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The exact discovery of Rpeak becomes very much crucial while extracting prominent features from Electrocardiogram (ECG) signal. However, identification of Rpeaks precisely becomes more challenging due to contamination of noise and fragmented QRS complexes. This paper presents an improved method of marking Rpeaks. Initially, an efficient Fourier Decomposition Methodology (FDM) is used for removing noise. The accuracy of finding Rpeaks can be improved by enhancing the QRS complexes using Teager Energy Operator. Hilbert Transform and Zero Cross Detector (ZCD) are used for marking the Rpeaks. The MITBIH arrhythmia database is used for validating the proposed scheme and attained 99.97% accuracy, 99.98% of sensitivity and 99.98% of positive predictivity. The findings proved that proposed method is superior as compared to the proven techniques in the literature.
Fourier decomposition method, Hilbert Transform, Teager Energy Operator, Zero Cross Detector, Rpeaks
The ECG signal is evolved as an extensively used rapid investigation tool to monitor cardiac abnormalities. It can give useful information about the functionality of the cardiovascular system. The threat of cardiovascular diseases is growing in India. The occurrence of cardiovascular diseases in India was estimated to be 5.45 cores in the year 2016 [1]. The ECG signal analyses and accurate detection of feature points take a big part in the identification of cardiac abnormalities. The standard ECG signal consists of five characteristic waves: P wave, Q wave, R wave, S wave and T wave. Ascertaining accurate Rpeaks becomes a benchmark for the extraction of remaining all fiducial points [2]. Nonetheless, Morphology of the ECG gets affected owing to the variation in the characteristic waves and noise interference. So, computeraided diagnosis is required to precisely delineate the Rwave to assist physicians and doctors with appropriate medical intervention. Conventionally, the wave functions were identified by both time and frequency domain signal processing technique [3, 4].
In recent developments, various wavelets transform techniques [5], timefrequency distribution of Stransform [6, 7], Circulant matrixbased continuous wavelet transform [8]. and convolution window [9] was used for ascertain Rpeaks. However, correct marking of the Rpeaks remains an open problem.
The primary objective of this work is to emphasizing the R wave and suppressing the effect of other wave functions while delineating the Rwaves. In this work simple and efficient FDM is used for preprocessing of the ECG signal. The combination of Teager Energy Operator (TEO), Hilbert Transform (HT) and Zero Cross Detector (ZCD) is used for implementing the peak finding Logic. In our proposed work, FDM has applied for denoise the ECG signal by suppressing the BW and PLI. In the subsequent stage, TEO is calculated to enhance the Rwaves. At last, Hilbert Transform and Zero Cross Detector are used for reliable estimation of Rwaves and its peak positions.
The reminder of the paper has been ordered as follows. We will present the previous research concerning to field of Rpeak identification in the second section. Section 3, presented proposed Rpeak identification methodology. Performance assessment this work and shown results in Section 4. In section 5 the work is concluded.
The reliable finding of Rpeaks is the most significant part while extracting characteristics of the ECG signal. Hence numerous Rpeak finding techniques are proposed in the literature. At first, identification of the QRS complex was established by Pan and Tompkins [10] using linear filtering and nonlinear processing techniques. Linear filtering composed by high pass and low pass filters is used for attenuate the noise. Differentiation, squaring and moving window integration are employed in nonlinear processing to generate the signal which consists of slope, amplitude and width information of QRS complex. Adaptive thresholds are used for marking the Rpeaks in the signal. Hamilton and Tompkins [11] have refined the decision rules to improve the efficiency of marking Rpeaks. Later various derivativebased approaches [411] have been developed for locating Rpeaks. Another method Empirical Mode Decomposition (EMD) decomposes the signal into different functions and process at different frequency ranges [8], but it has a problem of low frequency resolution. Digital filters [1214] also implemented for the elimination of noise and improving accuracy. These are optimum compared with standard FIR filters. Nonlinear energy operator and simple thresholding technique has also been used for efficient marking of RPeaks [1517]. Fractional Stock well transform is a combination of fractional fourier transform and Stockwell transform has been used by Bajaj and Kumar [18]. It becomes a popular tool for analyzing the time varying signals. Shannon Energy Envelope (SEE) is the average spectrum energy, and it is an improved method of marking Rpeaks [19, 20]. The quality of the ECG signal determines the proficiency of identifying Rwaves and its peaks. Over decades the proposed techniques have mainly two parts: the preprocessing stage and peak finding logic. Preprocessing of the signal is mainly employed for denoising the signal and enhancing the required wave function. For efficient detection of Rpeaks, a peak finding method is used. Various preprocessing techniques peak finding methods are described in the literature but reliable identification of Rpeaks remains an open challenge. The combination of Fourier decomposition methodology and Teager Energy Operator is used at the preprocessing stage and Hilbert Transform and Zero Cross Detector are used at the second stage for reliable identification of Rpeaks.
