the present method indicated quite a weak performance about records: 203, 19090, and 19830. Records 230, 114, 113, 107, and 106 contain high and sharp T peaks. Record number 207 includes some ventricular flutter (VF) intervals. Those intervals are not interpreted and they go out of studies. One of the constraints of the proposed method is when the QRS complex locations are very close to each other. The length (L) of moving average of phase 2 is assumed to be about 0.17×fs. The recorded signals of Fantasia Database included a variety of cardiac morphology, heart failures, and noises from sources like power lines, white Gaussian noise, and flicker noise1/f. Lowering the baseline is the main factor contributing to R-peak losses in the MIT-BIH Normal Sinus Rhythm Database.The advantages of the proposed method are a reduced number of steps to implement, no need for an excessive memory capacity or learning stage, a fast method of detection, a set baseline threshold, and no complex mathematical relationships.


## 5. Conclusion

The present study detects QRS complex based on Teager energy, which was tested on four databases. It is a novel algorithm with an acceptable accuracy for ECG baseline prediction. The obtained results from testing the presented method on the Fantasia Database involved: sensitivity (Se) = 99.971%, positive prediction (+P) = 99.973%, detection error rate (DER) = 0.056%, and accuracy (Acc) = 99.944%. On MIT-AD involvement, Se = 99.74%, +P = 99.97%, DER = 0.291%, and Acc = 99.71%. On MIT-NSD involvement, Se = 99.878%, +P = 99.989%, DER = 0.134%, and Acc = 99.867%. The provided results indicate that the presented method is reliable to detect QRS complex, and because the relationships are simple, the proposed method has a better performance than other sophisticated techniques such as neural networks. The results show that the proposed method is simple, effective, accurate, and suitable for practical application. To avoid the lag from zero-phase filter, a low-pass filter and a moving average were used, but still, the signal faced a shift that was about 0.026 s.



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*Source: 8360475-2018-09-18.xml*