The proposed method for accurate identification of RPeaks is depicted in Figure 1. It consists of four different stages i.e. cleaning of ECG signal, Emphasizing the QRS complex, Peak finding logic and Rpeaks detection. Initially, Fourier Decomposition Method (FDM) is applied as a part of preprocessing to remove the noise. The FDM uses DFT and IDFT based zerophase filter bank, to break down the given signal into multiple frequency bands and regenerate filtered signal from the required frequency components. Furthermore, FDM is the most effective way of cleaning the ECG signal. It can be done by eradicating the BW and PLI [21]. An amplitude normalization and Teager Energy Operator (TEO) is calculated in the second stage to emphasize the QRS complexes. TEO gives instantaneous frequency of the signal and also more sensitive to sudden changes. Initially, it was used for nonlinear signal processing and found many applications in speech signal analysis. It will also reduce the effect of P peak and Tpeak while detecting Rpeaks. The generated TEO Signal enhances the Rwave function and plays a significant part in finding the Rpeaks in the proposed algorithm. The third stage is designed using the combination of HT and ZCD for detection of Rpeaks. Accurate detection of local maxima is possible by finding Zero cross points on the Hilbert Transformation of TEO signal. Finally, the original Rpeaks on ECG signal can be detected by projecting zero cross points on to the original ECG signal. The following subsections describe all the stages in detailed.
3.1 Fourier decomposition method for noise suppression
The ECG signals can be distorted by multiple noise sources, which include PLI, BW, electrode contact noise and motion artifacts, etc. Owing to these noises the reliable identification of RPeaks becomes complicated. Different methodologies are formulated in the literature over the years to remove PLI and BW from the ECG signal. Some of these methods use high pass filters for removing PLI and low pass filters to remove BW. However, these methods generate computational delays and nonlinear phase distortion [2225]. This can be addressed by exploiting the advantage of Zero phase filter bank [26]. Another popular approach is signal decomposition using discrete wavelet transforms [2729] for ECG denoising, but noise is present at various levels of detailed coefficients. Thus, removing these coefficients eliminates the noise and sometimes it leads to loss required information also. In this paper, we are using FDM which clearly outperformed all other methods. FDM decomposes the given signal into a set of various frequency bands [21].
Figure 1. Block diagram of improved Rpeak marking method
Figure 2. Block diagram of Frequency Decomposition Method
The Discrete Fourier Transform (DFT) based zerophase filter bank is used for implementing the FDM. The block diagram of the FDM technique using Zero phase filtering is described in Figure 2.
The given ECG signal y[n] is break down into a set of orthogonal frequency bands using the following signal decomposition
$y[n]=b_{0}+\sum_{i=1}^{M} y_{i}[n]$ (1)
Here b_{0} is average value of the Signal y[n], and {y_{1}[n], y_{2}[n], y_{3}[n], … y_{k}[n]} are Fourier intrinsic band functions. Consider frequency below 0.7 Hz as baseline wander frequency and 50 Hz and above as powerline interference. The frequency response of i^{th} band in the filterbank can be obtained by defining H_{i}[k] = 1 for the required band of frequencies and zero for the range of noise frequencies (below 0.7 Hz and above 50Hz). Mathematically the filter bank can be defined as
$\left.\begin{array}{rl}
\mathrm{H}_{\mathrm{i}}[\mathrm{k}]=0, & \left(\mathrm{k}_{\mathrm{i}1}+1\right) \leq \mathrm{k} \leq\left(\mathrm{N}\mathrm{k}_{\mathrm{i}}\right) \\
=0, & \left(\mathrm{N}\mathrm{k}_{\mathrm{i}}\right) \leq \mathrm{k} \leq \mathrm{N}\mathrm{k}_{\mathrm{i}1}1 \\
=1, & \text { otherwise }
\end{array}\right\}$ (2)
where, i is 1, 2…M using inverse discrete Fourier transform (IDFT) operation, the signal components y_{j}[n] are obtained as
$\mathrm{y}_{\mathrm{i}}[\mathrm{n}]=\sum_{\mathrm{k}=0}^{\mathrm{N}1}\left[\mathrm{H}_{\mathrm{i}}[\mathrm{k}] \mathrm{Y}[\mathrm{k}] \exp \left(\frac{\mathrm{j} 2 \pi \mathrm{kn}}{\mathrm{N}}\right)\right]$ (3)
where, Y[k] is discrete Fourier transform of y[n].
The proposed zero phase filter bank preserve the significant features like positions of all peaks. So that we can extract meaningful information from filtered ECG signal. However, the computational complexity also reduced by implementing the required DFT and IDFT using fast Fourier transform (FFT) algorithm. Figure 3 illustrate the performance of FDM for Denoising the ECG signal. Figure 3 (a) depicts the Original ECG signal y[n], Figure 3 (b) shows the 0.2Hz frequency noise which resembles the BW, Figure 3 (c) illustrate the 50Hz frequency noise which resembles the PLI, Figure 3 (d) shows the noise contaminated signal generated by adding all the above three signal. The filtered ECG signal is shown in Figure 3 (e) after applying FDM.
3.2 Amplitude normalization and Teager energy signal generation
This is the second step of the proposed method to identify Rpeak. In this step, we implemented both amplitude normalization and generation of TEO signal for emphasizing the QRS complexes in the ECG signal. Normalization of the signal is useful for better discrimination of positive peaks and negative peaks. By doing this we can limit the signal amplitude to [1, 1]. We normalize the signal y (n) by
$\check{\mathrm{y}}(\mathrm{n})=\frac{\mathrm{y}(\mathrm{n})}{\max _{\mathrm{n}1}^{\mathrm{N}}(\mathrm{y}[\mathrm{n}])}$ (4)
Figure 3. Illustration of denoising ECG signal
Figure 4. Identifying Rpeaks using proposed method
where, each sample of y (n) is divided by maximum value of the signal. Amplitude normalization improves the detection of negative Rpeaks. The primary purpose of generating TEO signal is to boost the original amplitudes of Rpeaks. It was originally created by Kaiser [21]. TEO for a signal $\breve{\mathrm{y}}(\mathrm{n})$ in its discrete form can be generated by using following equation:
$\Psi_{y}[n]=\breve{y}(n)^{2}\breve{y}(n1) * \breve{y}(n+1)$ (5)
The TEO has been commonly used as a peak detector in many applications. Using TEO, it is possible to reduce the effect of P and T waves for reliable identification of Rpeaks.
3.3 Accurate Rpeak detection
From many years, the position of Rpeaks is detecting by comparing the amplitude of the signal with the predefined threshold values. The secondary threshold value and search back methods are also exploited for reduction of errors. Nevertheless, in the case of diseased patient with varying wave function characteristics the search back mechanism with the second threshold value also does not give efficient results. In this work, HT and ZCD are used to construct a novel automatic Rpeaks finding technique. The Figure 4 depicts how the HT signal identifies the Rpeaks by marking its zero crossing points using Zero Cross Detector. This eliminates the complexity of comparison with various threshold values.
The HT of given signal z (t) is defined as
$\tilde{z}(t)=H[z(t)]=\frac{1}{\pi t} * z(t)=\frac{1}{\pi} \int_{\alpha}^{\alpha} \frac{z(\tau)}{t\tau} d \tau$ (6)
The process of finding Rpeaks is depicted in Figure 4. Filtered ECG signal is shown in the Figure 4 (a). How the QRS complexes are enhanced in generated TEO signal is depicted in Figure 4 (b). Figure 4 (c) Illustrating the positive zero crossing points in the HT signal. Figure 4 (c) shows the identified Rpeaks on the given ECG signal. Locating RPeaks is difficult in the case of fragmented QRS complexes and lowfrequency drift in the signal. To overcome this HT signal is passed through the Moving Average filter. The location of positive zero crossing points on the HT signal represents the Rpeaks. which can resemble the positions of RPeaks. By projecting these locations on the ECG signal, we can find the RPeaks with ±20 samples. By searching the point which is more away from the zerodc line in the searching window of ±20 samples of the identified Rpeak locations in the previous test we can find the original Rpeak locations.
The proposed work is evaluated using the wellknown Massachusetts Institute of TechnologyBeth Israel Hospital (MITBIH) arrhythmia database [30]. This repository contains 48 ECG recordings, which are sampled at a rate of 360 Hz. The quality of these records is acceptable for performing the performance evaluation of proposed method. It was implemented on MATLAB 2018a. To validate the proposed work, we considered different performance metrics. Which are percentage of sensitivity (Se), percentage of positive predictivity (+P), percentage of detection error rate (DER) and percentage of accuracy (ACC) are chosen. The performance metrics are calculating using the following equations.
$\begin{array}{c}
\operatorname{Se}(\%)=\frac{T P}{T P+F N} X 100 \% \\
+P(\%)=\frac{T P}{T P+F P} X 100 \% \\
D E R(\%)=\frac{F P+F N}{T P} X 100 \% \\
A C C(\%)=\frac{T P}{T P+F P+F N} X 100 \%
\end{array}$
Here the true positive (TP) represents the exact identification of Rpeaks, false positive (FP) represents the number of false identified Rpeaks, false negative (FN) represents the number of missing Rpeaks. The experimental results for illustrating the efficiency of the proposed method are summarized in Table 1. The observed error rate of 0.19%, which is optimum among the methodologies taken from the proven literature. The records which are having baseline below the origin are giving more error rate. Record 232 has a number of long pauses, although our method performed well as shown in the Figure 5. The ECG record 232 is depicted in Figure 5 (a). Filtered ECG record 232 is shown in Figure 5 (b). TEO signal generated is depicted in Figure 5 (c). Figure 5(d) Illustrating the positive zero crossing points on HT signal. The Identified Rpeaks on record232 is shown in Figure 5 (e).
It was observed that an accuracy of 99.97%, the sensitivity of 99.98% and positive prediction of 99.98% is achieved with the proposed method. The efficiency of the given Rpeaks finding technique is compared with other exiting methodologies and summarized in Table 2. It shows the significant improvement compared with the techniques which use the nonlinear filtering in their preprocessing stage [1518]. and comparable results with the Fractional Fourier transform [14], Stransform [19], and wavelet transforms [20]. The proposed methodology works well in the presence of high frequency PLI and low frequency BW without affecting other features of the ECG signal.
Table 1. Performance evaluation of the proposed Rpeak finding method using MITBIH arrhythmia database
Record No. 
Total (beats) 
TP (beats) 
FN (beats) 
FP (beats) 
DER (%) 
Se (%) 
+P (%) 
Accuracy (%) 
100 
2273 
2273 
0 
0 
0.00 
100 
100 
100 
101 
1865 
1864 
1 
0 
0.05 
99.95 
100 
99.95 
102 
2187 
2187 
0 
0 
0.00 
100 
100 
100 
103 
2084 
2084 
0 
0 
0.00 
100 
100 
100 
104 
2229 
2229 
0 
0 
0.00 
100 
100 
100 
105 
2572 
2571 
1 
0 
0.04 
99.96 
100 
99.96 
106 
2027 
2027 
0 
1 
0.05 
100 
99.95 
99.95 
107 
2137 
2137 
0 
0 
0.00 
100 
100 
100 
108 
1763 
1761 
2 
1 
0.17 
99.89 
99.94 
99.83 
109 
2532 
2532 
0 
0 
0.00 
100 
100 
100 
111 
2124 
2124 
0 
0 
0.00 
100 
100 
100 
112 
2539 
2539 
0 
0 
0.00 
100 
100 
100 
113 
1795 
1795 
0 
0 
0.00 
100 
100 
100 
114 
1879 
1879 
0 
0 
0.00 
100 
100 
100 
115 
1953 
1952 
1 
1 
0.10 
99.95 
99.95 
99.90 
116 
2412 
2409 
3 
1 
0.17 
99.88 
99.96 
99.83 
117 
1535 
1535 
0 
0 
0.00 
100 
100 
100 
118 
2278 
2278 
0 
1 
0.04 
100 
99.96 
99.96 
119 
1987 
1987 
0 
0 
0.00 
100 
100 
100 
121 
1863 
1863 
0 
0 
0.00 
100 
100 
100 
122 
2476 
2476 
0 
0 
0.00 
100 
100 
100 
123 
1518 
1518 
0 
0 
0.00 
100 
100 
100 
124 
1619 
1619 
0 
0 
0.00 
100 
100 
100 
200 
2601 
2601 
0 
0 
0.00 
100 
100 
100 
201 
1963 
1963 
0 
0 
0.00 
100 
100 
100 
202 
2136 
2136 
0 
0 
0.00 
100 
100 
100 
203 
2980 
2978 
2 
0 
0.07 
99.9 
100 
99.93 
205 
2656 
2656 
0 
0 
0.00 
100 
100 
100 
207 
1862 
1862 
0 
0 
0.00 
100 
100 
100 
208 
2955 
2951 
0 
2 
0.07 
100 
99.93 
99.93 
209 
3005 
3005 
0 
0 
0.00 
100 
100 
100 
210 
2650 
2648 
2 
0 
0.08 
99.92 
100 
99.92 
212 
2748 
2744 
0 
0 
0.00 
100 
100 
100 
213 
3251 
3251 
0 
0 
0.00 
100 
100 
100 
214 
2262 
2261 
1 
1 
0.09 
99.96 
99.96 
99.91 
215 
3363 
3363 
0 
0 
0.00 
100 
100 
100 
217 
2208 
2207 
1 
0 
0.05 
99.95 
100 
99.95 
219 
2154 
2154 
0 
0 
0.00 
100 
100 
100 
220 
2048 
2048 
0 
0 
0.00 
100 
100 
100 
221 
2427 
2427 
0 
0 
0.00 
100 
100 
100 
222 
2483 
2483 
0 
0 
0.00 
100 
100 
100 
223 
2605 
2604 
1 
0 
0.04 
99.96 
100 
99.96 
228 
2053 
2051 
2 
0 
0.10 
99.90 
100 
99.90 
230 
2256 
2256 
0 
0 
0.00 
100 
100 
100 
231 
1571 
1569 
2 
0 
0.13 
99.87 
100 
99.87 
232 
1780 
1780 
0 
3 
1.011 
100 
98.99 
98.99 
233 
3079 
3077 
2 
0 
0.06 
99.94 
100 
99.94 
234 
2753 
2753 
0 
0 
0.00 
100 
100 
100 
Total 
1,09,496 
109467 
21 
11 
0.19 
99.98 
99.98 
99.97 
Table 2. Comparison of Rpeak identification methods
Ref. 
Methodology 


FP (beats) 
FN (beats) 
Se (%) 
+P (%) 
Acc (%) 

Preprocessing Stage 
Improving the QRS Complex 
Peaks identification method 





[14] 
Median filter and SG smoothing filtering 
RMS value of third power of ECG 
Threshold based Peak detection 
428 
509 
99.50 
99.56 
99.08 
[15] 
Filtering with LPF and HPF 
Teager Energy Operator 
Threshold based Peak detection 
33 
285 
99.74 
99.97 
99.71 
[16] 
Digital FIR Filtering’ 
Squaring, MA Filter and Normalization 
Adaptive Threshold Operation 
182 
184 
99.83 
99.83 
99.66 
[17] 
Shift Invariant Wavelet Transform (ShIWT) 
Nonlinear Energy Operator (NEO) 
Simple Thresholding Operation 
254 
264 
99.75 
99.76 
99.52 
[18] 
Fractional Fourier Transform 
Fractional Stock well Shannon energy (FrSS) 
Threshold based on the FrSS envelope and search back method 
67 
46 
99.95 
99.93 
99.89 
[19] 
Discrete Wavelet Transform 
Modified Shannon Energy Envelope 
Peak Energy determination 
99 
79 
99.93 
99.91 
99.83 
[20] 
STransform 
Shannon Energy Envelope 
Threshold based Peak detection 
97 
171 
99.84 
99.81 
99.66 
Proposed Method 
Fourier decomposition method 
Teager Energy operator 
Hilbert Transform and positive zero cross point detection technique 
11 
21 
99.98 
99.98 
99.97 
Figure 5. Illustration of Rpeaks identified on record232 using proposed method
An improved peak finding methodology for the reliable detection of Rpeaks described in four stages, which exploits the advantages of Fourier decomposition, Teager Energy Operator and Hilbert Transform. The preprocessor is implemented based on Fourier decomposition method using Zero phase filter bank which can eliminate the PLI and BW more efficiently without affecting required peak positions and other features of the signal. The QRS complexes are improved by TEO that significantly increases the accuracy of Rpeaks detection. The HT and positive ZCD are used for identification of Rpeaks. Comparison of amplitude thresholds is not required in this approach. The experimental results are presented and compared with the existing studies. The standard MITBIH database is used for evaluating the effectiveness of the proposed method. The proposed methodology improved the results and achieved accuracy of 99.97%, sensitivity of 99.98% and positive predictivity of 99.98%. From Table 2, it is observed that the proposed method gives a higher accuracy as compare to the existing methods.
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